performance modelling of computer systems and computer networks
DESCRIPTION
PERFORMANCE MODELLING OF COMPUTER SYSTEMS AND COMPUTER NETWORKS. Ramon Puigjaner Universitat de les Illes Balears Palma, Spain [email protected]. LANC 2007. San José, Costa Rica. October 2007. OUTLINE. INTRODUCTION CONCEPT OF QUEUE CONCEPT OF QUEUEING NETWORK NUMERICAL TECHNIQUES - PowerPoint PPT PresentationTRANSCRIPT
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PERFORMANCE MODELLING OF
COMPUTER SYSTEMS AND COMPUTER
NETWORKS
Ramon Puigjaner
Universitat de les Illes Balears
Palma, Spain
LANC 2007. San José, Costa Rica. October 2007..
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OUTLINE
INTRODUCTION
CONCEPT OF QUEUE
CONCEPT OF QUEUEING NETWORK
NUMERICAL TECHNIQUES
EXACT ANALYTICAL SOLUTIONS
APPROXIMATE ANALYTICAL SOLUTIONS
SIMULATION TECHNIQUES
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INTRODUCTION
What is the performance of a Computer Network?
Performance is how a software is using a hardware when they are serving a load.
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INTRODUCTION
This definition considers the three elements intervening in a system:
The load that is externally defined. The hardware to be used. The basic software that controls the hardware.
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INTRODUCTION: Performance measures
The performance of a Computer Network is not a unique value but a set of them to take into account the heterogeneous composition of such kind of systems. External performance measures
o response time
o throughput (flow through the system)
o loss rate
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INTRODUCTION: Performance measures
Internal performance measures
o mean queue length
o device utilisation (% of busy time)
o overlap
o overhead (operating system utilisation, paging, etc.)
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INTRODUCTION: Performance tools
Measuring Monitors Logs Hardware probes Software probes
Modelling
Benchmarking
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INTRODUCTION: Performance tools
Measuring
Modelling Queuing networks Petri nets Markov chains
Benchmarking Workload modelling
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INTRODUCTION: Measuring
Measuring is the technique to be used when system is installed and running. It is used to verify whether the performance requirements are met or not.
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INTRODUCTION: Modelling
A model is an abstract mathematical representation of the system behaviour in steady state. It is the appropriate technique when the computer network, partially or totally, does not exist. Main existing techniques are: Petri nets
o Better suited to represent synchronisation mechanismso Solving techniques may be either numerical (based on
Markov chains) or simulation.
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INTRODUCTION: Modelling
Queuing networkso Better suited to represent customer-server mechanisms
o Solving techniques may be either analytical (closed form formulae) or numerical (based on Markov chains) or simulation.
Markov chainso High abstraction level
o Solving techniques are most frequently numerical.
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OUTLINE
INTRODUCTION
CONCEPT OF QUEUE
CONCEPT OF QUEUEING NETWORK
NUMERICAL TECHNIQUES
EXACT ANALYTICAL SOLUTIONS
APPROXIMATE ANALYTICAL SOLUTIONS
SIMULATION TECHNIQUES
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CONCEPT OF QUEUE
Queue: A customer that arrives and finds the server busy joins the queue
Service mechanism: It consists of one or more servers that give service to the customers from the queue
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CONCEPT OF QUEUE
Customer source characteristics finite or infinite distribution of inter-arrival times between
consecutive customer arrivals customer service request
Service station characteristics queue number and capacity server number server capacity service discipline queue policy
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CONCEPT OF QUEUE
Single queue with single server
Single queue with single server with state dependent capacity
m(k )
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CONCEPT OF QUEUE
Single queue with multiple servers
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CONCEPT OF QUEUE
Multi-server with no queue
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CONCEPT OF QUEUE
Infinite server
.
.
.
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OUTLINE
INTRODUCTION
CONCEPT OF QUEUE
CONCEPT OF QUEUEING NETWORK
NUMERICAL TECHNIQUES
EXACT ANALYTICAL SOLUTIONS
APPROXIMATE ANALYTICAL SOLUTIONS
SIMULATION TECHNIQUES
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CONCEPT OF QUEUEING NETWORK
A queuing network is nothing else but a collection of single queues, which are arbitrarily interconnected.
A queuing network is an oriented graph that has in each node a server of some type.
The time in traversing the network is spent in the nodes and the arcs are traversed in a null time.
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CONCEPT OF QUEUEING NETWORK
Queuing networks may be either open or closed. In an open queuing network, customers arrive from
outside, circulate through the nodes, and finally they depart from the network.
In a closed queuing network, there is a fixed number of customers constantly circulating through the nodes. Neither departures from the network nor arrivals to the network are allowed.
It is possible to have a queuing network which is both open and closed. Such a network is known as a mixed network.
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EXAMPLES OF OPEN QUEUING NETWORKS
Tandem configuration
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EXAMPLES OF OPEN QUEUING NETWORKS
Tree-like configuration
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EXAMPLES OF OPEN QUEUING NETWORKS
Tree-like configuration
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EXAMPLES OF CLOSED QUEUING NETWORKS
Cyclic network (closed tandem configuration)
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EXAMPLES OF CLOSED QUEUING NETWORKS
Arbitrary configuration
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EXAMPLES OF CLOSED QUEUING NETWORKS
Central server model
C P U
D isk 2
D isk 3
D isk 4
D isk 1
A rriv a ls
E x its
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EXAMPLES OF CLOSED QUEUING NETWORKS
Central server model
C P U
D isk 2
D isk 3
D isk 4
D isk 1
A rriv a ls
E x its
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EXAMPLES OF CLOSED QUEUING NETWORKS
Central server model
C P U
D isk 2
D isk 3
D isk 4
D isk 1
A rriv a ls
E x its
T e rm in a ls
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EXAMPLES OF MIXED QUEUING NETWORKS
T e rm in a ls
C e n tra lsy s te mT ra n sa c tio n s
C o n v e rsa tio n a lta sk s
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CONCEPT OF QUEUEING NETWORK
Observations Each node can have any of the single-node
characteristics described above.
In order to specify the queuing network we need to
provide information concerning the routing; that is
to specify how a customer chooses the next node
when it leaves the current node. This routing can be
deterministic, probabilistic, function of the state,
etc.
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CONCEPT OF QUEUEING NETWORK
How to set-up a queuing network model? The notion of customer
o Typically a customer may be a piece of software in a
computer system, an information packet in a packet-
switched environment, a phone call in a circuit-
switched environment, etc.
o Customer classes will be defined if there are
differences in the resource consumption or in the
routing across the network
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CONCEPT OF QUEUEING NETWORK
How to set-up a queuing network model? The notion of node
o A node is a service mechanism that may be a hardware component or a piece of software or a combination of both, e.g. a CPU, a disk, a memory module, a bus, a trunk, a switching node, etc.
o Each service mechanism has a buffer (the queue), where customers wait until they are served. The buffer capacity is finite; that is, they can accommodate a finite number of customers. However, if a finite buffer has low probability of being full, then it can be assumed as infinite.
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CONCEPT OF QUEUEING NETWORK
How to set-up a queuing network model? Collecting information
o Once customers and server have been identified, it is
necessary to characterise service time distributions at
each node, routing probabilities and inter-arrival time
distributions.
o In many cases, this information can be compiled from
raw data (technical information, measurements, etc.);
in other cases it is based on an educated guess.
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CONCEPT OF QUEUEING NETWORK
Solution techniques for queuing networks
To study the steady state behavior of a network
the following techniques can be used:
Analytic solutions
Numerical techniques
Simulation techniques
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OUTLINE
INTRODUCTION
CONCEPT OF QUEUE
CONCEPT OF QUEUEING NETWORK
NUMERICAL TECHNIQUES
EXACT ANALYTICAL SOLUTIONS
APPROXIMATE ANALYTICAL SOLUTIONS
SIMULATION TECHNIQUES
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NUMERICAL TECHNIQUES
The behaviour of a queuing network can be described in terms of linear equations (known as the steady-state Kolmogorov equations). These equations can be solved numerically to obtain the solution.
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NUMERICAL TECHNIQUES
To highlight this approach, let us consider the following two-node closed queuing network
Let us assume that: there are 5 customers in the system. µ1 and µ2 are the service rates.
both services are exponentially distributed.
µ1 2µ
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NUMERICAL TECHNIQUES
The state of the system is described by (n1, n2), that there are the number of customers in each queue.
The numerical analysis approach involves the following steps: Generation of all feasible states. Setting-up the rate matrix. Solving the steady state equations.
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NUMERICAL TECHNIQUES
Generation of all feasible states.
The states for our example are:
(5,0) (4,1) (3,2) (2,3) (1,4) (0,5)
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NUMERICAL TECHNIQUES
Setting-up the rate matrix. This matrix which contains all the transitions and
their associated rates between each pair of states.(5,0) (4,1) (3,2) (2,3) (1,4) (0,5)
(5,0) * µ1
(4,1) µ2 * µ1
(3,2) µ2 * µ1
(2,3) µ2 * µ1
(1,4) µ2 * µ1
(0,5) µ2 *
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NUMERICAL TECHNIQUES
Setting-up the rate matrix.
Let us refer to the this matrix as Q.
All blanks are assumed to be zero.
Each diagonal element marked with * is equal to
the negative sum of the off-diagonal elements of
the same row.
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NUMERICAL TECHNIQUES
Solving the steady state equations. Let p(n1, n2) be the steady-state probability that the
system is in state (n1, n2) and P the row vector of these probabilities. To determine them we must solve the following system of equations:
P x Q = 0
together with the condition
1
21
21 n,n
n,np
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NUMERICAL TECHNIQUES
Solving the steady state equations. From the knowledge of these probabilities we can
determine performance measures such as:o Server utilisation:
r1 = p(5,0) + p(4,1) + p(3,2) + p(2,3) + p(1,4):
r2 = p(4,1) + p(3,2) + p(2,3) + p(1,4) + p(0,5)
o Throughputs:
l1 = r1 x µ1
l2 = r2 x µ2
o Queue lengths:
N1 = 5p(5,0) + 4p(4,1) + 3p(3,2) + 2p(2,3) + p(1,4)
N2 = p(4,1) + 2p(3,2) + 3p(2,3) + 4p(1,4) + 5p(0,5)
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NUMERICAL TECHNIQUES
Solving the steady state equations. Advantages/disadvantages
o There are packages, like QNAP2, that automatically set-up the rate matrix Q, solve it to find the P vector and give the performance results. Other packages give the vector P if the user is able to create the matrix Q.
o This numerical technique gives the exact solution. There are also approximated solutions in some cases in order to reduce the amount of computation.
o The approach is limited to cases where the number of states is not very large.
o In queuing networks, quite often, the rate matrix is sparse. In this cases, one can analyse larger systems by using compact storage techniques.
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OUTLINE
INTRODUCTION
CONCEPT OF QUEUE
CONCEPT OF QUEUEING NETWORK
NUMERICAL TECHNIQUES
EXACT ANALYTICAL SOLUTIONS
APPROXIMATE ANALYTICAL SOLUTIONS
SIMULATION TECHNIQUES
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EXACT ANALYTICAL SOLUTIONS
An analytical solution means that we can obtain the probabilities of the steady steady by the application of a closed formula.
This formula will obviously be a function of the parameters of the system.
Quite often an analytic solution is so complicated that we can not evaluate it "on the back of an envelope". In fact, one might need to write a fairly sophisticated program.
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EXACT ANALYTICAL SOLUTIONS
A certain class of queuing networks has an
analytic solution, known as a product-form
solution because the steady state probability has
the form of the product of the state probabilities
of each node.
Its solution can be easily evaluated.
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EXACT ANALYTICAL SOLUTIONS
Product-form networks have been proved to be
very useful in computer and communication
systems performance modelling.
Also, there are a lot of queuing networks which
do not have product-form solutions. These
networks are analysed approximately.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem It is the general theorem concerning queuing
networks with product-form solutions.
Let us consider a BCMP queuing network with: N nodes arbitrarily linked. Multiple classes of customers Probabilistic routing External arrivals with state-dependent rates Different service mechanisms
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Classes of customers Customers are grouped in different classes. Each
class has its own service characteristics at each node and its own routing probabilities. A class may be open or closed.
Thus, a BCMP network, in its most general form, can be seen as consisting of several open classes and closed classes of customers.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Classes of customers It is possible that upon departure from a node a
customer may change of class. A superclass or a
subchain is the set of classes among those the
customers can change.
The use of classes of customers provides the
modeller with a lot of modelling flexibility.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Classes of customersExample 1. A queuing network model of a multiprogramming system
C P U
D isk 2
D isk 3
D isk 4
D isk 1
A rriv a ls
E x its
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Classes of customersExample 1. A queuing network model of a multiprogramming system The total number of customers constantly
circulating through the system reflects the degree of multiprogramming. Implicitly it is assumed that when a job completes its execution and departs from the system, another job takes its place. That is, there is always at least one job waiting to get into the multiprogramming environment. This rather simplistic model captures the main features of a multiprogramming system.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Classes of customersExample 1. A queuing network model of a multiprogramming system Let us see, how can make this model more useful
by introducing classes. We can introduce different classes for different types of jobs, i. e.:
o Class 1: Interactive jobso Class 2: Short batch jobso Class 3: Medium batch jobso Class 4: Long batch jobs
Also, in a multiprogramming system, a process originally classified in some class may be changed to another one.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Classes of customers
Example 1. A queuing network model of a multiprogramming system Features as service requirements, visit rates to each
node, class change, etc. are captured through the use of classes.
However, the BCMP theorem is limited as it does not allow other features, such as priorities among classes.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Classes of customersExample 2. Queuing network of a packet-switching system
1
2
3
4
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Classes of customers
Example 2. Queuing network of a packet-switching system A packet is represented by a customer in the
queuing network and each logical end-to-end connection is represented by a class. This allows us to assign a different routing to each class, and, if need be, different service times at each node.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Classes of customers
Example 2. Queuing network of a packet-switching system So, we consider the following classes:
o Class 1: packets arrive at node 1, go to node 2, then to node 3 and then they depart from the system.
o Class 2: packets arrive at node 1, go to node 3, then to node 4 and then they depart from the system.
o Class 3: packets arrive at node 2, go to node 3 and then they depart from the system.
o etc.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Arrival processes
If we have open classes of customers, one needs to
specify how these customers arrive from outside. In
general, the rate of arrivals is allowed to be state-
dependent, i. e. it can be an arbitrary function of the
number of customers in the system.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Arrival processes Single arrival stream
o All external arrivals come from a single stream. When
a customer arrives to the network, it joins node i as
class r with probability pi,r.
o The inter-arrival times must be exponentially
distributed. The rate of arrivals may be constant or it
may be dependent upon the total number of customers
in the network.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Arrival processes
One arrival stream per class
o Each open class has its own arrival stream. A new
arrival of class r joins node i with probability pi.
o The inter-arrival times must be exponentially
distributed. The rate of class r arrivals may be constant
or it may be dependent upon the total number of class r
customers in the network.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Classes of customers
Example 2. Queuing network of a packet-switching system Window-flow control allows only up to a pre-
specified number of packets in the system. Any additional packets are forced to wait in an input queue.
In order to model a sliding-window flow-control scheme, we need to model the input queue. However, the BCMP theorem does not provide such features.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Classes of customers
Example 2. Queuing network of a packet-switching system We can consider in some way the window-flow
control by making the arrival process of customers state-dependent. That is, arrivals will occur as long as the total number of customers of some class is less than some threshold. When it becomes equal to this value, the arrival stream will be turned off. The arrival stream will start again when a customer of the considered class departs from the network.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Classes of customers
Example 2. Queuing network of a packet-switching system In this way, we make sure that the total number of
customers of each class does not exceed its threshold.
However, this is done by introducing the erroneous assumption that no arrivals occur during the time the window is full.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Service mechanisms Type 1
o State dependent exponentially distributed service times.
o Class independent service time distribution
o FIFO irrespective of classes.
o Single server
Type 2o Class and state dependent Coxian distributed service
times.
o Processor sharing (PS) discipline (or RR, round robin)
o Single servers
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Service mechanisms Type 3
o Class-dependent Coxian distributed service times
o Infinite servers
Type 4
o Class and state dependent Coxian distributed service
times
o Pre-emptive server LIFO queue (PI)
o Single server
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Classes of customers
Example 1. A queuing network model of a multiprogramming system In this model it makes sense to assume that the
CPU node is a type 2 node, i. e. customer are processor-shared, while the peripheral (disks 1 to 4) are type 1. If we assume an interactive system we would represent the terminals by means of a type 3 node.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem Assumption that the system reaches a steady state with
state probabilities p(S)
Balance equations:
Normalising equation
'
S toS' from going of rate'
from rateexit
S
Sp
SSp
1S
Sp
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem
G normalisation constant to obtain the addition the probabilities of all states is equal to 1.
o If the system is closed, the number of states is finite and the problem is numerical
o If the system is open, the number of states is infinite and the problem is analytical
N
iii SgSd
GSp
1
1
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem d(S) is a function that if the network is closed its value
is 1 and if the network is open its value is
if the arrival rate depends on M(S),
if the arrival rate to each subchain depends on M(S,Ek)
1
0
SM
i
i
K
k
ESM
ik
k
i1
1,
0
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem The expressions of gi(Si) are
o If the station is of type 1
o If the station is of type 2 or 4
c
c
m
i
C
c
mic
iciii e
mmSg
m
1
!
1!
1
cm
ic
icC
c iciii
e
mmSg
m
1 !
1!
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem The expressions of gi(Si) are
o If the station is of type 3
cm
ic
icC
c icii
e
mSg
m
1 !
1
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Solving of a BCMP
queuing network
The expression that gives the probability that the
system is in a precise state is quite complicated.
However it is still possible to write down the
solution in form of product of terms, each term
consisting of parameters related to the node.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Solving of a BCMP queuing network In the case of closed networks, as the number of
states is finite, it is necessary to compute a normalising constant.
o There are various algorithms to do that, such as the convolution algorithm and the mean value analysis.
o These algorithms are available through various network analysers, such as QNAP2, BEST-1 and RESQ. The user simply specifies the network characteristics, and the package produces the solution.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Solving of a BCMP queuing network In the case of open networks, as the number of
states is infinite, it is necessary to compute the result of a series.
o This computation is only possible for specific combinations of node characteristics.
o As for closed networks, these algorithms are available through various network analysers, such as QNAP2, BEST-1 and RESQ. The user simply specifies the network characteristics, and the package produces the solution.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Case studies
Transactional system The case proposed is a throughput input system
with two types of transactions (messages arriving to the system and requiring some process) that have different arrival frequency, CPU consumption and profile (number of accesses to the disks), but the same mean service time to each disk (but different from disk to disk).
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Case studies
Transactional system We assume that these transactions are executed
concurrently on the computer system and that the conflicts in the its execution are due to the access to the same servers (CPU and disks) but not to any kind of synchronisation or use of critical objects.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Case studiesTransactional system
C P U
D isk 2
D isk 3
D isk 4
D isk 1
A rriv a ls
E x its
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Transactional system 1 /DECLARE/ QUEUE CPU,DISC(4),ENTRADA1,ENTRADA2; 2 REAL PROF1(4)=(2,1.5,1,0.5); 3 REAL PROF2(4)=(1.5,2,3,3.5); 4 REAL TR1,TR2; 5 CLASS C1,C2; 6 INTEGER I; 7 /STATION/ NAME=CPU; 8 SCHED=PS; 9 SERVICE(C1)=CST(8.52); 10 SERVICE(C2)=CST(12.); 11 TRANSIT(C1)=DISC,PROF1,OUT,1; 12 TRANSIT(C2)=DISC,PROF2,OUT,1;
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Transactional system
13 /STATION/ NAME=DISC; 14 TRANSIT=CPU; 15 /STATION/ NAME=DISC(1); 16 SERVICE=EXP(23.); 17 /STATION/ NAME=DISC(2); 18 SERVICE=EXP(22.); 19 /STATION/ NAME=DISC(3); 20 SERVICE=EXP(21.); 21 /STATION/ NAME=DISC(4); 22 SERVICE=EXP(20.);
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Transactional system 23 /STATION/ NAME=ENTRADA1; 24 TYPE=SOURCE; 25 SERVICE=EXP(1000./7.); 26 TRANSIT=CPU,C1; 27 /STATION/ NAME=ENTRADA2; 28 TYPE=SOURCE; 29 SERVICE=EXP(1000./3.); 30 TRANSIT=CPU,C2; 31 /CONTROL/ CLASS=ALL QUEUE;
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Transactional system 32 /EXEC/ BEGIN 33 PRINT; 34 SOLVE; 35 TR1:=MCUSTNB(CPU,C1); 36 TR2:=MCUSTNB(CPU,C2); 37 FOR I:= 1 STEP 1 UNTIL 4 DO 38 BEGIN 39 TR1:=TR1+MCUSTNB(DISC(I),C1); 40 TR2:=TR2+MCUSTNB(DISC(I),C2); 41 END; 42 TR1:=TR1/MTHRUPUT(ENTRADA1); 43 TR2:=TR2/MTHRUPUT(ENTRADA2); 44 PRINT("RESPONSE TIME OF CLASS C1 =",TR1); 45 PRINT("RESPONSE TIME OF CLASS C2 =",TR2); 46 END;
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Transactional system - CONVOLUTION METHOD ("CONVOL") ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * * * * * * * * CPU * 10.05 *0.7538 * 3.062 * 40.83 *0.7500E-01* *(C1 )* 8.520 *0.3578 * 1.454 * 34.61 *0.4200E-01* *(C2 )* 12.00 *0.3960 * 1.609 * 48.75 *0.3300E-01* * * * * * * * * DISC 1 * 23.00 *0.4255 *0.7406 * 40.03 *0.1850E-01* *(C1 )* 23.00 *0.3220 *0.5605 * 40.03 *0.1400E-01* *(C2 )* 23.00 *0.1035 *0.1802 * 40.03 *0.4500E-02* * * * * * * * * DISC 2 * 22.00 *0.3630 *0.5699 * 34.54 *0.1650E-01* *(C1 )* 22.00 *0.2310 *0.3626 * 34.54 *0.1050E-01* *(C2 )* 22.00 *0.1320 *0.2072 * 34.54 *0.6000E-02* * * * * * * *
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Transactional system ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * DISC 3 * 21.00 *0.3360 *0.5060 * 31.63 *0.1600E-01* *(C1 )* 21.00 *0.1470 *0.2214 * 31.63 *0.7000E-02* *(C2 )* 21.00 *0.1890 *0.2846 * 31.63 *0.9000E-02* * * * * * * * * DISC 4 * 20.00 *0.2800 *0.3889 * 27.78 *0.1400E-01* *(C1 )* 20.00 *0.7000E-01*0.9722E-01* 27.78 *0.3500E-02* *(C2 )* 20.00 *0.2100 *0.2917 * 27.78 *0.1050E-01* * * * * * * * * ENTRADA1 * 142.9 * 1.000 * 1.000 * 142.9 *0.7000E-02* * * * * * * * * ENTRADA2 * 333.3 * 1.000 * 1.000 * 333.3 *0.3000E-02* ******************************************************************* RESPONSE TIME OF CLASS C1 = 385.1 RESPONSE TIME OF CLASS C2 = 857.5 47 /END/
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Case studies
Conversational system We assume that these programs are executed
concurrently on the computer system and that the
conflicts in the its execution are due to the access to
the same servers (CPU and disks) but not to any
kind of synchronisation or use of critical objects.
Also we assume that the human behaviour in front
of the terminal is different for each class.
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Case studiesConversational system
C P U
D isk 2
D isk 3
D isk 4
D isk 1
A rriv a ls
E x its
T e rm in a ls
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Conversational system 1 /DECLARE/ QUEUE CPU,DISC(4),TERMINAL; 2 REAL PROB1(4)=(2,1.5,1,0.5); 3 REAL PROB2(4)=(1.5,2,3,3.5); 4 REAL TR1,TR2; 5 CLASS C1,C2; 6 INTEGER I,N; 7 /STATION/ NAME=CPU; 8 SCHED=PS; 9 SERVICE(C1)=CST(8.52);10 SERVICE(C2)=CST(12.);11 TRANSIT(C1)=DISC,PROB1,TERMINAL,C1,0.6,TERMINAL,C2,0 ==> .4;12 TRANSIT(C2)=DISC,PROB2,TERMINAL,C1,0.6,TERMINAL,C2,0 ==> .4;
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Conversational system 13 /STATION/ NAME=DISC; 14 TRANSIT=CPU; 15 /STATION/ NAME=DISC(1); 16 SERVICE=EXP(23.); 17 /STATION/ NAME=DISC(2); 18 SERVICE=EXP(22.); 19 /STATION/ NAME=DISC(3); 20 SERVICE=EXP(21.); 21 /STATION/ NAME=DISC(4); 22 SERVICE=EXP(20.); 23 /STATION/ NAME=TERMINAL; 24 TYPE=INFINITE; 25 INIT(C1)=N; 26 SERVICE(C1)=EXP(30000.); 27 SERVICE(C2)=EXP(60000.); 28 TRANSIT=CPU; 29 /CONTROL/ CLASS=ALL QUEUE;
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EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Conversational system 30 /EXEC/ FOR N:=150 STEP 150 UNTIL 750 DO 31 BEGIN 32 PRINT; 33 PRINT("NOMBRE D’USUARIS =",N); 34 SOLVE; 35 TR1:=MCUSTNB(CPU,C1); 36 TR2:=MCUSTNB(CPU,C2); 37 FOR I:= 1 STEP 1 UNTIL 4 DO 38 BEGIN 39 TR1:=TR1+MCUSTNB(DISC(I),C1); 40 TR2:=TR2+MCUSTNB(DISC(I),C2); 41 END; 42 TR1:=TR1/MTHRUPUT(TERMINAL,C1); 43 TR2:=TR2/MTHRUPUT(TERMINAL,C2);; 44 PRINT("RESPONSE TIME OF CLASS C1 =",TR1); 45 PRINT("RESPONSE TIME OF CLASS C2 =",TR2); 46 END;
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LANC 2007. San José, Costa Rica. October 2007.91
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Conversational system NOMBRE D’USUARIS = 150 - MEAN VALUE ANALYSIS ("MVA") - ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * * * * * * * * CPU * 10.43 *0.2960 *0.4189 * 14.76 *0.2837E-01* *(C1 )* 8.520 *0.1088 *0.1539 * 12.06 *0.1277E-01* *(C2 )* 12.00 *0.1873 *0.2650 * 16.98 *0.1560E-01* * * * * * * * * DISC 1 * 23.00 *0.1468 *0.1719 * 26.92 *0.6384E-02* *(C1 )* 23.00 *0.9790E-01*0.1146 * 26.92 *0.4257E-02* *(C2 )* 23.00 *0.4894E-01*0.5729E-01* 26.92 *0.2128E-02* * * * * * * * * DISC 2 * 22.00 *0.1326 *0.1528 * 25.33 *0.6029E-02* *(C1 )* 22.00 *0.7023E-01*0.8088E-01* 25.33 *0.3192E-02* *(C2 )* 22.00 *0.6242E-01*0.7188E-01* 25.33 *0.2837E-02*
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LANC 2007. San José, Costa Rica. October 2007.92
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Conversational system ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * DISC 3 * 21.00 *0.1341 *0.1546 * 24.22 *0.6384E-02* *(C1 )* 21.00 *0.4469E-01*0.5155E-01* 24.22 *0.2128E-02* *(C2 )* 21.00 *0.8937E-01*0.1031 * 24.22 *0.4256E-02* * * * * * * * * DISC 4 * 20.00 *0.1206 *0.1370 * 22.72 *0.6029E-02* *(C1 )* 20.00 *0.2128E-01*0.2418E-01* 22.72 *0.1064E-02* *(C2 )* 20.00 *0.9930E-01*0.1128 * 22.72 *0.4965E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 149.0 *0.4200E+05*0.3547E-02* *(C1 )*0.3000E+05*0.0000E+00* 63.84 *0.3000E+05*0.2128E-02* *(C2 )*0.6000E+05*0.0000E+00* 85.12 *0.6000E+05*0.1419E-02* ******************************************************************* RESPONSE TIME OF CLASS C1 = 199.8 RESPONSE TIME OF CLASS C2 = 430.0
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LANC 2007. San José, Costa Rica. October 2007.93
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Conversational system NOMBRE D’USUARIS = 300 - MEAN VALUE ANALYSIS ("MVA") - ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * * * * * * * * CPU * 10.43 *0.5905 * 1.426 * 25.19 *0.5659E-01* *(C1 )* 8.520 *0.2170 *0.5239 * 20.57 *0.2547E-01* *(C2 )* 12.00 *0.3735 *0.9017 * 28.97 *0.3112E-01* * * * * * * * * DISC 1 * 23.00 *0.2929 *0.4134 * 32.46 *0.1273E-01* *(C1 )* 23.00 *0.1953 *0.2756 * 32.46 *0.8490E-02* *(C2 )* 23.00 *0.9761E-01*0.1378 * 32.46 *0.4244E-02* * * * * * * * * DISC 2 * 22.00 *0.2646 *0.3592 * 29.87 *0.1203E-01* *(C1 )* 22.00 *0.1401 *0.1902 * 29.87 *0.6367E-02* *(C2 )* 22.00 *0.1245 *0.1690 * 29.87 *0.5659E-02*
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LANC 2007. San José, Costa Rica. October 2007.94
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Conversational system ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * DISC 3 * 21.00 *0.2674 *0.3644 * 28.62 *0.1273E-01* *(C1 )* 21.00 *0.8914E-01*0.1215 * 28.62 *0.4245E-02* *(C2 )* 21.00 *0.1783 *0.2429 * 28.62 *0.8488E-02* * * * * * * * * DISC 4 * 20.00 *0.2405 *0.3162 * 26.30 *0.1203E-01* *(C1 )* 20.00 *0.4245E-01*0.5582E-01* 26.30 *0.2122E-02* *(C2 )* 20.00 *0.1981 *0.2604 * 26.30 *0.9903E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 297.1 *0.4200E+05*0.7074E-02* *(C1 )*0.3000E+05*0.0000E+00* 127.3 *0.3000E+05*0.4245E-02* *(C2 )*0.6000E+05*0.0000E+00* 169.8 *0.6000E+05*0.2830E-02* ******************************************************************* RESPONSE TIME OF CLASS C1 = 274.9 RESPONSE TIME OF CLASS C2 = 605.0
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LANC 2007. San José, Costa Rica. October 2007.95
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Conversational system NOMBRE D’USUARIS = 450 - MEAN VALUE ANALYSIS ("MVA") - ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * * * * * * * * CPU * 10.43 *0.8763 * 6.438 * 76.66 *0.8399E-01* *(C1 )* 8.520 *0.3220 * 2.366 * 62.60 *0.3780E-01* *(C2 )* 12.00 *0.5543 * 4.072 * 88.16 *0.4619E-01* * * * * * * * * DISC 1 * 23.00 *0.4347 *0.7667 * 40.57 *0.1890E-01* *(C1 )* 23.00 *0.2898 *0.5112 * 40.57 *0.1260E-01* *(C2 )* 23.00 *0.1449 *0.2555 * 40.57 *0.6298E-02* * * * * * * * * DISC 2 * 22.00 *0.3926 *0.6451 * 36.14 *0.1785E-01* *(C1 )* 22.00 *0.2079 *0.3415 * 36.14 *0.9449E-02*
*(C2 )* 22.00 *0.1848 *0.3035 * 36.14 *0.8398E-02*
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LANC 2007. San José, Costa Rica. October 2007.96
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Conversational system ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * DISC 3 * 21.00 *0.3968 *0.6564 * 34.74 *0.1890E-01* *(C1 )* 21.00 *0.1323 *0.2188 * 34.74 *0.6300E-02* *(C2 )* 21.00 *0.2645 *0.4376 * 34.74 *0.1260E-01* * * * * * * * * DISC 4 * 20.00 *0.3569 *0.5541 * 31.05 *0.1785E-01* *(C1 )* 20.00 *0.6300E-01*0.9779E-01* 31.05 *0.3150E-02* *(C2 )* 20.00 *0.2939 *0.4563 * 31.05 *0.1470E-01* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 440.9 *0.4200E+05*0.1050E-01* *(C1 )*0.3000E+05*0.0000E+00* 189.0 *0.3000E+05*0.6299E-02* *(C2 )*0.6000E+05*0.0000E+00* 252.0 *0.6000E+05*0.4199E-02* ******************************************************************* RESPONSE TIME OF CLASS C1 = 561.2 RESPONSE TIME OF CLASS C2 = 1316.
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LANC 2007. San José, Costa Rica. October 2007.97
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Conversational system NOMBRE D’USUARIS = 600 - MEAN VALUE ANALYSIS ("MVA") - ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * * * * * * * * CPU * 10.43 * 1.000 * 93.51 * 975.7 *0.9584E-01* *(C1 )* 8.520 *0.3675 * 34.37 * 796.7 *0.4313E-01* *(C2 )* 12.00 *0.6325 * 59.15 * 1122. *0.5271E-01* * * * * * * * * DISC 1 * 23.00 *0.4960 *0.9841 * 45.63 *0.2157E-01* *(C1 )* 23.00 *0.3307 *0.6561 * 45.63 *0.1438E-01* *(C2 )* 23.00 *0.1653 *0.3280 * 45.63 *0.7187E-02* * * * * * * * * DISC 2 * 22.00 *0.4481 *0.8118 * 39.86 *0.2037E-01* *(C1 )* 22.00 *0.2372 *0.4298 * 39.86 *0.1078E-01*
*(C2 )* 22.00 *0.2108 *0.3820 * 39.86 *0.9583E-02*
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LANC 2007. San José, Costa Rica. October 2007.98
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Conversational system ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * DISC 3 * 21.00 *0.4528 *0.8276 * 38.38 *0.2156E-01* *(C1 )* 21.00 *0.1510 *0.2759 * 38.38 *0.7189E-02* *(C2 )* 21.00 *0.3019 *0.5517 * 38.38 *0.1437E-01* * * * * * * * * DISC 4 * 20.00 *0.4073 *0.6872 * 33.74 *0.2037E-01* *(C1 )* 20.00 *0.7189E-01*0.1213 * 33.74 *0.3594E-02* *(C2 )* 20.00 *0.3354 *0.5659 * 33.74 *0.1677E-01* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 503.2 *0.4200E+05*0.1198E-01* *(C1 )*0.3000E+05*0.0000E+00* 215.7 *0.3000E+05*0.7188E-02* *(C2 )*0.6000E+05*0.0000E+00* 287.5 *0.6000E+05*0.4792E-02* ******************************************************************* RESPONSE TIME OF CLASS C1 = 4987. RESPONSE TIME OF CLASS C2 = 0.1272E+05
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LANC 2007. San José, Costa Rica. October 2007.99
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Conversational system NOMBRE D’USUARIS = 750 - MEAN VALUE ANALYSIS ("MVA") - ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * * * * * * * * CPU * 10.43 * 1.000 * 243.5 * 2541. *0.9584E-01* *(C1 )* 8.520 *0.3675 * 89.49 * 2075. *0.4313E-01* *(C2 )* 12.00 *0.6325 * 154.0 * 2922. *0.5271E-01* * * * * * * * * DISC 1 * 23.00 *0.4960 *0.9841 * 45.64 *0.2157E-01* *(C1 )* 23.00 *0.3307 *0.6561 * 45.64 *0.1438E-01* *(C2 )* 23.00 *0.1653 *0.3280 * 45.64 *0.7187E-02* * * * * * * * * DISC 2 * 22.00 *0.4481 *0.8118 * 39.86 *0.2037E-01* *(C1 )* 22.00 *0.2372 *0.4298 * 39.86 *0.1078E-01*
*(C2 )* 22.00 *0.2108 *0.3820 * 39.86 *0.9583E-02*
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LANC 2007. San José, Costa Rica. October 2007.100
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Conversational system ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * DISC 3 * 21.00 *0.4528 *0.8276 * 38.38 *0.2156E-01* *(C1 )* 21.00 *0.1510 *0.2759 * 38.38 *0.7189E-02* *(C2 )* 21.00 *0.3019 *0.5517 * 38.38 *0.1437E-01* * * * * * * * * DISC 4 * 20.00 *0.4073 *0.6872 * 33.74 *0.2037E-01* *(C1 )* 20.00 *0.7189E-01*0.1213 * 33.74 *0.3594E-02* *(C2 )* 20.00 *0.3354 *0.5659 * 33.74 *0.1677E-01* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 503.2 *0.4200E+05*0.1198E-01* *(C1 )*0.3000E+05*0.0000E+00* 215.7 *0.3000E+05*0.7188E-02* *(C2 )*0.6000E+05*0.0000E+00* 287.5 *0.6000E+05*0.4792E-02* ******************************************************************* RESPONSE TIME OF CLASS C1 = 0.1266E+05 RESPONSE TIME OF CLASS C2 = 0.3252E+05 47 /END/
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LANC 2007. San José, Costa Rica. October 2007.101
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Case studies
Communication network There are four sources of variable length messages.
Routing across the net is fixed. All the lines have the same capacity and the transmission is full duplex. We consider negligible the time spent in each node for protocol verifications, routing, etc. The end-to-end traffic is known and we want to determine the response time also end-to-end.
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LANC 2007. San José, Costa Rica. October 2007.102
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network
1
2
3
4
5
6
7
8
A
B
C
D
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LANC 2007. San José, Costa Rica. October 2007.103
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network
to
from A B C D
A 60 80 100
B 75 50 25
C 80 120 40
D 100 150 50
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LANC 2007. San José, Costa Rica. October 2007.104
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication networkA-1-2-4-3-B
A-1-2-4-6-5-C
A-1-2-8-7-D
B-3-4-2-1-A
B-3-4-6-5-C
B-3-4-8-7-D
C-5-6-8-2-1-A
C-5-6-4-3-B
C-5-6-8-7-D
D-7-8-2-1-A
D-7-8-4-3-B
D-7-8-6-5-C
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LANC 2007. San José, Costa Rica. October 2007.105
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network
1 /DECLARE/ QUEUE GEN,LINIA(8,8); 2 REAL TRAB,TRAC,TRAD,TRBA,TRBC,TRBD,TRCA,TRCB,TRCD,==> TRDA,TRDB,TRDC; 3 INTEGER I; 4 CLASS CLAB,CLAC,CLAD,CLBA,CLBC,CLBD,CLCA,CLCB,CLCD==> ,CLDA,CLDB,CLDC; 5
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LANC 2007. San José, Costa Rica. October 2007.106
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network 6 /STATION/ NAME = GEN; 7 TYPE = SOURCE; 8 SERVICE = EXP(60000./930.); 9 TRANSIT = LINIA(1,2),CLAB,60,LINIA(1,2),CLAC,80,L==> INIA(1,2),CLAD,100,10 LINIA(3,4),CLBA,75,LINIA(3,4),CLBC,50,L==> INIA(3,4),CLBD,25,11 LINIA(5,6),CLCA,80,LINIA(5,6),CLCB,120,==> LINIA(5,6),CLCD,40,12 LINIA(7,8),CLDA,100,LINIA(7,8),CLDB,150==> ,LINIA(7,8),CLDC,50;13
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LANC 2007. San José, Costa Rica. October 2007.107
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network 14 /STATION/ NAME = LINIA; 15 SERVICE = EXP(256.*8./64.); 16 17 /STATION/ NAME = LINIA(1,2); 18 TRANSIT(CLAB) = LINIA(2,4); 19 TRANSIT(CLAC) = LINIA(2,4); 20 TRANSIT(CLAD) = LINIA(2,8); 21 22 /STATION/ NAME = LINIA(2,1); 23 TRANSIT = OUT; 24 25 /STATION/ NAME = LINIA(2,4); 26 TRANSIT(CLAB) = LINIA(4,3); 27 TRANSIT(CLAC) = LINIA(4,6); 28 29 /STATION/ NAME = LINIA(2,8); 30 TRANSIT(CLAD) = LINIA(8,7); 31
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LANC 2007. San José, Costa Rica. October 2007.108
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network 32 /STATION/ NAME = LINIA(3,4); 33 TRANSIT(CLBA) = LINIA(4,2); 34 TRANSIT(CLBC) = LINIA(4,6); 35 TRANSIT(CLBD) = LINIA(4,8); 36 37 /STATION/ NAME = LINIA(4,2); 38 TRANSIT(CLBA) = LINIA(2,1); 39 40 /STATION/ NAME = LINIA(4,3); 41 TRANSIT = OUT; 42 43 /STATION/ NAME = LINIA(4,6); 44 TRANSIT(CLAC) = LINIA(6,5); 45 TRANSIT(CLBC) = LINIA(6,5); 46 47 /STATION/ NAME = LINIA(4,8); 48 TRANSIT(CLBD) = LINIA(8,7); 49
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LANC 2007. San José, Costa Rica. October 2007.109
EXACT ANALYTICAL SOLUTIONS The BCMP theorem: Communication network 50 /STATION/ NAME = LINIA(5,6); 51 TRANSIT(CLCA) = LINIA(6,8); 52 TRANSIT(CLCB) = LINIA(6,4); 53 TRANSIT(CLCD) = LINIA(6,8); 54 55 /STATION/ NAME = LINIA(6,4); 56 TRANSIT(CLCB) = LINIA(4,3); 57 58 /STATION/ NAME = LINIA(6,5); 59 TRANSIT = OUT; 60 61 /STATION/ NAME = LINIA(6,8); 62 TRANSIT(CLCA) = LINIA(8,2); 63 TRANSIT(CLCD) = LINIA(8,7); 64 65 /STATION/ NAME = LINIA(7,8); 66 TRANSIT(CLDA) = LINIA(8,2); 67 TRANSIT(CLDB) = LINIA(8,4); 68 TRANSIT(CLDC) = LINIA(8,6); 69
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LANC 2007. San José, Costa Rica. October 2007.110
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network 70 /STATION/ NAME = LINIA(8,2); 71 TRANSIT(CLCA) = LINIA(2,1); 72 TRANSIT(CLDA) = LINIA(2,1); 73 74 /STATION/ NAME = LINIA(8,4); 75 TRANSIT(CLDB) = LINIA(4,3); 76 77 /STATION/ NAME = LINIA(8,6); 78 TRANSIT(CLDC) = LINIA(6,5); 79 80 /STATION/ NAME = LINIA(8,7); 81 TRANSIT = OUT; 82
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LANC 2007. San José, Costa Rica. October 2007.111
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network83 /EXEC/ BEGIN84 NETWORK(GEN,85 LINIA(1,2),LINIA(2,1),LINIA(2,4),LINIA(2,8),86 LINIA(3,4),LINIA(4,2),LINIA(4,3),LINIA(4,6),87 LINIA(4,8),LINIA(5,6),LINIA(6,4),LINIA(6,5),88 LINIA(6,8),LINIA(7,8),LINIA(8,2),LINIA(8,4),89 LINIA(8,6),LINIA(8,7));90 PRINT;91 SOLVE;92 TRAB:=MRESPONSE(LINIA(1,2))+93 MRESPONSE(LINIA(2,4))+MRESPONSE(LINIA(4,3));94 TRAC:=MRESPONSE(LINIA(1,2))+MRESPONSE(LINIA(2,4))+95 MRESPONSE(LINIA(4,6))+MRESPONSE(LINIA(6,5));96 TRAD:=MRESPONSE(LINIA(1,2))+MRESPONSE(LINIA(2,8))+97 MRESPONSE(LINIA(8,7));98 TRBA:=MRESPONSE(LINIA(3,4))+MRESPONSE(LINIA(4,2))+99 MRESPONSE(LINIA(2,1));
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LANC 2007. San José, Costa Rica. October 2007.112
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network 100 TRBC:=MRESPONSE(LINIA(3,4))+MRESPONSE(LINIA(4,6))+101 MRESPONSE(LINIA(6,5));102 TRBD:=MRESPONSE(LINIA(3,4))+MRESPONSE(LINIA(4,8))+103 MRESPONSE(LINIA(8,7));104 TRCA:=MRESPONSE(LINIA(5,6))+MRESPONSE(LINIA(6,8))+105 MRESPONSE(LINIA(8,2))+MRESPONSE(LINIA(2,1));106 TRCB:=MRESPONSE(LINIA(5,6))+MRESPONSE(LINIA(6,4))+107 MRESPONSE(LINIA(4,3));108 TRCD:=MRESPONSE(LINIA(5,6))+MRESPONSE(LINIA(6,8))+109 MRESPONSE(LINIA(8,7));110 TRDA:=MRESPONSE(LINIA(7,8))+MRESPONSE(LINIA(8,2))+111 MRESPONSE(LINIA(2,1));112 TRDB:=MRESPONSE(LINIA(7,8))+MRESPONSE(LINIA(8,4))+113 MRESPONSE(LINIA(4,3));114 TRDC:=MRESPONSE(LINIA(7,8))+MRESPONSE(LINIA(8,6))+115 MRESPONSE(LINIA(6,5));
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LANC 2007. San José, Costa Rica. October 2007.113
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network 116 PRINT(TRAB,TRAC,TRAD); 117 PRINT(TRBA,TRBC,TRBD); 118 PRINT(TRCA,TRCB,TRCD); 119 PRINT(TRDA,TRDB,TRDC); 120 END;
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LANC 2007. San José, Costa Rica. October 2007.114
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network - CONVOLUTION METHOD ("CONVOL") -******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* * * * * * ** GEN * 64.52 * 1.000 * 1.000 * 64.52 *0.1550E-01** * * * * * ** LINIA 2 * 32.00 *0.1280 *0.1468 * 36.70 *0.4000E-02** * * * * * ** LINIA 9 * 32.00 *0.1360 *0.1574 * 37.04 *0.4250E-02** * * * * * ** LINIA 12 * 32.00 *0.7467E-01*0.8069E-01* 34.58 *0.2333E-02** * * * * * ** LINIA 16 * 32.00 *0.5333E-01*0.5634E-01* 33.80 *0.1667E-02** * * * * * ** LINIA 20 * 32.00 *0.8000E-01*0.8696E-01* 34.78 *0.2500E-02** * * * * * ** LINIA 26 * 32.00 *0.4000E-01*0.4167E-01* 33.33 *0.1250E-02** * * * * * *
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LANC 2007. San José, Costa Rica. October 2007.115
EXACT ANALYTICAL SOLUTIONS The BCMP theorem: Communication network******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* LINIA 27 * 32.00 *0.1760 *0.2136 * 38.83 *0.5500E-02** * * * * * ** LINIA 30 * 32.00 *0.6933E-01*0.7450E-01* 34.38 *0.2167E-02** * * * * * ** LINIA 32 * 32.00 *0.1333E-01*0.1351E-01* 32.43 *0.4167E-03** * * * * * ** LINIA 38 * 32.00 *0.1280 *0.1468 * 36.70 *0.4000E-02** * * * * * ** LINIA 44 * 32.00 *0.6400E-01*0.6838E-01* 34.19 *0.2000E-02** * * * * * ** LINIA 45 * 32.00 *0.9600E-01*0.1062 * 35.40 *0.3000E-02** * * * * * ** LINIA 48 * 32.00 *0.6400E-01*0.6838E-01* 34.19 *0.2000E-02** * * * * * ** LINIA 56 * 32.00 *0.1600 *0.1905 * 38.10 *0.5000E-02** * * * * * ** LINIA 58 * 32.00 *0.9600E-01*0.1062 * 35.40 *0.3000E-02** * * * * * *
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LANC 2007. San José, Costa Rica. October 2007.116
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network
******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* LINIA 60 * 32.00 *0.8000E-01*0.8696E-01* 34.78 *0.2500E-02** * * * * * ** LINIA 62 * 32.00 *0.2667E-01*0.2740E-01* 32.88 *0.8333E-03** * * * * * ** LINIA 63 * 32.00 *0.8800E-01*0.9649E-01* 35.09 *0.2750E-02** * * * * * ********************************************************************
110.1 141.1 105.6 105.2 104.6 102.3 143.3 109.7 106.0 110.5 111.7 106.4
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LANC 2007. San José, Costa Rica. October 2007.117
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Case studies
Communication network considering the nodes This case is identical to the previous one but
considering the process at each node.
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LANC 2007. San José, Costa Rica. October 2007.118
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network 1 /DECLARE/ QUEUE GEN,LINIA(8,8),CPU(8); 2 REAL TRAB,TRAC,TRAD,TRBA,TRBC,TRBD,TRCA,TRCB,TRCD,TRD ==> A,TRDB,TRDC; 3 INTEGER I; 4 CLASS CLAB,CLAC,CLAD,CLBA,CLBC,CLBD,CLCA,CLCB,CLCD,CL ==> DA,CLDB,CLDC; 5 6 /STATION/ NAME = GEN; 7 TYPE = SOURCE; 8 SERVICE = EXP(60000./930.); 9 TRANSIT = CPU(1),CLAB,60,CPU(1),CLAC,80,CPU(1),CLAD,1 ==> 00, 10 CPU(3),CLBA,75,CPU(3),CLBC,50,CPU(3),CLBD,2 ==> 5, 11 CPU(5),CLCA,80,CPU(5),CLCB,120,CPU(5),CLCD, ==> 40, 12 CPU(7),CLDA,100,CPU(7),CLDB,150,CPU(7),CLDC ==> ,50,
13
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LANC 2007. San José, Costa Rica. October 2007.119
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network 14 /STATION/ NAME = LINIA; 15 SERVICE = EXP(256.*8./64.); 16 17 /STATION/ NAME = LINIA(1,2); 18 TRANSIT = CPU(2); 19 20 /STATION/ NAME = LINIA(2,1); 21 TRANSIT = CPU(1); 22 23 /STATION/ NAME = LINIA(2,4); 24 TRANSIT = CPU(4); 25 26 /STATION/ NAME = LINIA(2,8); 27 TRANSIT = CPU(8); 28 29 /STATION/ NAME = LINIA(3,4); 30 TRANSIT = CPU(4); 31
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LANC 2007. San José, Costa Rica. October 2007.120
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network 32 /STATION/ NAME = LINIA(4,2); 33 TRANSIT = CPU(2); 34 35 /STATION/ NAME = LINIA(4,3); 36 TRANSIT = CPU(3); 37 38 /STATION/ NAME = LINIA(4,6); 39 TRANSIT = CPU(6); 40 41 /STATION/ NAME = LINIA(4,8); 42 TRANSIT = CPU(8); 43 44 /STATION/ NAME = LINIA(5,6); 45 TRANSIT = CPU(6); 46 47 /STATION/ NAME = LINIA(6,5); 48 TRANSIT = CPU(5); 49
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LANC 2007. San José, Costa Rica. October 2007.121
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network 50 /STATION/ NAME = LINIA(6,4); 51 TRANSIT = CPU(4); 52 53 /STATION/ NAME = LINIA(6,8); 54 TRANSIT = CPU(8); 55 56 /STATION/ NAME = LINIA(7,8); 57 TRANSIT = CPU(8); 58 59 /STATION/ NAME = LINIA(8,2); 60 TRANSIT = CPU(2); 61 62 /STATION/ NAME = LINIA(8,7); 63 TRANSIT = CPU(7); 64 65 /STATION/ NAME = LINIA(8,6); 66 TRANSIT = CPU(6); 67
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LANC 2007. San José, Costa Rica. October 2007.122
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network 68 /STATION/ NAME = LINIA(8,4); 69 TRANSIT = CPU(4); 70 71 /STATION/ NAME = CPU; 72 SERVICE = EXP(1.); 73 74 /STATION/ NAME = CPU(1); 75 TRANSIT(CLAB,CLAC,CLAD) = LINIA(1,2); 76 TRANSIT(CLBA,CLCA,CLDA) = OUT; 77 78 /STATION/ NAME = CPU(2); 79 TRANSIT(CLAB) = LINIA(2,4); 80 TRANSIT(CLAC) = LINIA(2,4); 81 TRANSIT(CLAD) = LINIA(2,8); 82 TRANSIT(CLBA) = LINIA(2,1); 83 TRANSIT(CLCA) = LINIA(2,1); 84 TRANSIT(CLDA) = LINIA(2,1);
85
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LANC 2007. San José, Costa Rica. October 2007.123
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network
86 /STATION/ NAME = CPU(3); 87 TRANSIT(CLBA,CLBC,CLBD) = LINIA(3,4); 88 TRANSIT(CLAB,CLCB,CLDB) = OUT; 89 90 /STATION/ NAME = CPU(4); 91 TRANSIT(CLAB) = LINIA(4,3); 92 TRANSIT(CLAC) = LINIA(4,6); 93 TRANSIT(CLBA) = LINIA(4,2); 94 TRANSIT(CLBC) = LINIA(4,6); 95 TRANSIT(CLBD) = LINIA(4,8); 96 TRANSIT(CLCB) = LINIA(4,3); 97 TRANSIT(CLDB) = LINIA(4,3); 98 99 /STATION/ NAME = CPU(5); 100 TRANSIT(CLCA,CLCB,CLCD) = LINIA(5,6); 101 TRANSIT(CLAC,CLBC,CLDC) = OUT;
102
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LANC 2007. San José, Costa Rica. October 2007.124
EXACT ANALYTICAL SOLUTIONS The BCMP theorem: Communication network 103 /STATION/ NAME = CPU(6); 104 TRANSIT(CLAC) = LINIA(6,5); 105 TRANSIT(CLBC) = LINIA(6,5); 106 TRANSIT(CLCA) = LINIA(6,8); 107 TRANSIT(CLCB) = LINIA(6,4); 108 TRANSIT(CLCD) = LINIA(6,8); 109 TRANSIT(CLDC) = LINIA(6,5); 110 111 /STATION/ NAME = CPU(7); 112 TRANSIT(CLDA,CLDB,CLDC) = LINIA(7,8); 113 TRANSIT(CLAD,CLBD,CLCD) = OUT; 114 115 /STATION/ NAME = CPU(8); 116 TRANSIT(CLAD) = LINIA(8,7); 117 TRANSIT(CLBD) = LINIA(8,7); 118 TRANSIT(CLCA) = LINIA(8,2); 119 TRANSIT(CLCD) = LINIA(8,7); 120 TRANSIT(CLDA) = LINIA(8,2); 121 TRANSIT(CLDB) = LINIA(8,4); 122 TRANSIT(CLDC) = LINIA(8,6); 123
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LANC 2007. San José, Costa Rica. October 2007.125
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network 124 /CONTROL/ CLASS = ALL QUEUE; 125 /EXEC/ BEGIN 126 NETWORK(GEN, 127 CPU(1 STEP 1 UNTIL 8), 128 LINIA(1,2),LINIA(2,1),LINIA(2,4),LINIA(2,8), 129 LINIA(3,4),LINIA(4,2),LINIA(4,3),LINIA(4,6), 130 LINIA(4,8),LINIA(5,6),LINIA(6,4),LINIA(6,5), 131 LINIA(6,8),LINIA(7,8),LINIA(8,2),LINIA(8,4), 132 LINIA(8,6),LINIA(8,7)); 133 PRINT; 134 SOLVE; 135 TRAB := MRESPONSE(CPU(1))+MRESPONSE(LINIA(1,2))+ 136 MRESPONSE(CPU(2))+MRESPONSE(LINIA(2,4))+ 137 MRESPONSE(CPU(4))+MRESPONSE(LINIA(4,3))+ 138 MRESPONSE(CPU(3)); 139 TRAC := MRESPONSE(CPU(1))+MRESPONSE(LINIA(1,2))+ 140 MRESPONSE(CPU(2))+MRESPONSE(LINIA(2,4))+ 141 MRESPONSE(CPU(4))+MRESPONSE(LINIA(4,6))+ 142 MRESPONSE(CPU(6))+MRESPONSE(LINIA(6,5))+ 143 MRESPONSE(CPU(5));
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LANC 2007. San José, Costa Rica. October 2007.126
EXACT ANALYTICAL SOLUTIONS The BCMP theorem: Communication network 144 TRAD := MRESPONSE(CPU(1))+MRESPONSE(LINIA(1,2))+ 145 MRESPONSE(CPU(2))+MRESPONSE(LINIA(2,8))+ 146 MRESPONSE(CPU(8))+MRESPONSE(LINIA(8,7))+ 147 MRESPONSE(CPU(7)); 148 TRBA := MRESPONSE(CPU(3))+MRESPONSE(LINIA(3,4))+ 149 MRESPONSE(CPU(4))+MRESPONSE(LINIA(4,2))+ 150 MRESPONSE(CPU(2))+MRESPONSE(LINIA(2,1))+ 151 MRESPONSE(CPU(1)); 152 TRBC := MRESPONSE(CPU(3))+MRESPONSE(LINIA(3,4))+ 153 MRESPONSE(CPU(4))+MRESPONSE(LINIA(4,6))+ 154 MRESPONSE(CPU(6))+MRESPONSE(LINIA(6,5))+ 155 MRESPONSE(CPU(5)); 156 TRBD := MRESPONSE(CPU(3))+MRESPONSE(LINIA(3,4))+ 157 MRESPONSE(CPU(4))+MRESPONSE(LINIA(4,8))+ 158 MRESPONSE(CPU(8))+MRESPONSE(LINIA(8,7))+ 159 MRESPONSE(CPU(7)); 160 TRCA := MRESPONSE(CPU(5))+MRESPONSE(LINIA(5,6))+ 161 MRESPONSE(CPU(6))+MRESPONSE(LINIA(6,8))+ 162 MRESPONSE(CPU(8))+MRESPONSE(LINIA(8,2))+ 163 MRESPONSE(CPU(2))+MRESPONSE(LINIA(2,1))+ 164 MRESPONSE(CPU(1));
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LANC 2007. San José, Costa Rica. October 2007.127
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network
165 TRCB := MRESPONSE(CPU(5))+MRESPONSE(LINIA(5,6))+ 166 MRESPONSE(CPU(6))+MRESPONSE(LINIA(6,4))+ 167 MRESPONSE(CPU(4))+MRESPONSE(LINIA(4,3))+ 168 MRESPONSE(CPU(3)); 169 TRCD := MRESPONSE(CPU(5))+MRESPONSE(LINIA(5,6))+ 170 MRESPONSE(CPU(6))+MRESPONSE(LINIA(6,8))+ 171 MRESPONSE(CPU(8))+MRESPONSE(LINIA(8,7))+ 172 MRESPONSE(CPU(7)); 173 TRDA := MRESPONSE(CPU(7))+MRESPONSE(LINIA(7,8))+ 174 MRESPONSE(CPU(8))+MRESPONSE(LINIA(8,2))+ 175 MRESPONSE(CPU(2))+MRESPONSE(LINIA(2,1))+ 176 MRESPONSE(CPU(1)); 177 TRDB := MRESPONSE(CPU(7))+MRESPONSE(LINIA(7,8))+ 178 MRESPONSE(CPU(8))+MRESPONSE(LINIA(8,4))+ 179 MRESPONSE(CPU(4))+MRESPONSE(LINIA(4,3))+
180 MRESPONSE(CPU(3));
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LANC 2007. San José, Costa Rica. October 2007.128
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network
181 TRDC := MRESPONSE(CPU(7))+MRESPONSE(LINIA(7,8))+
182 MRESPONSE(CPU(8))+MRESPONSE(LINIA(8,6))+
183 MRESPONSE(CPU(6))+MRESPONSE(LINIA(6,5))+
184 MRESPONSE(CPU(5)); 185 PRINT(TRAB,TRAC,TRAD); 186 PRINT(TRBA,TRBC,TRBD); 187 PRINT(TRCA,TRCB,TRCD); 188 PRINT(TRDA,TRDB,TRDC); 189 END;
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LANC 2007. San José, Costa Rica. October 2007.129
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network- CONVOLUTION METHOD ("CONVOL") -******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* GEN * 64.52 * 1.000 * 1.000 * 64.52 *0.1550E-01** * * * * * ** LINIA 2 * 32.00 *0.1280 *0.1468 * 36.70 *0.4000E-02**(CLAB )* 32.00 *0.3200E-01*0.3670E-01* 36.70 *0.1000E-02**(CLAC )* 32.00 *0.4267E-01*0.4893E-01* 36.70 *0.1333E-02**(CLAD )* 32.00 *0.5333E-01*0.6116E-01* 36.70 *0.1667E-02** * * * * * ** LINIA 9 * 32.00 *0.1360 *0.1574 * 37.04 *0.4250E-02**(CLBA )* 32.00 *0.4000E-01*0.4630E-01* 37.04 *0.1250E-02**(CLCA )* 32.00 *0.4267E-01*0.4938E-01* 37.04 *0.1333E-02**(CLDA )* 32.00 *0.5333E-01*0.6173E-01* 37.04 *0.1667E-02** * * * * * ** LINIA 12 * 32.00 *0.7467E-01*0.8069E-01* 34.58 *0.2333E-02**(CLAB )* 32.00 *0.3200E-01*0.3458E-01* 34.58 *0.1000E-02**(CLAC )* 32.00 *0.4267E-01*0.4611E-01* 34.58 *0.1333E-02** * * * * * *
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LANC 2007. San José, Costa Rica. October 2007.130
EXACT ANALYTICAL SOLUTIONS The BCMP theorem: Communication network******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* LINIA 16 * 32.00 *0.5333E-01*0.5634E-01* 33.80 *0.1667E-02**(CLAD )* 32.00 *0.5333E-01*0.5634E-01* 33.80 *0.1667E-02** * * * * * ** LINIA 20 * 32.00 *0.8000E-01*0.8696E-01* 34.78 *0.2500E-02**(CLBA )* 32.00 *0.4000E-01*0.4348E-01* 34.78 *0.1250E-02**(CLBC )* 32.00 *0.2667E-01*0.2899E-01* 34.78 *0.8333E-03**(CLBD )* 32.00 *0.1333E-01*0.1449E-01* 34.78 *0.4167E-03** * * * * * ** LINIA 26 * 32.00 *0.4000E-01*0.4167E-01* 33.33 *0.1250E-02**(CLBA )* 32.00 *0.4000E-01*0.4167E-01* 33.33 *0.1250E-02** * * * * * ** LINIA 27 * 32.00 *0.1760 *0.2136 * 38.83 *0.5500E-02**(CLAB )* 32.00 *0.3200E-01*0.3883E-01* 38.83 *0.1000E-02**(CLCB )* 32.00 *0.6400E-01*0.7767E-01* 38.83 *0.2000E-02**(CLDB )* 32.00 *0.8000E-01*0.9709E-01* 38.83 *0.2500E-02** * * * * * *
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LANC 2007. San José, Costa Rica. October 2007.131
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* LINIA 30 * 32.00 *0.6933E-01*0.7450E-01* 34.38 *0.2167E-02**(CLAC )* 32.00 *0.4267E-01*0.4585E-01* 34.38 *0.1333E-02**(CLBC )* 32.00 *0.2667E-01*0.2865E-01* 34.38 *0.8333E-03** * * * * * ** LINIA 32 * 32.00 *0.1333E-01*0.1351E-01* 32.43 *0.4167E-03**(CLBD )* 32.00 *0.1333E-01*0.1351E-01* 32.43 *0.4167E-03** * * * * * ** LINIA 38 * 32.00 *0.1280 *0.1468 * 36.70 *0.4000E-02**(CLCA )* 32.00 *0.4267E-01*0.4893E-01* 36.70 *0.1333E-02**(CLCB )* 32.00 *0.6400E-01*0.7339E-01* 36.70 *0.2000E-02**(CLCD )* 32.00 *0.2133E-01*0.2446E-01* 36.70 *0.6667E-03** * * * * * ** LINIA 44 * 32.00 *0.6400E-01*0.6838E-01* 34.19 *0.2000E-02**(CLCB )* 32.00 *0.6400E-01*0.6838E-01* 34.19 *0.2000E-02** * * * * * *
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LANC 2007. San José, Costa Rica. October 2007.132
EXACT ANALYTICAL SOLUTIONS
The BCMP theorem: Communication network******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* LINIA 45 * 32.00 *0.9600E-01*0.1062 * 35.40 *0.3000E-02**(CLAC )* 32.00 *0.4267E-01*0.4720E-01* 35.40 *0.1333E-02**(CLBC )* 32.00 *0.2667E-01*0.2950E-01* 35.40 *0.8333E-03**(CLDC )* 32.00 *0.2667E-01*0.2950E-01* 35.40 *0.8333E-03** * * * * * ** LINIA 48 * 32.00 *0.6400E-01*0.6838E-01* 34.19 *0.2000E-02**(CLCA )* 32.00 *0.4267E-01*0.4558E-01* 34.19 *0.1333E-02**(CLCD )* 32.00 *0.2133E-01*0.2279E-01* 34.19 *0.6667E-03** * * * * * ** LINIA 56 * 32.00 *0.1600 *0.1905 * 38.10 *0.5000E-02**(CLDA )* 32.00 *0.5333E-01*0.6349E-01* 38.10 *0.1667E-02**(CLDB )* 32.00 *0.8000E-01*0.9524E-01* 38.10 *0.2500E-02**(CLDC )* 32.00 *0.2667E-01*0.3175E-01* 38.10 *0.8333E-03** * * * * * ** LINIA 58 * 32.00 *0.9600E-01*0.1062 * 35.40 *0.3000E-02**(CLCA )* 32.00 *0.4267E-01*0.4720E-01* 35.40 *0.1333E-02**(CLDA )* 32.00 *0.5333E-01*0.5900E-01* 35.40 *0.1667E-02** * * * * * *
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EXACT ANALYTICAL SOLUTIONS The BCMP theorem: Communication network******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* LINIA 60 * 32.00 *0.8000E-01*0.8696E-01* 34.78 *0.2500E-02**(CLDB )* 32.00 *0.8000E-01*0.8696E-01* 34.78 *0.2500E-02** * * * * * ** LINIA 62 * 32.00 *0.2667E-01*0.2740E-01* 32.88 *0.8333E-03**(CLDC )* 32.00 *0.2667E-01*0.2740E-01* 32.88 *0.8333E-03** * * * * * ** LINIA 63 * 32.00 *0.8800E-01*0.9649E-01* 35.09 *0.2750E-02**(CLAD )* 32.00 *0.5333E-01*0.5848E-01* 35.09 *0.1667E-02**(CLBD )* 32.00 *0.1333E-01*0.1462E-01* 35.09 *0.4167E-03**(CLCD )* 32.00 *0.2133E-01*0.2339E-01* 35.09 *0.6667E-03** * * * * * ** CPU 1 * 1.000 *0.8250E-02*0.8319E-02* 1.008 *0.8250E-02**(CLAB )* 1.000 *0.1000E-02*0.1008E-02* 1.008 *0.1000E-02**(CLAC )* 1.000 *0.1333E-02*0.1344E-02* 1.008 *0.1333E-02**(CLAD )* 1.000 *0.1667E-02*0.1681E-02* 1.008 *0.1667E-02**(CLBA )* 1.000 *0.1250E-02*0.1260E-02* 1.008 *0.1250E-02**(CLCA )* 1.000 *0.1333E-02*0.1344E-02* 1.008 *0.1333E-02**(CLDA )* 1.000 *0.1667E-02*0.1681E-02* 1.008 *0.1667E-02*
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EXACT ANALYTICAL SOLUTIONS The BCMP theorem: Communication network******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* CPU 2 * 1.000 *0.8250E-02*0.8319E-02* 1.008 *0.8250E-02**(CLAB )* 1.000 *0.1000E-02*0.1008E-02* 1.008 *0.1000E-02**(CLAC )* 1.000 *0.1333E-02*0.1344E-02* 1.008 *0.1333E-02**(CLAD )* 1.000 *0.1667E-02*0.1681E-02* 1.008 *0.1667E-02**(CLBA )* 1.000 *0.1250E-02*0.1260E-02* 1.008 *0.1250E-02**(CLCA )* 1.000 *0.1333E-02*0.1344E-02* 1.008 *0.1333E-02**(CLDA )* 1.000 *0.1667E-02*0.1681E-02* 1.008 *0.1667E-02** * * * * * ** * * * * * ** CPU 3 * 1.000 *0.8000E-02*0.8065E-02* 1.008 *0.8000E-02**(CLAB )* 1.000 *0.1000E-02*0.1008E-02* 1.008 *0.1000E-02**(CLBA )* 1.000 *0.1250E-02*0.1260E-02* 1.008 *0.1250E-02**(CLBC )* 1.000 *0.8333E-03*0.8401E-03* 1.008 *0.8333E-03**(CLBD )* 1.000 *0.4167E-03*0.4200E-03* 1.008 *0.4167E-03**(CLCB )* 1.000 *0.2000E-02*0.2016E-02* 1.008 *0.2000E-02**(CLDB )* 1.000 *0.2500E-02*0.2520E-02* 1.008 *0.2500E-02*
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EXACT ANALYTICAL SOLUTIONS The BCMP theorem: Communication network******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* CPU 4 * 1.000 *0.9333E-02*0.9421E-02* 1.009 *0.9333E-02**(CLAB )* 1.000 *0.1000E-02*0.1009E-02* 1.009 *0.1000E-02**(CLAC )* 1.000 *0.1333E-02*0.1346E-02* 1.009 *0.1333E-02**(CLBA )* 1.000 *0.1250E-02*0.1262E-02* 1.009 *0.1250E-02**(CLBC )* 1.000 *0.8333E-03*0.8412E-03* 1.009 *0.8333E-03**(CLBD )* 1.000 *0.4167E-03*0.4206E-03* 1.009 *0.4167E-03**(CLCB )* 1.000 *0.2000E-02*0.2019E-02* 1.009 *0.2000E-02**(CLDB )* 1.000 *0.2500E-02*0.2524E-02* 1.009 *0.2500E-02** * * * * * ** CPU 5 * 1.000 *0.7000E-02*0.7049E-02* 1.007 *0.7000E-02**(CLAC )* 1.000 *0.1333E-02*0.1343E-02* 1.007 *0.1333E-02**(CLBC )* 1.000 *0.8333E-03*0.8392E-03* 1.007 *0.8333E-03**(CLCA )* 1.000 *0.1333E-02*0.1343E-02* 1.007 *0.1333E-02**(CLCB )* 1.000 *0.2000E-02*0.2014E-02* 1.007 *0.2000E-02**(CLCD )* 1.000 *0.6667E-03*0.6714E-03* 1.007 *0.6667E-03**(CLDC )* 1.000 *0.8333E-03*0.8392E-03* 1.007 *0.8333E-03*
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The BCMP theorem: Communication network******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* CPU 6 * 1.000 *0.7000E-02*0.7049E-02* 1.007 *0.7000E-02**(CLAC )* 1.000 *0.1333E-02*0.1343E-02* 1.007 *0.1333E-02**(CLBC )* 1.000 *0.8333E-03*0.8392E-03* 1.007 *0.8333E-03**(CLCA )* 1.000 *0.1333E-02*0.1343E-02* 1.007 *0.1333E-02**(CLCB )* 1.000 *0.2000E-02*0.2014E-02* 1.007 *0.2000E-02**(CLCD )* 1.000 *0.6667E-03*0.6714E-03* 1.007 *0.6667E-03**(CLDC )* 1.000 *0.8333E-03*0.8392E-03* 1.007 *0.8333E-03** * * * * * ** CPU 7 * 1.000 *0.7750E-02*0.7811E-02* 1.008 *0.7750E-02**(CLAD )* 1.000 *0.1667E-02*0.1680E-02* 1.008 *0.1667E-02**(CLBD )* 1.000 *0.4167E-03*0.4199E-03* 1.008 *0.4167E-03**(CLCD )* 1.000 *0.6667E-03*0.6719E-03* 1.008 *0.6667E-03**(CLDA )* 1.000 *0.1667E-02*0.1680E-02* 1.008 *0.1667E-02**(CLDB )* 1.000 *0.2500E-02*0.2520E-02* 1.008 *0.2500E-02**(CLDC )* 1.000 *0.8333E-03*0.8398E-03* 1.008 *0.8333E-03*
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EXACT ANALYTICAL SOLUTIONS The BCMP theorem: Communication network******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* CPU 8 * 1.000 *0.9083E-02*0.9167E-02* 1.009 *0.9083E-02**(CLAD )* 1.000 *0.1667E-02*0.1682E-02* 1.009 *0.1667E-02**(CLBD )* 1.000 *0.4167E-03*0.4205E-03* 1.009 *0.4167E-03**(CLCA )* 1.000 *0.1333E-02*0.1346E-02* 1.009 *0.1333E-02**(CLCD )* 1.000 *0.6667E-03*0.6728E-03* 1.009 *0.6667E-03**(CLDA )* 1.000 *0.1667E-02*0.1682E-02* 1.009 *0.1667E-02**(CLDB )* 1.000 *0.2500E-02*0.2523E-02* 1.009 *0.2500E-02**(CLDC )* 1.000 *0.8333E-03*0.8410E-03* 1.009 *0.8333E-03******************************************************************** 114.1 146.1 109.6 109.2 108.6 106.3 148.4 113.8 110.0 114.6 115.7 110.4
190 191 /END/
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OUTLINE
INTRODUCTION
CONCEPT OF QUEUE
CONCEPT OF QUEUEING NETWORK
NUMERICAL TECHNIQUES
EXACT ANALYTICAL SOLUTIONS
APPROXIMATE ANALYTICAL SOLUTIONS
SIMULATION TECHNIQUES
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APPROXIMATE ANALYTICAL SOLUTIONS
Approximate solutions for queuing networks are useful for tackling problems not covered by the product-form solutions as, for instance, priorities class dependent or non-exponential service times at
FIFO stations finite buffers simultaneous resource possession
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APPROXIMATE ANALYTICAL SOLUTIONS
There are a lot of different types of approximations in
the literature. Basically, they can be grouped in the
following classes of methods:
decomposition-aggregation
diffusion
iterative
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APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation methods The idea behind decomposition is to break up the queuing
network into smaller subsystems, so that each subsystem can be easily analysed in isolation, and then put together these partial solutions, in order to obtain the solution of the queuing network.
What is difficult to do is to find a good way to decompose the network under study into smaller more manageable subsystems and then put the solution together for the whole network.
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APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation methods
Various decomposition procedures have been developed
specifically for analysing queuing networks with particular
features.
Criteria for decomposing can be:
o Parts with different timing behaviour
o Norton theorem: inspired in the Norton theorem for electric circuits
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APPROXIMATE ANALYTICAL SOLUTIONS Decomposition-aggregation: Norton theorem
BCMP network with a non-BCMP node
m1
m2
m3
m4
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Decomposition-aggregation: Norton theorem
BCMP network with a non-BCMP node
o Let us assume that one node violate the BCMP assumptions. In our
particular case, node 3 is the culprit.
o Let us assume that we know all the parameters of the network, i. e. the
service times, routing probabilities, etc. Also, for simplicity, we
assume a single class of customers. Let N be the total number of
customers in it.
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Decomposition-aggregation: Norton theorem Decomposition step
o "Short-out" node 3 and analyse the queuing network as if this node did not exist. By "short-out" we mean simply that node 3 is removed without changing the incoming and outgoing flows.
o Now, the resulting network is a BCMP network and it can be easily solved. We study this network to compute the throughput along the "short".
o We do this computation assuming that there are k customers in the "shorted" network, where k = 1, 2, ..., N. Let (k) be the throughput along the "short" when there are k customers in it.
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APPROXIMATE ANALYTICAL SOLUTIONS Decomposition-aggregation: Norton theorem
m1
m2
m4
(k )
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APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Norton theorem
Aggregation step
o Now, the original network can be reduced to node 3 and another node,
known as the composite node, which represents approximately the
shorted-out network. The service rate of the composite node is (k),
where k is the number of customers in the composite node (state-
dependent service). The total number of customers in the network is
still N.
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APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Norton theorem
m3
(k )
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APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Norton theorem Aggregation step
o In general, this network is not a BCMP network because of node 3. So, we have to be able to analyse this aggregate system by either a numerical approach, or another approximate method or a simulation method. However, in any case as the system has only two nodes its analysis will be easier.
o Let us assume that we can obtain the queue length distribution of nodes 3 and composite. Then, the queue length distribution of node 3 is an approximation to the queue length distribution of node 3 in the original network.
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APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Norton theorem Aggregation step
o What about the queue length distributions of nodes 1, 2 and 4? They can be obtained by combining the results obtained in step 1 with the queue length distribution of the composite node obtained in step 2. To show how to obtain them, let us assume that we want to obtain the queue length of node 1.
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APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Norton theorem Aggregation step
o Let pc(k) be the probability that there are n customers in the composite node, where k = 1, 2, ..., N, and q1(n|k) be the probability that there are n customers in the node 1 when there are k customers in the shorted network. Then
o It is also possible to proceed in a similar way when instead of just one non-BCMP node we have a non-BCMP sub-network
N
k
c Nn,kpnqnq1
11 ..., 2, 1,for k|
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APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Multiprogramming system
D isk 1
D isk 2
D isk 3
D isk 4
C P U
T e rm in a ls
M e m o rym a n a g e m e n t
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Decomposition-aggregation: Multiprogramming system
D isk 1
D isk 2
D isk 3
D isk 4
C P U
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APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Multiprogramming system 1 /DECLARE/ QUEUE CPU,DISC(4),TERMINAL,SC;
2 REAL PROB1(4)=(2,1.5,1,0.5);
3 REAL PROB2(4)=(1.5,2,3,3.5);
4 REAL TR,CAP(20);
5 REAL TR1,TR2;
6 CLASS C1,C2;
7 INTEGER I,N,M;
8 /STATION/ NAME=CPU;
9 SCHED=PS;
10 INIT(C1)=N;
11 SERVICE(C1)=CST(8.52);
12 SERVICE(C2)=CST(12.);
13 TRANSIT(C1)=DISC,PROB1,CPU,C1,0.6,CPU,C2,0.4;
14 TRANSIT(C2)=DISC,PROB2,CPU,C1,0.6,CPU,C2,0.4;
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Decomposition-aggregation: Multiprogramming system
15 /STATION/ NAME=DISC; 16 TRANSIT=CPU; 17 /STATION/ NAME=DISC(1); 18 SERVICE=EXP(23.); 19 /STATION/ NAME=DISC(2); 20 SERVICE=EXP(22.); 21 /STATION/ NAME=DISC(3); 22 SERVICE=EXP(21.); 23 /STATION/ NAME=DISC(4); 24 SERVICE=EXP(20.);
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APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Multiprogramming system 25 /EXEC/ BEGIN 26 NETWORK(CPU,DISC); 27 FOR N := 1 STEP 1 UNTIL 20 DO 28 BEGIN 29 PRINT; 30 PRINT("FACTOR DE MULTIPROGRAMACIO =",N); 31 SOLVE; 32 CAP(N) := MTHRUPUT(CPU); 33 FOR I:=1 STEP 1 UNTIL 4 DO CAP(N):=CAP(N)-MTHRUP ==> UT(DISC(I)); 34 END; 35 FOR N := 1 STEP 1 UNTIL 20 DO PRINT(N,CAP(N)); 36 END;
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Decomposition-aggregation: Multiprogramming system
FACTOR DE MULTIPROGRAMACIO = 1 - MEAN VALUE ANALYSIS ("MVA") - ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 *0.3566 *0.3566 * 10.43 *0.3418E-01* * * * * * * * * DISC 1 * 23.00 *0.1769 *0.1769 * 23.00 *0.7690E-02* * * * * * * * * DISC 2 * 22.00 *0.1598 *0.1598 * 22.00 *0.7263E-02* * * * * * * * * DISC 3 * 21.00 *0.1615 *0.1615 * 21.00 *0.7690E-02* * * * * * * * * DISC 4 * 20.00 *0.1453 *0.1453 * 20.00 *0.7263E-02* *******************************************************************
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Decomposition-aggregation: Multiprogramming system
FACTOR DE MULTIPROGRAMACIO = 5 - MEAN VALUE ANALYSIS ("MVA") - ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 *0.8852 * 2.552 * 30.08 *0.8484E-01* * * * * * * * * DISC 1 * 23.00 *0.4390 *0.7037 * 36.87 *0.1909E-01* * * * * * * * * DISC 2 * 22.00 *0.3966 *0.6041 * 33.51 *0.1803E-01* * * * * * * * * DISC 3 * 21.00 *0.4009 *0.6137 * 32.15 *0.1909E-01* * * * * * * * * DISC 4 * 20.00 *0.3606 *0.5263 * 29.19 *0.1803E-01* *******************************************************************
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APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Multiprogramming system
FACTOR DE MULTIPROGRAMACIO = 10 - MEAN VALUE ANALYSIS ("MVA") - ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 *0.9905 * 6.801 * 71.65 *0.9493E-01* * * * * * * * * DISC 1 * 23.00 *0.4913 *0.9443 * 44.21 *0.2136E-01* * * * * * * * * DISC 2 * 22.00 *0.4438 *0.7855 * 38.94 *0.2017E-01* * * * * * * * * DISC 3 * 21.00 *0.4485 *0.8003 * 37.47 *0.2136E-01* * * * * * * * * DISC 4 * 20.00 *0.4034 *0.6685 * 33.14 *0.2017E-01* *******************************************************************
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LANC 2007. San José, Costa Rica. October 2007.160
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Multiprogramming system
FACTOR DE MULTIPROGRAMACIO = 15 - MEAN VALUE ANALYSIS ("MVA") - ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 *0.9995 * 11.70 * 122.1 *0.9579E-01* * * * * * * * * DISC 1 * 23.00 *0.4957 *0.9807 * 45.50 *0.2155E-01* * * * * * * * * DISC 2 * 22.00 *0.4478 *0.8098 * 39.78 *0.2036E-01* * * * * * * * * DISC 3 * 21.00 *0.4526 *0.8256 * 38.31 *0.2155E-01* * * * * * * * * DISC 4 * 20.00 *0.4071 *0.6860 * 33.70 *0.2036E-01* *******************************************************************
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LANC 2007. San José, Costa Rica. October 2007.161
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Multiprogramming system
FACTOR DE MULTIPROGRAMACIO = 20 - MEAN VALUE ANALYSIS ("MVA") - ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 * 1.000 * 16.69 * 174.1 *0.9584E-01* * * * * * * * * DISC 1 * 23.00 *0.4960 *0.9838 * 45.62 *0.2156E-01* * * * * * * * * DISC 2 * 22.00 *0.4480 *0.8117 * 39.85 *0.2037E-01* * * * * * * * * DISC 3 * 21.00 *0.4528 *0.8275 * 38.38 *0.2156E-01* * * * * * * * * DISC 4 * 20.00 *0.4073 *0.6872 * 33.74 *0.2037E-01* *******************************************************************
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LANC 2007. San José, Costa Rica. October 2007.162
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Multiprogramming system
1 0.4272E-02 11 0.1191E-01
2 0.6940E-02 12 0.1194E-01
3 0.8680E-02 13 0.1196E-01
4 0.9835E-02 14 0.1197E-01
5 0.1060E-01 15 0.1197E-01
6 0.1111E-01 16 0.1198E-01
7 0.1144E-01 17 0.1198E-01
8 0.1165E-01 18 0.1198E-01
9 0.1179E-01 19 0.1198E-01
10 0.1187E-01 20 0.1198E-01
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LANC 2007. San José, Costa Rica. October 2007.163
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Multiprogramming system
T erm in a ls
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LANC 2007. San José, Costa Rica. October 2007.164
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Multiprogramming system
37 38 /STATION/ NAME=TERMINAL; 39 TYPE=INFINITE; 40 INIT(C1)=N; 41 SERVICE(C1)=EXP(30000.); 42 SERVICE(C2)=EXP(60000.); 43 TRANSIT=SC; 44 /STATION/ NAME=SC; 45 SERVICE=EXP(1.); 46 RATE=CAP(1 STEP 1 UNTIL M); 47 TRANSIT=TERMINAL,C1,0.6,TERMINAL,C2; 48 /CONTROL/ OPTION=NRESULT;
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LANC 2007. San José, Costa Rica. October 2007.165
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Multiprogramming system
49 /EXEC/ BEGIN 50 NETWORK(TERMINAL,SC); 51 PRINT(" TERM FM PRODUCTIVITAT ==> RESPOSTA"); 52 FOR N := 150 STEP 150 UNTIL 750 DO 53 FOR M := 1 STEP 1 UNTIL 20 DO 54 BEGIN 55 SOLVE; 56 PRINT(N,M,MTHRUPUT(SC),MRESPONSE(SC)); 57 END; 58 END;
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LANC 2007. San José, Costa Rica. October 2007.166
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Multiprogramming system
TERM FM PRODUCTIVITAT RESPOSTA 150 1 0.3478E-02 1124. 150 2 0.3541E-02 358.5 150 3 0.3546E-02 304.1 150 4 0.3547E-02 294.4 150 5 0.3547E-02 292.4 150 6 0.3547E-02 292.0 150 7 0.3547E-02 291.9 150 8 0.3547E-02 291.9 ……. 150 20 0.3547E-02 291.9
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LANC 2007. San José, Costa Rica. October 2007.167
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Multiprogramming system
TERM FM PRODUCTIVITAT RESPOSTA 300 1 0.4272E-02 0.2822E+05 300 2 0.6735E-02 2545. 300 3 0.7031E-02 668.5 300 4 0.7062E-02 482.4 300 5 0.7070E-02 433.6 300 6 0.7073E-02 417.0 300 7 0.7074E-02 410.8 300 8 0.7074E-02 408.4 300 9 0.7074E-02 407.5 300 10 0.7074E-02 407.2 300 11 0.7074E-02 407.0 300 12 0.7074E-02 407.0 ………. 300 20 0.7074E-02 407.0
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LANC 2007. San José, Costa Rica. October 2007.168
APPROXIMATE ANALYTICAL SOLUTIONS Decomposition-aggregation: Multiprogramming system
TERM FM PRODUCTIVITAT RESPOSTA 450 1 0.4272E-02 0.6334E+05 450 2 0.6940E-02 0.2284E+05 450 3 0.8679E-02 9847. 450 4 0.9792E-02 3956. 450 5 0.1026E-01 1872. 450 6 0.1040E-01 1270. 450 7 0.1045E-01 1052. 450 8 0.1048E-01 956.3 450 9 0.1049E-01 910.5 450 10 0.1049E-01 887.4 450 11 0.1050E-01 875.5 450 12 0.1050E-01 869.4 450 13 0.1050E-01 866.3 450 14 0.1050E-01 864.7 450 15 0.1050E-01 864.0 450 16 0.1050E-01 863.6 450 17 0.1050E-01 863.4 450 18 0.1050E-01 863.3 450 19 0.1050E-01 863.2 450 20 0.1050E-01 863.2
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LANC 2007. San José, Costa Rica. October 2007.169
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Multiprogramming system
TERM FM PRODUCTIVITAT RESPOSTA 600 1 0.4272E-02 0.9845E+05 600 2 0.6940E-02 0.4446E+05 600 3 0.8679E-02 0.2713E+05 600 4 0.9835E-02 0.1901E+05 600 5 0.1060E-01 0.1458E+05 600 6 0.1111E-01 0.1199E+05 600 7 0.1144E-01 0.1043E+05 600 8 0.1165E-01 9486. 600 9 0.1179E-01 8910. 600 10 0.1187E-01 8565. 600 11 0.1191E-01 8360. 600 12 0.1194E-01 8241. 600 13 0.1196E-01 8172. 600 14 0.1197E-01 8133. 600 15 0.1197E-01 8111. 600 16 0.1198E-01 8099. 600 17 0.1198E-01 8092. 600 18 0.1198E-01 8088. 600 19 0.1198E-01 8086. 600 20 0.1198E-01 8085.
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LANC 2007. San José, Costa Rica. October 2007.170
APPROXIMATE ANALYTICAL SOLUTIONS Decomposition-aggregation: Multiprogramming system TERM FM PRODUCTIVITAT RESPOSTA 750 1 0.4272E-02 0.1336E+06 750 2 0.6940E-02 0.6607E+05 750 3 0.8679E-02 0.4441E+05 750 4 0.9835E-02 0.3426E+05 750 5 0.1060E-01 0.2873E+05 750 6 0.1111E-01 0.2549E+05 750 7 0.1144E-01 0.2354E+05 750 8 0.1165E-01 0.2236E+05 750 9 0.1179E-01 0.2164E+05 750 10 0.1187E-01 0.2121E+05 750 11 0.1191E-01 0.2095E+05 750 12 0.1194E-01 0.2080E+05 750 13 0.1196E-01 0.2071E+05 750 14 0.1197E-01 0.2067E+05 750 15 0.1197E-01 0.2064E+05 750 16 0.1198E-01 0.2062E+05 750 17 0.1198E-01 0.2061E+05 750 18 0.1198E-01 0.2061E+05 750 19 0.1198E-01 0.2061E+05 750 20 0.1198E-01 0.2061E+05 59 /END/
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LANC 2007. San José, Costa Rica. October 2007.171
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Sliding window flow control mechanisms
N etw o rk 1
f(S )
e (S )
t j
N etw o rk 2
tf
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LANC 2007. San José, Costa Rica. October 2007.172
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Sliding window flow control mechanisms Step 1: Decomposition
N etw o rk 1
N e tw o rk 2
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LANC 2007. San José, Costa Rica. October 2007.173
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Sliding window flow control
mechanisms
Step 1: Decomposition
o We analyze this queuing network to obtain its throughput when there
are k customers where k = 1, 2, …, C.
o Let (k) be the throughput we obtain when there are k customers in the
network. The final result of this step is a set of values (1), (2), …,
(C).
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LANC 2007. San José, Costa Rica. October 2007.174
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Sliding window flow control mechanisms Step 2: Aggregation
f(S )
e (S )
t j
g(k )
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LANC 2007. San José, Costa Rica. October 2007.175
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Sliding window flow control mechanisms Step 2: Aggregation
o The arrival process at queue f(S) is Poisson distributed of mean o There are C tokens.
o The inter-arrival times at queue e(S) are exponentially distributed with a rate g(k), where k is the number of outstanding tokens, i. e. C - k is the number of tokens in queue e(S).
o We set g(k) = (k), for k = 1, 2, …, C.
o The state of this system can be described by the tuple (i, j), where i is the number of customers in queue f(S) and j is the number of tokens in queue e(S).
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LANC 2007. San José, Costa Rica. October 2007.176
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Sliding window flow control mechanisms Step 2: Aggregation
g(C ) g(C ) g(C ) g(C ) g(C -1 ) g(C -2 ) g(C - j) g(1 )
1 ,0 1 ,0 0 ,0 0 ,1 0 ,2 0 ,j 0 ,C
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LANC 2007. San José, Costa Rica. October 2007.177
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Sliding window flow control
mechanisms
Step 2: Aggregation
o This system is identical to an M/M/1 queue with an arrival rate and a state
dependent service rate g(nq) if nq C, and g(C) if nq > C, where nq is the number of
customers in this M/M/1 queue. The random variables i and j are related to nq as
follows:
i = max(0, nq - C)
j = max(0, C - nq)
o The solution of this system can be obtained by a direct application of classical results.
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LANC 2007. San José, Costa Rica. October 2007.178
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Sliding window flow control mechanisms Step 2: Aggregation
where
= /g(C)
000
000
,pj
j,p
,p,ip
j
i
g
0 1
0 1
0j
jkCj
j
k
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LANC 2007. San José, Costa Rica. October 2007.179
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Sliding window flow control mechanisms Step 2: Aggregation
o The probability p(0, 0) is chosen so that the addition of the state probabilities is equal to 1:
C
jj
j,p
1
1
1
100
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LANC 2007. San José, Costa Rica. October 2007.180
APPROXIMATE ANALYTICAL SOLUTIONS
Decomposition-aggregation: Sliding window flow control mechanisms Step 2: Aggregation
o We obtain the following marginal probabilities for each queue (index 1 is for queue f(S) and 2 for queue e(S)):
Cj,pj
jp
,pp
i,pip
,pp
j
i
0 00
1
000
0 00
1
00110
2
2
1
1
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LANC 2007. San José, Costa Rica. October 2007.181
APPROXIMATE ANALYTICAL SOLUTIONS
Diffusion Method Based on the assumption that very probably the queues are never
empty. Under this hypothesis for each queue:o the queue length discrete distribution is studied
o this discrete distribution is replaced by a continuous one with the same first two moments (first approximation)
o this continuous probability distribution is described by a diffusion equation
o this equation is solved with the appropriate contour conditions for the steady state
o the continuous probability distribution of the queue length is discretised by means of some heuristic criteria (second approximation)
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LANC 2007. San José, Costa Rica. October 2007.182
APPROXIMATE ANALYTICAL SOLUTIONS
Diffusion Method To solve a queuing network it is assumed that it will have a
product-form.
If the system is open it is possible to determine for each node the characteristics of the inter-arrival time distribution and those of the service time are assumed to be known.
From the state probabilities, the performance measures can be computed.
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LANC 2007. San José, Costa Rica. October 2007.183
EXACT ANALYTICAL SOLUTIONS
Diffusion method: Packet communication network
1
2
3
4
5
6
7
8
A
B
C
D
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LANC 2007. San José, Costa Rica. October 2007.184
EXACT ANALYTICAL SOLUTIONS
Diffusion method: Packet communication network
1 /DECLARE/ QUEUE GEN,LINIA(8,8); 2 REAL TRAB,TRAC,TRAD,TRBA,TRBC,TRBD,TRCA,TRCB,TRCD,==> TRDA,TRDB,TRDC; 3 INTEGER I; 4 CLASS CLAB,CLAC,CLAD,CLBA,CLBC,CLBD,CLCA,CLCB,CLCD==> ,CLDA,CLDB,CLDC; 5
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LANC 2007. San José, Costa Rica. October 2007.185
EXACT ANALYTICAL SOLUTIONS
Diffusion method: Packet communication network 6 /STATION/ NAME = GEN; 7 TYPE = SOURCE; 8 SERVICE = EXP(60000./930.); 9 TRANSIT = LINIA(1,2),CLAB,60,LINIA(1,2),CLAC,80,L==> INIA(1,2),CLAD,100,10 LINIA(3,4),CLBA,75,LINIA(3,4),CLBC,50,L==> INIA(3,4),CLBD,25,11 LINIA(5,6),CLCA,80,LINIA(5,6),CLCB,120,==> LINIA(5,6),CLCD,40,12 LINIA(7,8),CLDA,100,LINIA(7,8),CLDB,150==> ,LINIA(7,8),CLDC,50;13
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LANC 2007. San José, Costa Rica. October 2007.186
EXACT ANALYTICAL SOLUTIONS
Diffusion method: Packet communication network 14 /STATION/ NAME = LINIA; 15 SERVICE = CST(256.*8./64.); 16 17 /STATION/ NAME = LINIA(1,2); 18 TRANSIT(CLAB) = LINIA(2,4); 19 TRANSIT(CLAC) = LINIA(2,4); 20 TRANSIT(CLAD) = LINIA(2,8); 21 22 /STATION/ NAME = LINIA(2,1); 23 TRANSIT = OUT; 24 25 /STATION/ NAME = LINIA(2,4); 26 TRANSIT(CLAB) = LINIA(4,3); 27 TRANSIT(CLAC) = LINIA(4,6); 28 29 /STATION/ NAME = LINIA(2,8); 30 TRANSIT(CLAD) = LINIA(8,7); 31
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LANC 2007. San José, Costa Rica. October 2007.187
EXACT ANALYTICAL SOLUTIONS
Diffusion method: Packet communication network 32 /STATION/ NAME = LINIA(3,4); 33 TRANSIT(CLBA) = LINIA(4,2); 34 TRANSIT(CLBC) = LINIA(4,6); 35 TRANSIT(CLBD) = LINIA(4,8); 36 37 /STATION/ NAME = LINIA(4,2); 38 TRANSIT(CLBA) = LINIA(2,1); 39 40 /STATION/ NAME = LINIA(4,3); 41 TRANSIT = OUT; 42 43 /STATION/ NAME = LINIA(4,6); 44 TRANSIT(CLAC) = LINIA(6,5); 45 TRANSIT(CLBC) = LINIA(6,5); 46 47 /STATION/ NAME = LINIA(4,8); 48 TRANSIT(CLBD) = LINIA(8,7); 49
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LANC 2007. San José, Costa Rica. October 2007.188
EXACT ANALYTICAL SOLUTIONS Diffusion method: Packet communication network 50 /STATION/ NAME = LINIA(5,6); 51 TRANSIT(CLCA) = LINIA(6,8); 52 TRANSIT(CLCB) = LINIA(6,4); 53 TRANSIT(CLCD) = LINIA(6,8); 54 55 /STATION/ NAME = LINIA(6,4); 56 TRANSIT(CLCB) = LINIA(4,3); 57 58 /STATION/ NAME = LINIA(6,5); 59 TRANSIT = OUT; 60 61 /STATION/ NAME = LINIA(6,8); 62 TRANSIT(CLCA) = LINIA(8,2); 63 TRANSIT(CLCD) = LINIA(8,7); 64 65 /STATION/ NAME = LINIA(7,8); 66 TRANSIT(CLDA) = LINIA(8,2); 67 TRANSIT(CLDB) = LINIA(8,4); 68 TRANSIT(CLDC) = LINIA(8,6); 69
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LANC 2007. San José, Costa Rica. October 2007.189
EXACT ANALYTICAL SOLUTIONS
Diffusion method: Packet communication network 70 /STATION/ NAME = LINIA(8,2); 71 TRANSIT(CLCA) = LINIA(2,1); 72 TRANSIT(CLDA) = LINIA(2,1); 73 74 /STATION/ NAME = LINIA(8,4); 75 TRANSIT(CLDB) = LINIA(4,3); 76 77 /STATION/ NAME = LINIA(8,6); 78 TRANSIT(CLDC) = LINIA(6,5); 79 80 /STATION/ NAME = LINIA(8,7); 81 TRANSIT = OUT; 82
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LANC 2007. San José, Costa Rica. October 2007.190
EXACT ANALYTICAL SOLUTIONS
Diffusion method: Packet communication network 83 /EXEC/ BEGIN84 NETWORK(GEN,85 LINIA(1,2),LINIA(2,1),LINIA(2,4),LINIA(2,8),86 LINIA(3,4),LINIA(4,2),LINIA(4,3),LINIA(4,6),87 LINIA(4,8),LINIA(5,6),LINIA(6,4),LINIA(6,5),88 LINIA(6,8),LINIA(7,8),LINIA(8,2),LINIA(8,4),89 LINIA(8,6),LINIA(8,7));90 PRINT;91 SOLVE;92 TRAB:=MRESPONSE(LINIA(1,2))+93 MRESPONSE(LINIA(2,4))+MRESPONSE(LINIA(4,3));94 TRAC:=MRESPONSE(LINIA(1,2))+MRESPONSE(LINIA(2,4))+95 MRESPONSE(LINIA(4,6))+MRESPONSE(LINIA(6,5));96 TRAD:=MRESPONSE(LINIA(1,2))+MRESPONSE(LINIA(2,8))+97 MRESPONSE(LINIA(8,7));98 TRBA:=MRESPONSE(LINIA(3,4))+MRESPONSE(LINIA(4,2))+99 MRESPONSE(LINIA(2,1));
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EXACT ANALYTICAL SOLUTIONS
Diffusion method: Packet communication network 100 TRBC:=MRESPONSE(LINIA(3,4))+MRESPONSE(LINIA(4,6))+101 MRESPONSE(LINIA(6,5));102 TRBD:=MRESPONSE(LINIA(3,4))+MRESPONSE(LINIA(4,8))+103 MRESPONSE(LINIA(8,7));104 TRCA:=MRESPONSE(LINIA(5,6))+MRESPONSE(LINIA(6,8))+105 MRESPONSE(LINIA(8,2))+MRESPONSE(LINIA(2,1));106 TRCB:=MRESPONSE(LINIA(5,6))+MRESPONSE(LINIA(6,4))+107 MRESPONSE(LINIA(4,3));108 TRCD:=MRESPONSE(LINIA(5,6))+MRESPONSE(LINIA(6,8))+109 MRESPONSE(LINIA(8,7));110 TRDA:=MRESPONSE(LINIA(7,8))+MRESPONSE(LINIA(8,2))+111 MRESPONSE(LINIA(2,1));112 TRDB:=MRESPONSE(LINIA(7,8))+MRESPONSE(LINIA(8,4))+113 MRESPONSE(LINIA(4,3));114 TRDC:=MRESPONSE(LINIA(7,8))+MRESPONSE(LINIA(8,6))+115 MRESPONSE(LINIA(6,5));
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Diffusion method: Packet communication network 116 PRINT(TRAB,TRAC,TRAD); 117 PRINT(TRBA,TRBC,TRBD); 118 PRINT(TRCA,TRCB,TRCD); 119 PRINT(TRDA,TRDB,TRDC); 120 END;
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Diffusion method: Packet communication network - APPROXIMATE DIFFUSIONS METHOD ("DIFFU") -******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* * * * * * ** GEN * 64.52 * 1.000 * 1.000 * 64.52 *0.1550E-01** * * * * * ** LINIA 2 * 32.00 *0.1280 *0.1374 * 34.35 *0.4000E-02** * * * * * ** LINIA 9 * 32.00 *0.1360 *0.1466 * 34.48 *0.4250E-02** * * * * * ** LINIA 12 * 32.00 *0.7467E-01*0.7765E-01* 33.28 *0.2333E-02** * * * * * ** LINIA 16 * 32.00 *0.5333E-01*0.5482E-01* 32.89 *0.1667E-02** * * * * * ** LINIA 20 * 32.00 *0.8000E-01*0.8348E-01* 33.39 *0.2500E-02** * * * * * ** LINIA 26 * 32.00 *0.4000E-01*0.4083E-01* 32.66 *0.1250E-02** * * * * * *
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EXACT ANALYTICAL SOLUTIONS
Diffusion method: Packet communication network******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* LINIA 27 * 32.00 *0.1760 *0.1945 * 35.37 *0.5500E-02** * * * * * ** LINIA 30 * 32.00 *0.6933E-01*0.7190E-01* 33.18 *0.2167E-02** * * * * * ** LINIA 32 * 32.00 *0.1333E-01*0.1342E-01* 32.22 *0.4167E-03** * * * * * ** LINIA 38 * 32.00 *0.1280 *0.1374 * 34.35 *0.4000E-02** * * * * * ** LINIA 44 * 32.00 *0.6400E-01*0.6617E-01* 33.08 *0.2000E-02** * * * * * ** LINIA 45 * 32.00 *0.9600E-01*0.1011 * 33.68 *0.3000E-02** * * * * * ** LINIA 48 * 32.00 *0.6400E-01*0.6617E-01* 33.08 *0.2000E-02** * * * * * ** LINIA 56 * 32.00 *0.1600 *0.1752 * 35.05 *0.5000E-02** * * * * * ** LINIA 58 * 32.00 *0.9600E-01*0.1011 * 33.68 *0.3000E-02** * * * * * *
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Diffusion method: Packet communication network******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT ********************************************************************* LINIA 60 * 32.00 *0.8000E-01*0.8343E-01* 33.37 *0.2500E-02** * * * * * ** LINIA 62 * 32.00 *0.2667E-01*0.2703E-01* 32.44 *0.8333E-03** * * * * * ** LINIA 63 * 32.00 *0.8800E-01*0.9222E-01* 33.53 *0.2750E-02******************************************************************** MEMORY USED: 19812 WORDS OF 4 BYTES ( 2.48 % OF TOTAL MEMORY)
103.0 134.5 100.8 100.5 100.3 99.14 135.6 102.8 101.0 103.2 103.8 101.2
121 122 /END/
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APPROXIMATE ANALYTICAL SOLUTIONS
Iterative methods In this family of methods we establish an iterative computation
of the result from a reasonable conjecture.
They have neither any theoretical justification of the iteration
convergence nor the coincidence of the limit of the iteration with
the theoretical result; however the experience shows that there
are no counter-examples in the normal domain of use of such
methods.
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APPROXIMATE ANALYTICAL SOLUTIONS
Iterative methods They are useful tools to study cases not covered by exact methods, as,
for instance:o closed queuing networks with FIFO stations that have with non-
exponentially distributed service time
o systems with customers seizing simultaneously more than one server (for example, in a disk input-output there are simultaneous seizing of the disk and the path between disks and memory).
o systems with customers affected of priorities
They are also useful to reduce the computing time in methods derived from the BCMP theorem when they are applied to large dimension systems.
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Iterative methods: Conversational system This case is identical to the previous one with an important difference:
o the disk path to memory is shared by several disks and should be taken into account in the modelling process
o the scheduling policy of disks accesses in the control unit is SLTF (Shortest Latency Time First).
As in this case the basic assumption of analytical models is not fulfilled, we are obliged to build an iterative model starting with the assumption that there will not be conflicts in the path; from this assumption it is possible to compute the throughput in the disks. With this data we recompute the path conflict time due to the lost rotations. This time is introduced in the disks service time and we restart the iteration.
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Iterative methods: Conversational system 1 /DECLARE/ QUEUE CPU,DISC(4),TERMINAL;
2 REAL PROB1(4)=(2,1.5,1,0.5); 3 REAL PROB2(4)=(1.5,2,3,3.5); 4 REAL TR1,TR2; 5 REAL SD(4),VP,VPN,LT,TF,VR=3600,TAU,UC, 6 SK(4)=(13.,12.,11.,10.); 7 REAL EPS; 8 CLASS C1,C2; 9 INTEGER I,N; 10 /STATION/ NAME=CPU; 11 SCHED=PS; 12 SERVICE(C1)=CST(8.52); 13 SERVICE(C2)=CST(12.); 14 TRANSIT(C1)=DISC,PROB1,TERMINAL,C1,0.6,TERMINAL,C2,0 ==> .4; 15 TRANSIT(C2)=DISC,PROB2,TERMINAL,C1,0.6,TERMINAL,C2,0 ==> .4;
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APPROXIMATE ANALYTICAL SOLUTIONS
Iterative methods: Conversational system
16 /STATION/ NAME=DISC; 17 TRANSIT=CPU; 18 /STATION/ NAME=DISC(1); 19 SERVICE=EXP(SD(1)); 20 /STATION/ NAME=DISC(2); 21 SERVICE=EXP(SD(2)); 22 /STATION/ NAME=DISC(3); 23 SERVICE=EXP(SD(3)); 24 /STATION/ NAME=DISC(4); 25 SERVICE=EXP(SD(4)); 26 /STATION/ NAME=TERMINAL; 27 TYPE=INFINITE; 28 INIT(C1)=N; 29 SERVICE(C1)=EXP(30000.); 30 SERVICE(C2)=EXP(60000.); 31 TRANSIT=CPU; 32 /CONTROL/ CLASS=ALL QUEUE;
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APPROXIMATE ANALYTICAL SOLUTIONS
Iterative methods: Conversational system
33 /EXEC/ BEGIN 34 TAU:=60.*1000./VR; 35 TF:=TAU/10.; 36 LT:=TAU/2.; 37 FOR N:=150 STEP 150 UNTIL 750 DO 38 BEGIN 39 PRINT("NOMBRE D’USUARIS =",N); 40 EPS:=1.; 41 VP:=0.; 42 WHILE EPS>=1.E-4 DO 43 BEGIN 44 FOR I:=1 STEP 1 UNTIL 4 DO SD(I):=SK(I)+LT+VP+ ==> TF; 45 PRINT; 46 SOLVE;
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APPROXIMATE ANALYTICAL SOLUTIONS Iterative methods: Conversational system 47 UC:=0.; 48 FOR I:=1 STEP 1 UNTIL 4 DO UC := UC + TF * MTH ==> RUPUT(DISC(I)); 49 VPN:=TAU*UC/(1.-UC); 50 EPS:=ABS(VP-VPN)/VPN; 51 VP:=VPN; 52 END; 53 TR1:=MCUSTNB(CPU,C1); 54 TR2:=MCUSTNB(CPU,C2); 55 FOR I:= 1 STEP 1 UNTIL 4 DO 56 BEGIN 57 TR1:=TR1+MCUSTNB(DISC(I),C1); 58 TR2:=TR2+MCUSTNB(DISC(I),C2); 59 END; 60 TR1:=TR1/MTHRUPUT(TERMINAL,C1); 61 TR2:=TR2/MTHRUPUT(TERMINAL,C2);; 62 PRINT("RESPONSE TIME OF CLASS C1 =",TR1); 63 PRINT("RESPONSE TIME OF CLASS C2 =",TR2); 64 END; 65 END;
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APPROXIMATE ANALYTICAL SOLUTIONS
Iterative methods: Conversational systemNOMBRE D’USUARIS = 150 - MEAN VALUE ANALYSIS ("MVA") - ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* *(C1 )* 8.520 *0.1088 *0.1539 * 12.06 *0.1277E-01* *(C2 )* 12.00 *0.1873 *0.2650 * 16.98 *0.1560E-01* * * * * * * * * DISC 1 * 23.00 *0.1468 *0.1719 * 26.92 *0.6384E-02* *(C1 )* 23.00 *0.9790E-01*0.1146 * 26.92 *0.4257E-02* *(C2 )* 23.00 *0.4894E-01*0.5729E-01* 26.92 *0.2128E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 149.0 *0.4200E+05*0.3547E-02* *(C1 )*0.3000E+05*0.0000E+00* 63.84 *0.3000E+05*0.2128E-02* *(C2 )*0.6000E+05*0.0000E+00* 85.12 *0.6000E+05*0.1419E-02* * * * * * * * *******************************************************************
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Iterative methods: Conversational systemNOMBRE D’USUARIS = 150 ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 *0.2960 *0.4188 * 14.76 *0.2837E-01* *(C1 )* 8.520 *0.1088 *0.1539 * 12.05 *0.1277E-01* *(C2 )* 12.00 *0.1872 *0.2649 * 16.98 *0.1560E-01* * * * * * * * * DISC 1 * 23.72 *0.1514 *0.1782 * 27.91 *0.6383E-02* *(C1 )* 23.72 *0.1009 *0.1188 * 27.91 *0.4256E-02* *(C2 )* 23.72 *0.5046E-01*0.5938E-01* 27.91 *0.2127E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 148.9 *0.4200E+05*0.3546E-02* *(C1 )*0.3000E+05*0.0000E+00* 63.83 *0.3000E+05*0.2128E-02* *(C2 )*0.6000E+05*0.0000E+00* 85.11 *0.6000E+05*0.1418E-02* *******************************************************************
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Iterative methods: Conversational systemNOMBRE D’USUARIS = 150 ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 *0.2960 *0.4188 * 14.76 *0.2837E-01* *(C1 )* 8.520 *0.1088 *0.1539 * 12.05 *0.1277E-01* *(C2 )* 12.00 *0.1872 *0.2649 * 16.98 *0.1560E-01* * * * * * * * * DISC 1 * 23.72 *0.1514 *0.1782 * 27.91 *0.6383E-02* *(C1 )* 23.72 *0.1009 *0.1188 * 27.91 *0.4256E-02* *(C2 )* 23.72 *0.5046E-01*0.5938E-01* 27.91 *0.2127E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 148.9 *0.4200E+05*0.3546E-02* *(C1 )*0.3000E+05*0.0000E+00* 63.83 *0.3000E+05*0.2128E-02* *(C2 )*0.6000E+05*0.0000E+00* 85.11 *0.6000E+05*0.1418E-02******************************************************************** RESPONSE TIME OF CLASS C1 = 204.6 RESPONSE TIME OF CLASS C2 = 439.5
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Iterative methods: Conversational system
NOMBRE D’USUARIS = 300 ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 *0.5905 * 1.426 * 25.19 *0.5659E-01* *(C1 )* 8.520 *0.2170 *0.5239 * 20.57 *0.2547E-01* *(C2 )* 12.00 *0.3735 *0.9017 * 28.97 *0.3112E-01* * * * * * * * * DISC 1 * 23.00 *0.2929 *0.4134 * 32.46 *0.1273E-01* *(C1 )* 23.00 *0.1953 *0.2756 * 32.46 *0.8490E-02* *(C2 )* 23.00 *0.9761E-01*0.1378 * 32.46 *0.4244E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 297.1 *0.4200E+05*0.7074E-02* *(C1 )*0.3000E+05*0.0000E+00* 127.3 *0.3000E+05*0.4245E-02* *(C2 )*0.6000E+05*0.0000E+00* 169.8 *0.6000E+05*0.2830E-02* *******************************************************************
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Iterative methods: Conversational system
NOMBRE D’USUARIS = 300 ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 *0.5902 * 1.424 * 25.17 *0.5657E-01* *(C1 )* 8.520 *0.2169 *0.5233 * 20.56 *0.2546E-01* *(C2 )* 12.00 *0.3733 *0.9007 * 28.95 *0.3111E-01* * * * * * * * * DISC 1 * 24.50 *0.3118 *0.4521 * 35.52 *0.1273E-01* *(C1 )* 24.50 *0.2079 *0.3015 * 35.52 *0.8486E-02* *(C2 )* 24.50 *0.1039 *0.1507 * 35.52 *0.4242E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 297.0 *0.4200E+05*0.7071E-02* *(C1 )*0.3000E+05*0.0000E+00* 127.3 *0.3000E+05*0.4243E-02* *(C2 )*0.6000E+05*0.0000E+00* 169.7 *0.6000E+05*0.2828E-02* *******************************************************************
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APPROXIMATE ANALYTICAL SOLUTIONS Iterative methods: Conversational system
NOMBRE D’USUARIS = 300 ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 *0.5902 * 1.424 * 25.17 *0.5657E-01* *(C1 )* 8.520 *0.2169 *0.5233 * 20.56 *0.2546E-01* *(C2 )* 12.00 *0.3733 *0.9007 * 28.95 *0.3111E-01* * * * * * * * * DISC 1 * 24.50 *0.3118 *0.4521 * 35.52 *0.1273E-01* *(C1 )* 24.50 *0.2079 *0.3014 * 35.52 *0.8486E-02* *(C2 )* 24.50 *0.1039 *0.1507 * 35.52 *0.4242E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 297.0 *0.4200E+05*0.7071E-02* *(C1 )*0.3000E+05*0.0000E+00* 127.3 *0.3000E+05*0.4243E-02* *(C2 )*0.6000E+05*0.0000E+00* 169.7 *0.6000E+05*0.2828E-02* ******************************************************************* RESPONSE TIME OF CLASS C1 = 289.4 RESPONSE TIME OF CLASS C2 = 632.8
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Iterative methods: Conversational system
NOMBRE D’USUARIS = 450 ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 *0.8763 * 6.438 * 76.66 *0.8399E-01* *(C1 )* 8.520 *0.3220 * 2.366 * 62.60 *0.3780E-01* *(C2 )* 12.00 *0.5543 * 4.072 * 88.16 *0.4619E-01* * * * * * * * * DISC 1 * 23.00 *0.4347 *0.7667 * 40.57 *0.1890E-01* *(C1 )* 23.00 *0.2898 *0.5112 * 40.57 *0.1260E-01* *(C2 )* 23.00 *0.1449 *0.2555 * 40.57 *0.6298E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 440.9 *0.4200E+05*0.1050E-01* *(C1 )*0.3000E+05*0.0000E+00* 189.0 *0.3000E+05*0.6299E-02* *(C2 )*0.6000E+05*0.0000E+00* 252.0 *0.6000E+05*0.4199E-02* *******************************************************************
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Iterative methods: Conversational system
NOMBRE D’USUARIS = 450 ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 *0.8754 * 6.393 * 76.20 *0.8390E-01* *(C1 )* 8.520 *0.3217 * 2.349 * 62.22 *0.3776E-01* *(C2 )* 12.00 *0.5537 * 4.044 * 87.64 *0.4614E-01* * DISC 1 * 25.33 *0.4781 *0.9129 * 48.36 *0.1888E-01* *(C1 )* 25.33 *0.3188 *0.6086 * 48.36 *0.1259E-01* *(C2 )* 25.33 *0.1594 *0.3043 * 48.36 *0.6292E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 440.5 *0.4200E+05*0.1049E-01* *(C1 )*0.3000E+05*0.0000E+00* 188.8 *0.3000E+05*0.6293E-02* *(C2 )*0.6000E+05*0.0000E+00* 251.7 *0.6000E+05*0.4195E-02* *******************************************************************
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APPROXIMATE ANALYTICAL SOLUTIONS Iterative methods: Conversational system
NOMBRE D’USUARIS = 450 ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 *0.8754 * 6.393 * 76.20 *0.8390E-01* *(C1 )* 8.520 *0.3217 * 2.349 * 62.22 *0.3776E-01* *(C2 )* 12.00 *0.5537 * 4.044 * 87.64 *0.4614E-01* * * * * * * * * DISC 1 * 25.32 *0.4781 *0.9127 * 48.35 *0.1888E-01* *(C1 )* 25.32 *0.3187 *0.6085 * 48.35 *0.1259E-01* *(C2 )* 25.32 *0.1593 *0.3042 * 48.35 *0.6292E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 440.5 *0.4200E+05*0.1049E-01* *(C1 )*0.3000E+05*0.0000E+00* 188.8 *0.3000E+05*0.6293E-02* *(C2 )*0.6000E+05*0.0000E+00* 251.7 *0.6000E+05*0.4195E-02* ******************************************************************* RESPONSE TIME OF CLASS C1 = 594.4 RESPONSE TIME OF CLASS C2 = 1376.
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APPROXIMATE ANALYTICAL SOLUTIONS
Iterative methods: Conversational system
NOMBRE D’USUARIS = 600 ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 * 1.000 * 93.51 * 975.7 *0.9584E-01* *(C1 )* 8.520 *0.3675 * 34.37 * 796.7 *0.4313E-01* *(C2 )* 12.00 *0.6325 * 59.15 * 1122. *0.5271E-01* * * * * * * * * DISC 1 * 23.00 *0.4960 *0.9841 * 45.63 *0.2157E-01* *(C1 )* 23.00 *0.3307 *0.6561 * 45.63 *0.1438E-01* *(C2 )* 23.00 *0.1653 *0.3280 * 45.63 *0.7187E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 503.2 *0.4200E+05*0.1198E-01* *(C1 )*0.3000E+05*0.0000E+00* 215.7 *0.3000E+05*0.7188E-02* *(C2 )*0.6000E+05*0.0000E+00* 287.5 *0.6000E+05*0.4792E-02* *******************************************************************
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APPROXIMATE ANALYTICAL SOLUTIONS Iterative methods: Conversational system NOMBRE D’USUARIS = 600 ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 * 1.000 * 92.66 * 966.8 *0.9584E-01* *(C1 )* 8.520 *0.3675 * 34.05 * 789.5 *0.4313E-01* *(C2 )* 12.00 *0.6325 * 58.61 * 1112. *0.5271E-01* * * * * * * * * DISC 1 * 25.71 *0.5544 * 1.244 * 57.69 *0.2157E-01* *(C1 )* 25.71 *0.3696 *0.8295 * 57.69 *0.1438E-01* *(C2 )* 25.71 *0.1848 *0.4147 * 57.69 *0.7187E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 503.2 *0.4200E+05*0.1198E-01* *(C1 )*0.3000E+05*0.0000E+00* 215.7 *0.3000E+05*0.7188E-02* *(C2 )*0.6000E+05*0.0000E+00* 287.5 *0.6000E+05*0.4792E-02* ******************************************************************* RESPONSE TIME OF CLASS C1 = 4997. RESPONSE TIME OF CLASS C2 = 0.1271E+05
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APPROXIMATE ANALYTICAL SOLUTIONS
Iterative methods: Conversational system
NOMBRE D’USUARIS = 750 ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 * 1.000 * 243.5 * 2541. *0.9584E-01* *(C1 )* 8.520 *0.3675 * 89.49 * 2075. *0.4313E-01* *(C2 )* 12.00 *0.6325 * 154.0 * 2922. *0.5271E-01* * * * * * * * * DISC 1 * 23.00 *0.4960 *0.9841 * 45.64 *0.2157E-01* *(C1 )* 23.00 *0.3307 *0.6561 * 45.64 *0.1438E-01* *(C2 )* 23.00 *0.1653 *0.3280 * 45.64 *0.7187E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 503.2 *0.4200E+05*0.1198E-01* *(C1 )*0.3000E+05*0.0000E+00* 215.7 *0.3000E+05*0.7188E-02* *(C2 )*0.6000E+05*0.0000E+00* 287.5 *0.6000E+05*0.4792E-02* *******************************************************************
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APPROXIMATE ANALYTICAL SOLUTIONS
Iterative methods: Conversational system
NOMBRE D’USUARIS = 750 ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * THRUPUT * ******************************************************************* * CPU * 10.43 * 1.000 * 242.7 * 2532. *0.9584E-01* *(C1 )* 8.520 *0.3675 * 89.18 * 2067. *0.4313E-01* *(C2 )* 12.00 *0.6325 * 153.5 * 2912. *0.5271E-01* * * * * * * * * DISC 1 * 25.71 *0.5544 * 1.244 * 57.69 *0.2157E-01* *(C1 )* 25.71 *0.3696 *0.8295 * 57.69 *0.1438E-01* *(C2 )* 25.71 *0.1848 *0.4147 * 57.69 *0.7187E-02* * * * * * * * * TERMINAL *0.4200E+05*0.0000E+00* 503.2 *0.4200E+05*0.1198E-01* *(C1 )*0.3000E+05*0.0000E+00* 215.7 *0.3000E+05*0.7188E-02* *(C2 )*0.6000E+05*0.0000E+00* 287.5 *0.6000E+05*0.4792E-02******************************************************************** RESPONSE TIME OF CLASS C1 = 0.1266E+05 RESPONSE TIME OF CLASS C2 = 0.3251E+05
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OUTLINE
INTRODUCTION
CONCEPT OF QUEUE
CONCEPT OF QUEUEING NETWORK
NUMERICAL TECHNIQUES
EXACT ANALYTICAL SOLUTIONS
APPROXIMATE ANALYTICAL SOLUTIONS
SIMULATION TECHNIQUES
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SIMULATION TECHNIQUES
Computer based simulation implies writing a computer
program which depicts the system operations.
Running this program permits us to "imitate" the
system behaviour in a very short time. Thus, we are
able to "observe" the system and collect performance
statistics.
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SIMULATION TECHNIQUES
Simulation advantage are: there is no theoretical limitation and it allows us to study
systems not able to be studied by means of analytical or numerical techniques.
It is easy to learn and to apply.
Simulation disadvantages are: the effort (mainly time) to develop and to debug a
simulation program. the execution time, that can be quite long to obtain results
with enough significance.
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SIMULATION TECHNIQUES
The complexity of the simulation model depend on the detail of
the system behaviour representation.
To build up simulation models it is convenient to use: modelling languages as QNAP2, RESQ, PAWS, etc., that make easier to
build up queuing network models and that include analytical, numerical
and simulation procedures.
simulation languages, such as SIMSCRIPT, GPSS, SIMULA, etc., that
offer greater simulation capabilities.
high level programming language for building up very detailed models.
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SIMULATION TECHNIQUES
The intrinsic problems of any simulation are:
random numbers generation
simulated time management
extraction of statistical estimations of the simulated behaviour
evaluation of the confidence interval of the estimations
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SIMULATION TECHNIQUES
Conversational system Identical to the previously studied by analytical
techniques
Influence of the memory management by a multiprogramming factor
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SIMULATION TECHNIQUES
Conversational system
D isk 1
D isk 2
D isk 3
D isk 4
C P U
T e rm in a ls
M e m o rym a n a g e m e n t
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SIMULATION TECHNIQUESConversational system
1 /DECLARE/ QUEUE CPU,DISC(4),MEM,SMEM,TERMINAL,R(2);
2 REAL PROF1(4)=(2.,3.5,4.5,5.);
3 REAL PROF2(4)=(1.5,3.5,6.5,10.);
4 REAL TR1,TR2;
5 REAL D;
6 CLASS C1,C2;
7 INTEGER I,N,M;
8 REF CUSTOMER C;
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SIMULATION TECHNIQUESConversational system
9 /STATION/ NAME=CPU;
10 SCHED=PS;
11 SERVICE(C1)=BEGIN
12 CST(8.52);
13 D := UNIFORM(0., 6.);
14 FOR I := 1 STEP 1 UNTIL 4 DO
15 IF D <= PROF1(I) THEN TRANSIT(DISC(I));
16 C:=R(1).FIRST;
17 WHILE C.FATHER <> CUSTOMER DO C:=C.NEXT;
18 TRANSIT(C,OUT);
19 V(SMEM);
20 IF D <= 5.6 THEN TRANSIT(TERMINAL,C1)
21 ELSE TRANSIT(TERMINAL,C2);
22 END;
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SIMULATION TECHNIQUESConversational system 23 SERVICE(C2)=BEGIN 24 CST(12.); 25 D := UNIFORM(0., 11.); 26 FOR I := 1 STEP 1 UNTIL 4 DO 27 IF D <= PROF2(I) THEN TRANSIT(DISC(I)); 28 C:=R(2).FIRST; 29 WHILE C.FATHER <> CUSTOMER DO C:=C.NEXT; 30 TRANSIT(C,OUT); 31 V(SMEM); 32 IF D <= 10.6 THEN TRANSIT(TERMINAL,C1) 33 ELSE TRANSIT(TERMINAL,C2); 34 END; 35 /STATION/ NAME=DISC; 36 TRANSIT=CPU; 37 /STATION/ NAME=DISC(1); 38 SERVICE=EXP(23.); 39 /STATION/ NAME=DISC(2); 40 SERVICE=EXP(22.);
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SIMULATION TECHNIQUES
Conversational system
41 /STATION/ NAME=DISC(3);
42 SERVICE=EXP(21.);
43 /STATION/ NAME=DISC(4);
44 SERVICE=EXP(20.);
45 /STATION/ NAME=MEM;
46 SERVICE=BEGIN
47 P(SMEM);
48 TRANSIT(CPU);
49 END;
50 /STATION/ NAME=SMEM;
51 TYPE=SEMAPHORE,MULTIPLE(M);
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SIMULATION TECHNIQUESConversational system 52 /STATION/ NAME=TERMINAL; 53 TYPE=INFINITE; 54 INIT(C1)=6*N/10; 55 INIT(C2)=4*N/10; 56 SERVICE(C1)=BEGIN 57 EXP(30000.); 58 TRANSIT(NEW(CUSTOMER),R(1),C1); 59 END; 60 SERVICE(C2)=BEGIN 61 EXP(60000.); 62 TRANSIT(NEW(CUSTOMER),R(2),C2); 63 END; 64 TRANSIT=MEM; 65 /CONTROL/ TMAX=5000000.; 66 CLASS=ALL QUEUE; 67 ACCURACY=ALL QUEUE,ALL CLASS; 68 OPTION=NRESULT;
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SIMULATION TECHNIQUESConversational system 69 /EXEC/ BEGIN 70 FOR N:=150 STEP 150 UNTIL 750 DO 71 FOR M:=1 STEP 1 UNTIL 20 DO 72 BEGIN 73 PRINT(" "); 74 PRINT("NUMERO DE USUARIOS =",N); 75 PRINT("FACTOR DE MULTIPROGRAMACION =",M); 76 SIMUL; 77 PRINT("TIEMPO DE RESPUESTA DE LA CLASE C1 =",MRESPONS ==> E(R(1))," +/-"),CRESPONSE(R(1)); 78 PRINT("TIEMPO DE RESPUESTA DE LA CLASE C2 =",MRESPONS ==> E(R(2))," +/-",CRESPONSE(R(2))); 79 PRINT("PRODUCTIVIDAD C1 =",MTHRUPUT(TERMINAL,C1)); 80 PRINT("PRODUCTIVIDAD C2 =",MTHRUPUT(TERMINAL,C2)); 81 PRINT("PRODUCTIVIDAD TOTAL =",MTHRUPUT(TERMINAL)); 82 END; 83 END;
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SIMULATION TECHNIQUESConversational system NUMERO DE USUARIOS = 150 FACTOR DE MULTIPROGRAMACION = 1 TIEMPO DE RESPUESTA DE LA CLASE C1 = 1203. +/- 132.0 TIEMPO DE RESPUESTA DE LA CLASE C2 = 1368. +/- 145.4 PRODUCTIVIDAD C1 = 0.2059E-02 PRODUCTIVIDAD C2 = 0.1356E-02 PRODUCTIVIDAD TOTAL = 0.3415E-02
NUMERO DE USUARIOS = 150 FACTOR DE MULTIPROGRAMACION = 2 TIEMPO DE RESPUESTA DE LA CLASE C1 = 292.9 +/- 14.44 TIEMPO DE RESPUESTA DE LA CLASE C2 = 499.6 +/- 23.42 PRODUCTIVIDAD C1 = 0.2131E-02 PRODUCTIVIDAD C2 = 0.1380E-02 PRODUCTIVIDAD TOTAL = 0.3511E-02
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SIMULATION TECHNIQUES
Communication network Identical to the previously studied by analytical
techniques
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SIMULATION TECHNIQUESCommunication network 1 /DECLARE/ QUEUE INTEGER J; 2 QUEUE GEN,LINIA(8,8),R(4,4); 3 INTEGER DIREC(8,4)=(0,2,2,2, 4 1,4,4,8, 5 4,0,4,4, 6 2,3,6,8, 7 6,6,0,6, 8 8,4,5,8, 9 8,8,8,0, 10 2,4,6,7); 11 12 REAL TRAB,TRAC,TRAD,TRBA,TRBC,TRBD,TRCA,TRCB,TRCD,TR ==> DA,TRDB,TRDC; 13 INTEGER OD(4,4) = ( 0, 60,140,240, 14 315,315,365,390, 15 470,590,590,630, 16 730,880,930,930); 17 INTEGER INIC(4) = (1, 3, 5, 7);
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SIMULATION TECHNIQUESCommunication network 18 INTEGER I,K; 19 CUSTOMER INTEGER ORIG,DESTI; 20 REF CUSTOMER C; 21 /EXEC/ FOR I := 1 STEP 1 UNTIL 8 DO FOR K := 1 STEP 1 UNTIL ==> 8 DO 22 LINIA(I,K).J := K; 23 /STATION/ NAME = GEN; 24 TYPE = SOURCE; 25 SERVICE = BEGIN 26 EXP(60000./930.); 27 I:= RINT(1,930); 28 ORIG := 1; 29 DESTI := 1; 30 WHILE (I > OD(ORIG,DESTI)) DO 31 IF DESTI < 4 THEN DESTI := DESTI + 1 32 ELSE 33 BEGIN 34 ORIG := ORIG + 1; 35 DESTI := 1; 36 END; 37 C := NEW(CUSTOMER); 38 TRANSIT(C,R(ORIG,DESTI)); 39 TRANSIT(LINIA(INIC(ORIG),DIREC(INIC(ORIG ==> ),DESTI))); 40 END;
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SIMULATION TECHNIQUES
Communication network 42 /STATION/ NAME = LINIA; 43 SERVICE = BEGIN 44 EXP(256.*8./64.); 45 I:=DIREC(J,DESTI); 46 IF I=0 THEN 47 BEGIN 48 C := R(ORIG,DESTI).FIRST; 49 WHILE C <> SON DO C := C.NEXT; 50 TRANSIT(C,OUT); 51 TRANSIT (OUT); 52 END; 53 TRANSIT (LINIA(J,I)); 54 END; 55 56 /CONTROL/ TMAX= 300000; 57 ACCURACY= ALL QUEUE;
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SIMULATION TECHNIQUES
Communication network 59 /EXEC/ BEGIN 60 PRINT; 61 SIMUL; 62 TRAB:=MRESPONSE(LINIA(1,2))+MRESPONSE(LINIA(2,4))+ 63 MRESPONSE(LINIA(4,3)); 64 TRAC:=MRESPONSE(LINIA(1,2))+MRESPONSE(LINIA(2,4))+ 65 MRESPONSE(LINIA(4,6))+MRESPONSE(LINIA(6,5)); 66 TRAD:=MRESPONSE(LINIA(1,2))+MRESPONSE(LINIA(2,8))+ 67 MRESPONSE(LINIA(8,7)); 68 TRBA:=MRESPONSE(LINIA(3,4))+MRESPONSE(LINIA(4,2))+ 69 MRESPONSE(LINIA(2,1)); 70 TRBC:=MRESPONSE(LINIA(3,4))+MRESPONSE(LINIA(4,6))+ 71 MRESPONSE(LINIA(6,5)); 72 TRBD:=MRESPONSE(LINIA(3,4))+MRESPONSE(LINIA(4,8))+ 73 MRESPONSE(LINIA(8,7)); 74 TRCA:=MRESPONSE(LINIA(5,6))+MRESPONSE(LINIA(6,8))+ 75 MRESPONSE(LINIA(8,2))+MRESPONSE(LINIA(2,1));
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SIMULATION TECHNIQUES
Communication network 76 TRCD:=MRESPONSE(LINIA(5,6))+MRESPONSE(LINIA(6,8))+ 77 MRESPONSE(LINIA(8,7)); 78 TRCB:=MRESPONSE(LINIA(5,6))+MRESPONSE(LINIA(6,4))+ 79 MRESPONSE(LINIA(4,3)); 80 TRDA:=MRESPONSE(LINIA(7,8))+MRESPONSE(LINIA(8,2))+ 81 MRESPONSE(LINIA(2,1)); 82 TRDB:=MRESPONSE(LINIA(7,8))+MRESPONSE(LINIA(8,4))+ 83 MRESPONSE(LINIA(4,3)); 84 TRDC:=MRESPONSE(LINIA(7,8))+MRESPONSE(LINIA(8,6))+ 85 MRESPONSE(LINIA(6,5)); 86 PRINT(TRAB,TRAC,TRAD); 87 PRINT(TRBA,TRBC,TRBD); 88 PRINT(TRCA,TRCB,TRCD); 89 PRINT(TRDA,TRDB,TRDC); 90 END;
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SIMULATION TECHNIQUES
Communication network ***SIMULATION WITH SPECTRAL METHOD ***
.. TIME = 300000.00 , NB SAMPLES = 512 , CONF. LEVEL = 0.95 ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * SERV NB * ******************************************************************* * * * * * * * * GEN * 64.03 * 1.000 * 1.000 * 64.03 * 4684* * +/- * 1.829 *0.0000E+00*0.0000E+00* 1.829 * * * * * * * * * * LINIA 2 * 30.88 *0.1246 *0.1477 * 36.61 * 1210* * +/- * 2.017 *0.1055E-01*0.1607E-01* 3.188 * * * * * * * * * * LINIA 9 * 31.34 *0.1347 *0.1531 * 35.63 * 1289* * +/- * 1.999 *0.1170E-01*0.1384E-01* 2.597 * * * * * * * * * * LINIA 12 * 31.07 *0.7519E-01*0.8277E-01* 34.20 * 726* * +/- * 2.504 *0.7059E-02*0.1367E-01* 3.444 * * * * * * * * *
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SIMULATION TECHNIQUES
Communication network ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * SERV NB * ******************************************************************* * LINIA 16 * 34.91 *0.5632E-01*0.6102E-01* 37.82 * 484* * +/- * 4.215 *0.9778E-02*0.1091E-01* 5.125 * * * * * * * * * * LINIA 20 * 32.59 *0.7801E-01*0.8174E-01* 34.15 * 718* * +/- * 2.378 *0.7146E-02*0.8014E-02* 2.579 * * * * * * * * * * LINIA 26 * 34.57 *0.4171E-01*0.4353E-01* 36.08 * 362* * +/- * 3.707 *0.6404E-02*0.6778E-02* 4.122 * * * * * * * * * * LINIA 27 * 32.92 *0.1857 *0.2277 * 40.37 * 1691* * +/- * 1.851 *0.1625E-01*0.2106E-01* 3.039 * * * * * * * * * * LINIA 30 * 35.30 *0.7448E-01*0.8044E-01* 38.12 * 633* * +/- * 3.819 *0.9264E-02*0.1115E-01* 4.429 * *
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SIMULATION TECHNIQUESCommunication network ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * SERV NB * ******************************************************************* * LINIA 32 * 28.69 *0.1243E-01*0.1243E-01* 28.69 * 130* * +/- * 4.742 *0.2918E-02*0.2918E-02* 4.742 * * * * * * * * * * LINIA 38 * 30.73 *0.1345 *0.1547 * 35.35 * 1313* * +/- * 1.734 *0.1065E-01*0.1591E-01* 2.745 * * * * * * * * * * LINIA 44 * 32.35 *0.6922E-01*0.7420E-01* 34.68 * 642* * +/- * 2.659 *0.8011E-02*0.9049E-02* 3.228 * * * * * * * * * * LINIA 45 * 31.92 *0.9321E-01*0.1024 * 35.07 * 876* * +/- * 2.950 *0.8071E-02*0.1099E-01* 3.485 * * * * * * * * * * LINIA 48 * 29.55 *0.6609E-01*0.6892E-01* 30.81 * 671* * +/- * 2.910 *0.6452E-02*0.6856E-02* 2.968 * * * * * * * * *
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SIMULATION TECHNIQUESCommunication network ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * SERV NB * ******************************************************************* * LINIA 56 * 32.19 *0.1548 *0.1929 * 40.11 * 1443* * +/- * 2.196 *0.1281E-01*0.2053E-01* 3.851 * * * * * * * * * * LINIA 58 * 32.63 *0.1008 *0.1104 * 35.71 * 927* * +/- * 2.415 *0.9855E-02*0.1273E-01* 3.771 * * * * * * * * * * LINIA 60 * 33.53 *0.8171E-01*0.8924E-01* 36.62 * 731* * +/- * 2.046 *0.8194E-02*0.9643E-02* 3.040 * * * * * * * * * * LINIA 62 * 35.31 *0.2860E-01*0.2887E-01* 35.64 * 243* * +/- * 5.058 *0.5594E-02*0.5755E-02* 5.120 * * * * * * * * * * LINIA 63 * 34.11 *0.9402E-01*0.1019 * 36.97 * 827* * +/- * 2.188 *0.8583E-02*0.9742E-02* 2.344 * *
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SIMULATION TECHNIQUESCommunication network ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * SERV NB * ******************************************************************* * R 2 *0.0000E+00*0.0000E+00*0.1180 * 110.9 * 319* * +/- *0.0000E+00*0.0000E+00*0.3193E-01* 9.902 * * * * * * * * * * R 3 *0.0000E+00*0.0000E+00*0.1920 * 141.5 * 407* * +/- *0.0000E+00*0.0000E+00*0.2514E-01* 14.12 * * * * * * * * * * R 4 *0.0000E+00*0.0000E+00*0.1836 * 113.8 * 484* * +/- *0.0000E+00*0.0000E+00*0.2303E-01* 8.691 * * * * * * * * * * R 5 *0.0000E+00*0.0000E+00*0.1280 * 106.1 * 362* * +/- *0.0000E+00*0.0000E+00*0.1609E-01* 7.103 * * * * * * * * * * R 7 *0.0000E+00*0.0000E+00*0.8297E-01* 110.1 * 226* * +/- *0.0000E+00*0.0000E+00*0.1289E-01* 9.790 * *
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SIMULATION TECHNIQUESCommunication network ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * SERV NB * ******************************************************************* * R 8 *0.0000E+00*0.0000E+00*0.4081E-01* 94.18 * 130* * +/- *0.0000E+00*0.0000E+00*0.7638E-02* 9.646 * * * * * * * * * * R 9 *0.0000E+00*0.0000E+00*0.2082 * 136.4 * 458* * +/- *0.0000E+00*0.0000E+00*0.2374E-01* 6.981 * * * * * * * * * * R 10 *0.0000E+00*0.0000E+00*0.2370 * 110.8 * 642* * +/- *0.0000E+00*0.0000E+00*0.2296E-01* 6.225 * * * * * * * * * * R 12 *0.0000E+00*0.0000E+00*0.7255E-01* 102.2 * 213* * +/- *0.0000E+00*0.0000E+00*0.7541E-02* 7.903 * * * * * * * * * * R 13 *0.0000E+00*0.0000E+00*0.1787 * 114.3 * 469* * +/- *0.0000E+00*0.0000E+00*0.2146E-01* 8.399 * *
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SIMULATION TECHNIQUESCommunication network ******************************************************************* * NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * SERV NB * ******************************************************************* * R 14 *0.0000E+00*0.0000E+00*0.2829 * 116.2 * 730* * +/- *0.0000E+00*0.0000E+00*0.3170E-01* 6.388 * * * * * * * * * * R 15 *0.0000E+00*0.0000E+00*0.8914E-01* 110.0 * 243* * +/- *0.0000E+00*0.0000E+00*0.1678E-01* 9.066 * * * * * * * * * ******************************************************************* ... END OF SIMULATION ... 111.2 144.0 111.4 105.9 107.3 99.80 137.5 110.4 103.1 111.4 117.1 110.8
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SIMULATION TECHNIQUES
Token ring network 8 nodes
Uniform traffic
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SIMULATION TECHNIQUES
Token ring network
1 /DECLARE/ QUEUE INTEGER N, M; 2 QUEUE NUS(8),ESP(8),S,R; 3 INTEGER I; 4 REAL TARR; 5 CUSTOMER REAL TSERV; 6 CUSTOMER INTEGER ORIGEN,DESTI; 7 REF CUSTOMER C,D; 8 FLAG SEM; 9 CLASS TOK,MIS; 10
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SIMULATION TECHNIQUES
Token ring network
11 /STATION/ NAME = S; 12 TYPE = SOURCE; 13 SERVICE = BEGIN 14 EXP(TARR); 15 ORIGEN := RINT(1,8); 16 DESTI := RINT(1,7); 17 IF DESTI >= ORIGEN THEN DESTI := DESTI + 1; 18 TSERV := EXP(800.); & microsegons 19 C := NEW(CUSTOMER); 20 TRANSIT(C,R,MIS); 21 TRANSIT(ESP(ORIGEN),MIS); 22 END; 23
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SIMULATION TECHNIQUES
Token ring network
24 /STATION/ NAME = NUS; 25 TYPE = MULTIPLE(2); 26 SERVICE(TOK) = BEGIN 27 WHILE ESP(N).NB > 0 DO 28 BEGIN 29 D := ESP(N).FIRST; 30 CST(D.TSERV); 31 TRANSIT(D,NUS(M)); 32 UNSET(SEM); 33 WAIT(SEM); 34 END; 35 CST(20); & microsegons 36 TRANSIT(NUS(M)); 37 END;
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SIMULATION TECHNIQUESToken ring network
38 SERVICE(MIS) = BEGIN 39 IF N = ORIGEN THEN 40 BEGIN 41 SET(SEM); 42 TRANSIT(OUT); 43 END; 44 IF N = DESTI THEN 45 BEGIN 46 C := R.FIRST; 47 WHILE SON <> C DO C := C.NEXT; 48 TRANSIT(C,OUT); 49 END; 50 CST(1.6); & microsegons 51 TRANSIT(NUS(M)); 52 END; 53 54 /STATION/ NAME = NUS(1); 55 INIT(TOK) = 1;
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SIMULATION TECHNIQUESToken ring network 57 /CONTROL/ TMAX = 10000000; CLASS = ALL QUEUE; 58 ACCURACY = ALL QUEUE, ALL CLASS; 59 60 /EXEC/ BEGIN 61 FOR I := 1 STEP 1 UNTIL 8 DO 62 BEGIN 63 NUS(I).N := I; 64 ESP(I).N := I; 65 NUS(I).M := I + 1; 66 END; 67 NUS(8).M := 1; 68 FOR TARR := 100000, 10000, 1000, 800 DO 69 BEGIN 70 PRINT; 71 PRINT ("TEMPS ENTRE ARRIBADES ",TARR,"MICROSEG"); 72 SIMUL; 73 END; 74 END;
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SIMULATION TECHNIQUESToken ring network TEMPS ENTRE ARRIBADES 0.1000E+06MICROSEG
***SIMULATION WITH SPECTRAL METHOD ***... TIME = 10000000.00 , NB SAMPLES = 512 , CONF. LEVEL = 0.95******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * SERV NB ********************************************************************* NUS 1 * 20.11 *0.6248E-01*0.1250 * 20.11 * 62141** +/- *0.1347 *0.3563E-03*0.7126E-03*0.1347 * **(TOK )* 20.14 *0.6247E-01*0.1249 * 20.14 * 62038** +/- *0.1349 *0.3569E-03*0.7137E-03*0.1349 * **(MIS )* 1.398 *0.7199E-05*0.1440E-04* 1.398 * 103** +/- *-1.000 *0.1365E-05*0.2730E-05*-1.000 * *
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SIMULATION TECHNIQUESToken ring network* NUS 2 * 20.07 *0.6237E-01*0.1247 * 20.07 * 62140** +/- *0.8790E-01*0.3143E-03*0.6286E-03*0.8790E-01* **(TOK )* 20.10 *0.6236E-01*0.1247 * 20.10 * 62037** +/- *0.8881E-01*0.3151E-03*0.6302E-03*0.8881E-01* **(MIS )* 1.382 *0.7119E-05*0.1424E-04* 1.382 * 103** +/- *-1.000 *0.1691E-05*0.3381E-05*-1.000 * ** NUS 3 * 20.09 *0.6242E-01*0.1248 * 20.09 * 62140** +/- *0.7185E-01*0.2305E-03*0.4610E-03*0.7185E-01* **(TOK )* 20.12 *0.6241E-01*0.1248 * 20.12 * 62037** +/- *0.7276E-01*0.2315E-03*0.4629E-03*0.7276E-01* **(MIS )* 1.351 *0.6959E-05*0.1392E-04* 1.351 * 103** +/- *-1.000 *0.1862E-05*0.3724E-05*-1.000 * ** NUS 4 * 20.08 *0.6239E-01*0.1248 * 20.08 * 62140** +/- *0.1148 *0.3504E-03*0.7009E-03*0.1148 * **(TOK )* 20.11 *0.6238E-01*0.1248 * 20.11 * 62037** +/- *0.1140 *0.3514E-03*0.7028E-03*0.1140 * **(MIS )* 1.522 *0.7839E-05*0.1568E-04* 1.522 * 103** +/- *-1.000 *0.1646E-05*0.3292E-05*-1.000 * *
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SIMULATION TECHNIQUESToken ring network* NUS 5 * 20.19 *0.6274E-01*0.1255 * 20.19 * 62140** +/- *0.1325 *0.3989E-03*0.7978E-03*0.1325 * **(TOK )* 20.22 *0.6273E-01*0.1255 * 20.22 * 62037** +/- *0.1470 *0.3994E-03*0.7988E-03*0.1470 * **(MIS )* 1.382 *0.7119E-05*0.1424E-04* 1.382 * 103** +/- *-1.000 *0.1337E-05*0.2674E-05*-1.000 * ** NUS 6 * 20.11 *0.6249E-01*0.1250 * 20.11 * 62140** +/- *0.1433 *0.4475E-03*0.8951E-03*0.1433 * **(TOK )* 20.14 *0.6248E-01*0.1250 * 20.14 * 62037** +/- *0.1429 *0.4480E-03*0.8960E-03*0.1429 * **(MIS )* 1.398 *0.7199E-05*0.1440E-04* 1.398 * 103** +/- *-1.000 *0.1526E-05*0.3053E-05*-1.000 * ** NUS 7 * 20.11 *0.6249E-01*0.1250 * 20.11 * 62140** +/- *0.1094 *0.3093E-03*0.6186E-03*0.1094 * **(TOK )* 20.15 *0.6249E-01*0.1250 * 20.15 * 62037** +/- *0.9936E-01*0.3094E-03*0.6187E-03*0.9936E-01* **(MIS )* 1.398 *0.7199E-05*0.1440E-04* 1.398 * 103** +/- *-1.000 *0.1483E-05*0.2966E-05*-1.000 * *
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SIMULATION TECHNIQUESToken ring network* NUS 8 * 20.17 *0.6268E-01*0.1254 * 20.17 * 62140** +/- *0.1637 *0.4324E-03*0.8647E-03*0.1637 * **(TOK )* 20.20 *0.6267E-01*0.1253 * 20.20 * 62037** +/- *0.1642 *0.4327E-03*0.8654E-03*0.1642 * **(MIS )* 1.367 *0.7039E-05*0.1408E-04* 1.367 * 103** +/- *-1.000 *0.1334E-05*0.2667E-05*-1.000 * ** ESP 1 *0.0000E+00*0.0000E+00*0.9553E-03* 734.8 * 13** +/- *-1.000 *0.0000E+00*0.8521E-03*-1.000 * **(MIS )*0.0000E+00*0.0000E+00*0.9553E-03* 734.8 * 13** +/- *-1.000 *0.0000E+00*0.8521E-03*-1.000 * ** ESP 2 *0.0000E+00*0.0000E+00*0.7404E-03* 528.8 * 14** +/- *-1.000 *0.0000E+00*0.6695E-03*-1.000 * **(MIS )*0.0000E+00*0.0000E+00*0.7404E-03* 528.8 * 14** +/- *-1.000 *0.0000E+00*0.6695E-03*-1.000 * ** ESP 3 *0.0000E+00*0.0000E+00*0.8659E-03* 541.2 * 16** +/- *-1.000 *0.0000E+00*0.4874E-03*-1.000 * **(MIS )*0.0000E+00*0.0000E+00*0.8659E-03* 541.2 * 16** +/- *-1.000 *0.0000E+00*0.4874E-03*-1.000 * *
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SIMULATION TECHNIQUES
Token ring network* ESP 4 *0.0000E+00*0.0000E+00*0.7169E-03* 1434. * 5** +/- *-1.000 *0.0000E+00*0.6916E-03*-1.000 * **(MIS )*0.0000E+00*0.0000E+00*0.7169E-03* 1434. * 5** +/- *-1.000 *0.0000E+00*0.6916E-03*-1.000 * ** ESP 5 *0.0000E+00*0.0000E+00*0.1484E-02* 1060. * 14** +/- *-1.000 *0.0000E+00*0.9771E-03*-1.000 * **(MIS )*0.0000E+00*0.0000E+00*0.1484E-02* 1060. * 14** +/- *-1.000 *0.0000E+00*0.9771E-03*-1.000 * ** ESP 6 *0.0000E+00*0.0000E+00*0.9811E-03* 754.7 * 13** +/- *-1.000 *0.0000E+00*0.9433E-03*-1.000 * **(MIS )*0.0000E+00*0.0000E+00*0.9811E-03* 754.7 * 13** +/- *-1.000 *0.0000E+00*0.9433E-03*-1.000 * ** ESP 7 *0.0000E+00*0.0000E+00*0.9871E-03* 759.3 * 13** +/- *-1.000 *0.0000E+00*0.6366E-03*-1.000 * **(MIS )*0.0000E+00*0.0000E+00*0.9871E-03* 759.3 * 13** +/- *-1.000 *0.0000E+00*0.6366E-03*-1.000 * *
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SIMULATION TECHNIQUESToken ring network* ESP 8 *0.0000E+00*0.0000E+00*0.1368E-02* 912.0 * 15** +/- *-1.000 *0.0000E+00*0.1041E-02*-1.000 * **(MIS )*0.0000E+00*0.0000E+00*0.1368E-02* 912.0 * 15** +/- *-1.000 *0.0000E+00*0.1041E-02*-1.000 * ** S *0.9609E+05* 1.000 * 1.000 *0.9609E+05* 103** +/- *-1.000 *0.0000E+00*0.0000E+00*-1.000 * ** * * * * * ** R *0.0000E+00*0.0000E+00*0.8148E-02* 791.0 * 103** +/- *-1.000 *0.0000E+00*0.2265E-02*-1.000 * **(MIS )*0.0000E+00*0.0000E+00*0.8148E-02* 791.0 * 103** +/- *-1.000 *0.0000E+00*0.2265E-02*-1.000 * ** * * * * * ********************************************************************... END OF SIMULATION ...
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SIMULATION TECHNIQUESToken ring network TEMPS ENTRE ARRIBADES 0.1000E+05MICROSEG
***SIMULATION WITH SPECTRAL METHOD ***... TIME = 10000000.00 , NB SAMPLES = 512 , CONF. LEVEL = 0.95******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * SERV NB ********************************************************************* NUS 1 * 21.31 *0.6245E-01*0.1249 * 21.31 * 58612** +/- *0.4077 *0.1228E-02*0.2456E-02*0.4077 * **(TOK )* 21.66 *0.6238E-01*0.1248 * 21.66 * 57608** +/- *0.4775 *0.1230E-02*0.2460E-02*0.4775 * **(MIS )* 1.402 *0.7039E-04*0.1408E-03* 1.402 * 1004** +/- *0.3061E-01*0.5425E-05*0.1085E-04*0.3061E-01* *
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SIMULATION TECHNIQUESToken ring network* NUS 2 * 21.70 *0.6360E-01*0.1272 * 21.70 * 58612** +/- *0.5427 *0.1433E-02*0.2866E-02*0.5427 * **(TOK )* 22.06 *0.6353E-01*0.1271 * 22.06 * 57608** +/- *0.5847 *0.1434E-02*0.2868E-02*0.5847 * **(MIS )* 1.381 *0.6935E-04*0.1387E-03* 1.381 * 1004** +/- *0.4022E-01*0.4872E-05*0.9745E-05*0.4022E-01* ** NUS 3 * 21.54 *0.6314E-01*0.1263 * 21.54 * 58612** +/- *0.5847 *0.1705E-02*0.3410E-02*0.5847 * **(TOK )* 21.90 *0.6307E-01*0.1261 * 21.90 * 57608** +/- *0.5530 *0.1706E-02*0.3412E-02*0.5530 * **(MIS )* 1.393 *0.6991E-04*0.1398E-03* 1.393 * 1004** +/- *0.3717E-01*0.4980E-05*0.9959E-05*0.3717E-01* ** NUS 4 * 21.30 *0.6241E-01*0.1248 * 21.30 * 58611** +/- *0.4710 *0.1174E-02*0.2348E-02*0.4710 * **(TOK )* 21.64 *0.6234E-01*0.1247 * 21.64 * 57607** +/- *0.4629 *0.1175E-02*0.2349E-02*0.4629 * **(MIS )* 1.399 *0.7023E-04*0.1405E-03* 1.399 * 1004** +/- *0.3573E-01*0.4258E-05*0.8516E-05*0.3573E-01* *
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SIMULATION TECHNIQUESToken ring network* NUS 5 * 21.02 *0.6161E-01*0.1232 * 21.02 * 58611** +/- *0.4159 *0.9359E-03*0.1872E-02*0.4159 * **(TOK )* 21.37 *0.6154E-01*0.1231 * 21.37 * 57607** +/- *0.4241 *0.9370E-03*0.1874E-02*0.4241 * **(MIS )* 1.415 *0.7103E-04*0.1421E-03* 1.415 * 1004** +/- *0.3856E-01*0.7813E-05*0.1563E-04*0.3856E-01* ** NUS 6 * 21.06 *0.6171E-01*0.1234 * 21.06 * 58611** +/- *0.4502 *0.1248E-02*0.2497E-02*0.4502 * **(TOK )* 21.40 *0.6164E-01*0.1233 * 21.40 * 57607** +/- *0.4786 *0.1249E-02*0.2499E-02*0.4786 * **(MIS )* 1.413 *0.7095E-04*0.1419E-03* 1.413 * 1004** +/- *0.3104E-01*0.4489E-05*0.8978E-05*0.3104E-01* ** NUS 7 * 21.39 *0.6269E-01*0.1254 * 21.39 * 58611** +/- *0.4933 *0.1266E-02*0.2532E-02*0.4933 * **(TOK )* 21.74 *0.6262E-01*0.1252 * 21.74 * 57607** +/- *0.3923 *0.1268E-02*0.2537E-02*0.3923 * **(MIS )* 1.410 *0.7079E-04*0.1416E-03* 1.410 * 1004** +/- *0.3545E-01*0.7663E-05*0.1533E-04*0.3545E-01* *
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LANC 2007. San José, Costa Rica. October 2007.258
SIMULATION TECHNIQUESToken ring network* NUS 8 * 21.48 *0.6294E-01*0.1259 * 21.48 * 58611** +/- *0.6782 *0.1235E-02*0.2471E-02*0.6782 * **(TOK )* 21.83 *0.6287E-01*0.1257 * 21.83 * 57607** +/- *0.7549 *0.1235E-02*0.2470E-02*0.7549 * **(MIS )* 1.385 *0.6951E-04*0.1390E-03* 1.385 * 1004** +/- *0.3685E-01*0.4594E-05*0.9188E-05*0.3685E-01* ** ESP 1 *0.0000E+00*0.0000E+00*0.1149E-01* 926.7 * 124** +/- *-1.000 *0.0000E+00*0.3546E-02*-1.000 * **(MIS )*0.0000E+00*0.0000E+00*0.1149E-01* 926.7 * 124** +/- *-1.000 *0.0000E+00*0.3546E-02*-1.000 * ** ESP 2 *0.0000E+00*0.0000E+00*0.1344E-01* 980.8 * 137** +/- *0.0000E+00*0.0000E+00*0.3167E-02* 125.4 * **(MIS )*0.0000E+00*0.0000E+00*0.1344E-01* 980.8 * 137** +/- *0.0000E+00*0.0000E+00*0.3167E-02* 125.4 * ** ESP 3 *0.0000E+00*0.0000E+00*0.1317E-01* 1013. * 130** +/- *0.0000E+00*0.0000E+00*0.3675E-02* 180.5 * **(MIS )*0.0000E+00*0.0000E+00*0.1317E-01* 1013. * 130** +/- *0.0000E+00*0.0000E+00*0.3675E-02* 180.5 * *
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LANC 2007. San José, Costa Rica. October 2007.259
SIMULATION TECHNIQUES
Token ring network* ESP 4 *0.0000E+00*0.0000E+00*0.1155E-01* 916.4 * 126** +/- *-1.000 *0.0000E+00*0.3341E-02*-1.000 * **(MIS )*0.0000E+00*0.0000E+00*0.1155E-01* 916.4 * 126** +/- *-1.000 *0.0000E+00*0.3341E-02*-1.000 * ** ESP 5 *0.0000E+00*0.0000E+00*0.1060E-01* 914.1 * 116** +/- *-1.000 *0.0000E+00*0.3776E-02*-1.000 * **(MIS )*0.0000E+00*0.0000E+00*0.1060E-01* 914.1 * 116** +/- *-1.000 *0.0000E+00*0.3776E-02*-1.000 * ** ESP 6 *0.0000E+00*0.0000E+00*0.9766E-02* 834.7 * 117** +/- *-1.000 *0.0000E+00*0.2652E-02*-1.000 * **(MIS )*0.0000E+00*0.0000E+00*0.9766E-02* 834.7 * 117** +/- *-1.000 *0.0000E+00*0.2652E-02*-1.000 * ** ESP 7 *0.0000E+00*0.0000E+00*0.1208E-01* 1015. * 119** +/- *-1.000 *0.0000E+00*0.3174E-02*-1.000 * **(MIS )*0.0000E+00*0.0000E+00*0.1208E-01* 1015. * 119** +/- *-1.000 *0.0000E+00*0.3174E-02*-1.000 * *
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LANC 2007. San José, Costa Rica. October 2007.260
SIMULATION TECHNIQUESToken ring network* ESP 8 *0.0000E+00*0.0000E+00*0.1295E-01* 959.5 * 135** +/- *0.0000E+00*0.0000E+00*0.3163E-02* 200.6 * **(MIS )*0.0000E+00*0.0000E+00*0.1295E-01* 959.5 * 135** +/- *0.0000E+00*0.0000E+00*0.3163E-02* 200.6 * ** S * 9958. * 1.000 * 1.000 * 9958. * 1004** +/- * 670.0 *0.0000E+00*0.0000E+00* 670.0 * ** * * * * * ** R *0.0000E+00*0.0000E+00*0.9552E-01* 951.4 * 1004** +/- *0.0000E+00*0.0000E+00*0.9458E-02* 75.77 * **(MIS )*0.0000E+00*0.0000E+00*0.9552E-01* 951.4 * 1004** +/- *0.0000E+00*0.0000E+00*0.9458E-02* 75.77 * ** * * * * * ********************************************************************... END OF SIMULATION ...
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SIMULATION TECHNIQUESToken ring network TEMPS ENTRE ARRIBADES 1000. MICROSEG
***SIMULATION WITH SPECTRAL METHOD ***... TIME = 10000000.00 , NB SAMPLES = 512 , CONF. LEVEL = 0.95******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * SERV NB ********************************************************************* * * * * * ** NUS 1 * 61.63 *0.6358E-01*0.1272 * 61.63 * 20631** +/- * 6.193 *0.3718E-02*0.7435E-02* 6.193 * **(TOK )* 119.1 *0.6288E-01*0.1258 * 119.1 * 10562** +/- * 20.65 *0.3716E-02*0.7433E-02* 20.65 * **(MIS )* 1.390 *0.6999E-03*0.1400E-02* 1.390 * 10069** +/- *0.9350E-02*0.1776E-04*0.3552E-04*0.9350E-02* *
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SIMULATION TECHNIQUESToken ring network* NUS 2 * 63.39 *0.6539E-01*0.1308 * 63.39 * 20631** +/- * 4.534 *0.3894E-02*0.7787E-02* 4.534 * **(TOK )* 122.5 *0.6468E-01*0.1294 * 122.5 * 10562** +/- * 16.47 *0.3904E-02*0.7809E-02* 16.47 * **(MIS )* 1.396 *0.7026E-03*0.1405E-02* 1.396 * 10069** +/- *0.1102E-01*0.2228E-04*0.4456E-04*0.1102E-01* ** NUS 3 * 62.98 *0.6497E-01*0.1299 * 62.98 * 20631** +/- * 5.727 *0.3575E-02*0.7150E-02* 5.727 * **(TOK )* 121.7 *0.6427E-01*0.1285 * 121.7 * 10562** +/- * 29.96 *0.3579E-02*0.7158E-02* 29.96 * **(MIS )* 1.389 *0.6994E-03*0.1399E-02* 1.389 * 10069** +/- *0.9545E-02*0.1971E-04*0.3942E-04*0.9545E-02* ** NUS 4 * 60.30 *0.6220E-01*0.1244 * 60.30 * 20631** +/- * 5.706 *0.4437E-02*0.8874E-02* 5.706 * **(TOK )* 116.4 *0.6149E-01*0.1230 * 116.4 * 10562** +/- * 19.09 *0.4432E-02*0.8865E-02* 19.09 * **(MIS )* 1.409 *0.7095E-03*0.1419E-02* 1.409 * 10069** +/- *0.1115E-01*0.2008E-04*0.4017E-04*0.1115E-01* *
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SIMULATION TECHNIQUESToken ring network* NUS 5 * 60.82 *0.6274E-01*0.1255 * 60.82 * 20631** +/- * 7.048 *0.4138E-02*0.8275E-02* 7.048 * **(TOK )* 117.5 *0.6203E-01*0.1241 * 117.5 * 10562** +/- * 19.66 *0.4143E-02*0.8285E-02* 19.66 * **(MIS )* 1.404 *0.7069E-03*0.1414E-02* 1.404 * 10069** +/- *0.1153E-01*0.1863E-04*0.3726E-04*0.1153E-01* ** NUS 6 * 58.71 *0.6056E-01*0.1211 * 58.71 * 20631** +/- * 6.512 *0.4101E-02*0.8203E-02* 6.512 * **(TOK )* 113.3 *0.5985E-01*0.1197 * 113.3 * 10562** +/- * 30.61 *0.4105E-02*0.8210E-02* 30.61 * **(MIS )* 1.411 *0.7102E-03*0.1420E-02* 1.411 * 10069** +/- *0.1168E-01*0.2026E-04*0.4051E-04*0.1168E-01* ** NUS 7 * 57.14 *0.5913E-01*0.1183 * 57.14 * 20630** +/- * 6.698 *0.3162E-02*0.6325E-02* 6.698 * **(TOK )* 110.3 *0.5842E-01*0.1168 * 110.3 * 10561** +/- * 18.34 *0.3164E-02*0.6328E-02* 18.34 * **(MIS )* 1.409 *0.7096E-03*0.1419E-02* 1.409 * 10069** +/- *0.9951E-02*0.2002E-04*0.4005E-04*0.9951E-02* *
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SIMULATION TECHNIQUESToken ring network* NUS 8 * 65.03 *0.6708E-01*0.1342 * 65.03 * 20630** +/- * 6.675 *0.3661E-02*0.7321E-02* 6.675 * **(TOK )* 125.7 *0.6638E-01*0.1328 * 125.7 * 10561** +/- * 32.18 *0.3660E-02*0.7320E-02* 32.18 * **(MIS )* 1.390 *0.6998E-03*0.1400E-02* 1.390 * 10069** +/- *0.1438E-01*0.1897E-04*0.3795E-04*0.1438E-01* ** ESP 1 *0.0000E+00*0.0000E+00*0.7598 * 5756. * 1319** +/- *0.0000E+00*0.0000E+00*0.1753 * 1254. * **(MIS )*0.0000E+00*0.0000E+00*0.7598 * 5756. * 1319** +/- *0.0000E+00*0.0000E+00*0.1753 * 1254. * ** ESP 2 *0.0000E+00*0.0000E+00*0.7163 * 5564. * 1285** +/- *0.0000E+00*0.0000E+00*0.1420 * 1172. * **(MIS )*0.0000E+00*0.0000E+00*0.7163 * 5564. * 1285** +/- *0.0000E+00*0.0000E+00*0.1420 * 1172. * ** ESP 3 *0.0000E+00*0.0000E+00*0.7218 * 5436. * 1325** +/- *0.0000E+00*0.0000E+00*0.1340 * 1028. * **(MIS )*0.0000E+00*0.0000E+00*0.7218 * 5436. * 1325** +/- *0.0000E+00*0.0000E+00*0.1340 * 1028. * *
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SIMULATION TECHNIQUES
Token ring network* ESP 4 *0.0000E+00*0.0000E+00*0.6485 * 5402. * 1199** +/- *0.0000E+00*0.0000E+00*0.1442 * 1177. * **(MIS )*0.0000E+00*0.0000E+00*0.6485 * 5402. * 1199** +/- *0.0000E+00*0.0000E+00*0.1442 * 1177. * ** ESP 5 *0.0000E+00*0.0000E+00*0.7021 * 5699. * 1232** +/- *0.0000E+00*0.0000E+00*0.1777 * 1054. * **(MIS )*0.0000E+00*0.0000E+00*0.7021 * 5699. * 1232** +/- *0.0000E+00*0.0000E+00*0.1777 * 1054. * ** ESP 6 *0.0000E+00*0.0000E+00*0.6706 * 5635. * 1190** +/- *0.0000E+00*0.0000E+00*0.1593 * 1203. * **(MIS )*0.0000E+00*0.0000E+00*0.6706 * 5635. * 1190** +/- *0.0000E+00*0.0000E+00*0.1593 * 1203. * ** ESP 7 *0.0000E+00*0.0000E+00*0.6491 * 5413. * 1198** +/- *0.0000E+00*0.0000E+00*0.1391 * 1111. * **(MIS )*0.0000E+00*0.0000E+00*0.6491 * 5413. * 1198** +/- *0.0000E+00*0.0000E+00*0.1391 * 1111. * *
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LANC 2007. San José, Costa Rica. October 2007.266
SIMULATION TECHNIQUESToken ring network* ESP 8 *0.0000E+00*0.0000E+00*0.6883 * 5200. * 1321** +/- *0.0000E+00*0.0000E+00*0.1291 * 907.1 * **(MIS )*0.0000E+00*0.0000E+00*0.6883 * 5200. * 1321** +/- *0.0000E+00*0.0000E+00*0.1291 * 907.1 * ** S * 992.0 * 1.000 * 1.000 * 992.0 * 10079** +/- * 23.59 *0.0000E+00*0.0000E+00* 23.59 * ** * * * * * ** R *0.0000E+00*0.0000E+00* 5.561 * 5517. * 10069** +/- *0.0000E+00*0.0000E+00* 1.161 * 1063. * **(MIS )*0.0000E+00*0.0000E+00* 5.561 * 5517. * 10069** +/- *0.0000E+00*0.0000E+00* 1.161 * 1063. * ** * * * * * ********************************************************************... END OF SIMULATION ...
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SIMULATION TECHNIQUESToken ring network TEMPS ENTRE ARRIBADES 800.0 MICROSEG
***SIMULATION WITH SPECTRAL METHOD ***... TIME = 10000000.00 , NB SAMPLES = 512 , CONF. LEVEL = 0.95******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * SERV NB ********************************************************************* NUS 1 * 109.5 *0.6738E-01*0.1348 * 109.5 * 12306** +/- * 6.905 *0.3586E-02*0.7173E-02* 6.905 * **(TOK )*0.2511E+05*0.6653E-01*0.1331 *0.2511E+05* 53** +/- *-1.000 *0.3590E-02*0.7179E-02*-1.000 * **(MIS )* 1.388 *0.8504E-03*0.1701E-02* 1.388 * 12253** +/- *0.6208E-02*0.9743E-05*0.1949E-04*0.6208E-02* *
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SIMULATION TECHNIQUESToken ring network* NUS 2 * 101.4 *0.6239E-01*0.1248 * 101.4 * 12306** +/- * 5.621 *0.2796E-02*0.5592E-02* 5.621 * **(TOK )*0.2322E+05*0.6154E-01*0.1231 *0.2322E+05* 53** +/- *-1.000 *0.2801E-02*0.5602E-02*-1.000 * **(MIS )* 1.401 *0.8583E-03*0.1717E-02* 1.401 * 12253** +/- *0.6746E-02*0.1243E-04*0.2486E-04*0.6746E-02* ** NUS 3 * 96.70 *0.5950E-01*0.1190 * 96.70 * 12306** +/- * 5.425 *0.3074E-02*0.6148E-02* 5.425 * **(TOK )*0.2213E+05*0.5864E-01*0.1173 *0.2213E+05* 53** +/- *-1.000 *0.3074E-02*0.6148E-02*-1.000 * **(MIS )* 1.409 *0.8635E-03*0.1727E-02* 1.409 * 12253** +/- *0.6752E-02*0.1281E-04*0.2563E-04*0.6752E-02* ** NUS 4 * 102.6 *0.6311E-01*0.1262 * 102.6 * 12306** +/- * 5.116 *0.2576E-02*0.5152E-02* 5.116 * **(TOK )*0.2349E+05*0.6225E-01*0.1245 *0.2349E+05* 53** +/- *-1.000 *0.2576E-02*0.5152E-02*-1.000 * **(MIS )* 1.407 *0.8622E-03*0.1724E-02* 1.407 * 12253** +/- *0.6784E-02*0.1131E-04*0.2261E-04*0.6784E-02* *
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SIMULATION TECHNIQUESToken ring network* NUS 5 * 107.5 *0.6615E-01*0.1323 * 107.5 * 12306** +/- * 3.395 *0.1742E-02*0.3485E-02* 3.395 * **(TOK )*0.2464E+05*0.6529E-01*0.1306 *0.2464E+05* 53** +/- *-1.000 *0.1747E-02*0.3494E-02*-1.000 * **(MIS )* 1.399 *0.8573E-03*0.1715E-02* 1.399 * 12253** +/- *0.5035E-02*0.1366E-04*0.2733E-04*0.5035E-02* ** NUS 6 * 97.64 *0.6008E-01*0.1202 * 97.64 * 12306** +/- * 3.719 *0.3193E-02*0.6385E-02* 3.719 * **(TOK )*0.2235E+05*0.5922E-01*0.1184 *0.2235E+05* 53** +/- *-1.000 *0.3198E-02*0.6396E-02*-1.000 * **(MIS )* 1.402 *0.8588E-03*0.1718E-02* 1.402 * 12253** +/- *0.6413E-02*0.1194E-04*0.2389E-04*0.6413E-02* ** NUS 7 * 104.8 *0.6473E-01*0.1295 * 104.8 * 12305** +/- * 4.550 *0.3379E-02*0.6758E-02* 4.550 * **(TOK )*0.2446E+05*0.6387E-01*0.1277 *0.2446E+05* 52** +/- *-1.000 *0.3384E-02*0.6769E-02*-1.000 * **(MIS )* 1.396 *0.8553E-03*0.1711E-02* 1.396 * 12253** +/- *0.4878E-02*0.1412E-04*0.2824E-04*0.4878E-02* *
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SIMULATION TECHNIQUESToken ring network* NUS 8 * 103.2 *0.6352E-01*0.1270 * 103.2 * 12305** +/- * 4.519 *0.2117E-02*0.4234E-02* 4.519 * **(TOK )*0.2410E+05*0.6266E-01*0.1253 *0.2410E+05* 52** +/- *-1.000 *0.2115E-02*0.4230E-02*-1.000 * **(MIS )* 1.396 *0.8551E-03*0.1710E-02* 1.396 * 12253** +/- *0.5278E-02*0.1169E-04*0.2338E-04*0.5278E-02* ** ESP 1 *0.0000E+00*0.0000E+00* 20.89 *0.1285E+06* 1622** +/- *0.0000E+00*0.0000E+00* 2.330 *0.1118E+05* **(MIS )*0.0000E+00*0.0000E+00* 20.89 *0.1285E+06* 1622** +/- *0.0000E+00*0.0000E+00* 2.330 *0.1118E+05* ** ESP 2 *0.0000E+00*0.0000E+00* 19.79 *0.1297E+06* 1523** +/- *0.0000E+00*0.0000E+00* 2.213 *0.1044E+05* **(MIS )*0.0000E+00*0.0000E+00* 19.79 *0.1297E+06* 1523** +/- *0.0000E+00*0.0000E+00* 2.213 *0.1044E+05* ** ESP 3 *0.0000E+00*0.0000E+00* 18.60 *0.1274E+06* 1458** +/- *0.0000E+00*0.0000E+00* 1.609 *0.1332E+05* **(MIS )*0.0000E+00*0.0000E+00* 18.60 *0.1274E+06* 1458** +/- *0.0000E+00*0.0000E+00* 1.609 *0.1332E+05* *
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SIMULATION TECHNIQUES
Token ring network* ESP 4 *0.0000E+00*0.0000E+00* 18.17 *0.1232E+06* 1474** +/- *0.0000E+00*0.0000E+00* 1.572 *0.1280E+05* **(MIS )*0.0000E+00*0.0000E+00* 18.17 *0.1232E+06* 1474** +/- *0.0000E+00*0.0000E+00* 1.572 *0.1280E+05* ** ESP 5 *0.0000E+00*0.0000E+00* 19.04 *0.1240E+06* 1535** +/- *0.0000E+00*0.0000E+00* 2.000 *0.1414E+05* **(MIS )*0.0000E+00*0.0000E+00* 19.04 *0.1240E+06* 1535** +/- *0.0000E+00*0.0000E+00* 2.000 *0.1414E+05* ** ESP 6 *0.0000E+00*0.0000E+00* 19.32 *0.1273E+06* 1517** +/- *0.0000E+00*0.0000E+00* 2.245 *0.1378E+05* **(MIS )*0.0000E+00*0.0000E+00* 19.32 *0.1273E+06* 1517** +/- *0.0000E+00*0.0000E+00* 2.245 *0.1378E+05* ** ESP 7 *0.0000E+00*0.0000E+00* 20.31 *0.1297E+06* 1561** +/- *0.0000E+00*0.0000E+00* 1.996 *0.1299E+05* **(MIS )*0.0000E+00*0.0000E+00* 20.31 *0.1297E+06* 1561** +/- *0.0000E+00*0.0000E+00* 1.996 *0.1299E+05* *
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SIMULATION TECHNIQUESToken ring network* ESP 8 *0.0000E+00*0.0000E+00* 19.63 *0.1249E+06* 1563** +/- *0.0000E+00*0.0000E+00* 1.951 *0.1021E+05* **(MIS )*0.0000E+00*0.0000E+00* 19.63 *0.1249E+06* 1563** +/- *0.0000E+00*0.0000E+00* 1.951 *0.1021E+05* ** S * 811.1 * 1.000 * 1.000 * 811.1 * 12328** +/- * 14.66 *0.0000E+00*0.0000E+00* 14.66 * ** * * * * * ** R *0.0000E+00*0.0000E+00* 155.7 *0.1269E+06* 12253** +/- *0.0000E+00*0.0000E+00* 24.78 *0.2250E+05* **(MIS )*0.0000E+00*0.0000E+00* 155.7 *0.1269E+06* 12253** +/- *0.0000E+00*0.0000E+00* 24.78 *0.2250E+05* ** * * * * * ********************************************************************... END OF SIMULATION ...
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SIMULATION TECHNIQUES
Ethernet network 8 nodes
Uniform traffic
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SIMULATION TECHNIQUES
Ethernet network
1 /DECLARE/ QUEUE S, EST(8), BUS, R, SF; 2 CUSTOMER INTEGER I; 3 CUSTOMER REAL TSERV, TESP; 4 REAL TARR, SERV, ESP, TEMPS, TPROP, TEMPSC; 5 REF CUSTOMER C,D; 6 LABEL L; 7 FLAG FL, BL; 8 INTEGER CONF = 0; 9
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SIMULATION TECHNIQUES
Ethernet network
1 /DECLARE/ QUEUE S, EST(8), BUS, R, SF; 2 CUSTOMER INTEGER I; 3 CUSTOMER REAL TSERV, TESP; 4 REAL TARR, SERV, ESP, TEMPS, TPROP, TEMPSC; 5 REF CUSTOMER C,D; 6 LABEL L; 7 FLAG FL, BL; 8 INTEGER CONF = 0; 9
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SIMULATION TECHNIQUES
Ethernet network
10 /STATION/ NAME = S; 11 TYPE = SOURCE; 12 SERVICE = BEGIN 13 EXP(TARR); 14 I := RINT(1,8); 15 TSERV := EXP(SERV); 16 IF TSERV < 3.*TPROP THEN TSERV := 3.*TPROP; 17 C := NEW(CUSTOMER); 18 TRANSIT(C,R); 19 TRANSIT(EST(I)); 20 END; 21
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SIMULATION TECHNIQUES
Ethernet network
22 /STATION/ NAME = EST; 23 SERVICE = BEGIN 24 L: IF BUS.NB = 0 THEN 25 BEGIN 26 C := NEW(CUSTOMER); 27 C.TSERV := TSERV; 28 UNSET(FL); 29 UNSET(BL); 30 TEMPS := TIME + TPROP; 31 TRANSIT(C, BUS); 32 WAIT(FL);
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SIMULATION TECHNIQUES
Ethernet network
33 IF CONF = 0 THEN 34 BEGIN 35 SET(BL); 36 TRANSIT(OUT); 37 END; 38 SET(BL); 39 CONF := 0; 40 TESP := EXP(ESP); 41 IF TESP<2.*TPROP THEN TESP := 2. * TPROP; 42 CST(TESP); 43 GOTO L; 44 END;
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SIMULATION TECHNIQUES
Ethernet network
45 IF (TIME < TEMPS) AND (CONF = 0) THEN 46 BEGIN 47 CONF := 1; 48 D := BUS.FIRST; 49 TEMPSC := TEMPS - TIME; 50 CST(TEMPSC); 51 TRANSIT(D, OUT); 52 SET(FL); 53 TESP := EXP(ESP); 54 IF TESP<2.*TPROP THEN TESP := 2. * TPROP; 55 CST(TESP); 56 GOTO L; 57 END;
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SIMULATION TECHNIQUES
Ethernet network
58 IF (TIME < TEMPS) AND (CONF = 1) THEN 59 BEGIN 60 TESP := EXP(ESP); 61 IF TESP<2.*TPROP THEN TESP := 2. * TPROP; 62 CST(TESP); 63 GOTO L; 64 END; 65 WAIT(BL); 66 GOTO L; 67 END; 68
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SIMULATION TECHNIQUES
Ethernet network
69 /STATION/ NAME = BUS; 70 SERVICE = BEGIN 71 CST(TSERV + 2.*TPROP); 72 C := R.FIRST; 73 WHILE C.FATHER <> FATHER DO C := C.NEXT; 74 TRANSIT(C, OUT); 75 SET(FL); 76 TRANSIT(OUT); 77 END; 78
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SIMULATION TECHNIQUES
Ethernet network 79 /STATION/ NAME = SF; 80 INIT = 1; 81 SERVICE = BEGIN 82 SET(FL); 83 SET(BL); 84 TRANSIT(OUT); 85 END; 86 87 /CONTROL/ TMAX = 100000.; ACCURACY = ALL QUEUE; 88 89 /EXEC/ BEGIN 90 TPROP := 0.01; 91 SERV := 0.8; 92 ESP := 0.1; 93 TEMPS := -TPROP; 94 FOR TARR := 5, 2.5, 1.25 DO SIMUL; 95 END;
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SIMULATION TECHNIQUESEthernet network ***SIMULATION WITH SPECTRAL METHOD ***
... TIME = 100000.00 , NB SAMPLES = 512 , CONF. LEVEL = 0.95
*******************************************************************
* NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * SERV NB *
*******************************************************************
* S * 5.073 * 1.000 * 1.000 * 5.073 * 19713*
* +/- *0.7027E-01*0.0000E+00*0.0000E+00*0.7027E-01* *
* EST 1 *0.9595 *0.2390E-01*0.2459E-01*0.9873 * 2491*
* +/- *0.4293E-01*0.1102E-02*0.1180E-02*0.5266E-01* *
* EST 2 *0.9714 *0.2364E-01*0.2425E-01*0.9966 * 2433*
* +/- *0.3115E-01*0.1343E-02*0.1491E-02*0.3891E-01* *
* EST 3 *0.9993 *0.2534E-01*0.2609E-01* 1.029 * 2536*
* +/- *0.4504E-01*0.1101E-02*0.1159E-02*0.4904E-01* *
* EST 4 *0.9660 *0.2350E-01*0.2407E-01*0.9892 * 2433*
* +/- *0.4483E-01*0.1456E-02*0.1518E-02*0.7335E-01* *
* EST 5 *0.9709 *0.2321E-01*0.2356E-01*0.9856 * 2390*
* +/- *0.4695E-01*0.1439E-02*0.1497E-02*0.4730E-01* *
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SIMULATION TECHNIQUES
Ethernet network
* EST 6 *0.9677 *0.2312E-01*0.2366E-01*0.9905 * 2389*
* +/- *0.3450E-01*0.9612E-03*0.1328E-02*0.4168E-01* ** EST 7 *0.9455 *0.2308E-01*0.2367E-01*0.9696 * 2441** +/- *0.3795E-01*0.1200E-02*0.1322E-02*0.3643E-01* ** EST 8 *0.9635 *0.2505E-01*0.2576E-01*0.9906 * 2600** +/- *0.3988E-01*0.1589E-02*0.1727E-02*0.4196E-01* ** BUS *0.7994 *0.1624 *0.1624 *0.7994 * 20314** +/- *0.9631E-02*0.2830E-02*0.2830E-02*0.9631E-02* ** R *0.0000E+00*0.0000E+00*0.1956 *0.9924 * 19713** +/- *0.0000E+00*0.0000E+00*0.5210E-02*0.2011E-01* ********************************************************************... END OF SIMULATION ...
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SIMULATION TECHNIQUESEthernet network ***SIMULATION WITH SPECTRAL METHOD ***... TIME = 100000.00 , NB SAMPLES = 512 , CONF. LEVEL = 0.95******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * SERV NB ********************************************************************* S * 2.523 * 1.000 * 1.000 * 2.523 * 39639** +/- *0.3238E-01*0.0000E+00*0.0000E+00*0.3238E-01* ** EST 1 * 1.190 *0.6058E-01*0.6443E-01* 1.266 * 5091** +/- *0.3643E-01*0.1890E-02*0.2066E-02*0.4254E-01* ** EST 2 * 1.189 *0.5951E-01*0.6372E-01* 1.274 * 5003** +/- *0.3580E-01*0.4234E-02*0.3192E-02*0.4344E-01* ** EST 3 * 1.174 *0.5754E-01*0.6086E-01* 1.242 * 4901** +/- *0.4252E-01*0.2450E-02*0.2627E-02*0.4427E-01* ** EST 4 * 1.191 *0.5883E-01*0.6312E-01* 1.278 * 4937** +/- *0.3555E-01*0.2305E-02*0.2675E-02*0.4592E-01* ** EST 5 * 1.198 *0.5927E-01*0.6323E-01* 1.278 * 4949** +/- *0.4266E-01*0.2633E-02*0.2816E-02*0.4674E-01* *
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SIMULATION TECHNIQUES
Ethernet network
* EST 6 * 1.185 *0.5835E-01*0.6266E-01* 1.272 * 4926** +/- *0.3425E-01*0.2123E-02*0.2498E-02*0.4209E-01* ** EST 7 * 1.181 *0.5895E-01*0.6315E-01* 1.265 * 4993** +/- *0.3740E-01*0.2661E-02*0.3207E-02*0.5317E-01* ** EST 8 * 1.182 *0.5717E-01*0.6104E-01* 1.262 * 4837** +/- *0.3262E-01*0.2484E-02*0.3251E-02*0.4343E-01* ** BUS *0.7520 *0.3316 *0.3316 *0.7520 * 44091** +/- *0.1085E-01*0.4436E-02*0.4436E-02*0.1085E-01* ** R *0.0000E+00*0.0000E+00*0.5022 * 1.267 * 39637** +/- *0.0000E+00*0.0000E+00*0.1750E-01*0.2458E-01* ********************************************************************... END OF SIMULATION ...
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SIMULATION TECHNIQUESEthernet network ***SIMULATION WITH SPECTRAL METHOD ***... TIME = 100000.00 , NB SAMPLES = 512 , CONF. LEVEL = 0.95******************************************************************** NAME * SERVICE * BUSY PCT * CUST NB * RESPONSE * SERV NB ********************************************************************* S * 1.257 * 1.000 * 1.000 * 1.257 * 79568** +/- *0.9795E-02*0.0000E+00*0.0000E+00*0.9795E-02* ** EST 1 * 2.045 *0.2052 *0.2709 * 2.699 * 10034** +/- *0.5773E-01*0.8730E-02*0.1612E-01*0.1282 * ** EST 2 * 2.020 *0.2039 *0.2667 * 2.642 * 10096** +/- *0.7101E-01*0.8998E-02*0.1768E-01*0.1390 * ** EST 3 * 2.011 *0.1991 *0.2592 * 2.617 * 9904** +/- *0.6745E-01*0.8805E-02*0.1469E-01*0.1115 * ** EST 4 * 2.028 *0.2000 *0.2602 * 2.637 * 9864** +/- *0.5786E-01*0.6761E-02*0.1179E-01*0.1073 * ** EST 5 * 2.001 *0.2017 *0.2622 * 2.601 * 10079** +/- *0.6415E-01*0.6065E-02*0.1510E-01*0.1624 * *
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SIMULATION TECHNIQUES
Ethernet network
* EST 6 * 2.035 *0.1993 *0.2610 * 2.664 * 9797** +/- *0.7039E-01*0.8648E-02*0.1688E-01*0.1333 * ** EST 7 * 2.021 *0.2007 *0.2594 * 2.611 * 9934** +/- *0.6259E-01*0.7496E-02*0.1742E-01*0.2369 * ** EST 8 * 2.014 *0.1985 *0.2571 * 2.608 * 9858** +/- *0.7488E-01*0.7814E-02*0.1403E-01*0.1413 * ** BUS *0.5523 *0.6622 *0.6622 *0.5523 * 119899** +/- *0.5897E-02*0.7369E-02*0.7369E-02*0.5897E-02* ** R *0.0000E+00*0.0000E+00* 2.096 * 2.635 * 79566** +/- *0.0000E+00*0.0000E+00*0.8279E-01*0.1023 * ********************************************************************... END OF SIMULATION ...