resource allocation and queuing theory -...

IntroductionResource Allocation

Resource Allocation and Queuing TheoryModeling

Joseph Spring

Modeling Networks

Joseph Spring Queuing Theory


Outline

1 IntroductionWhy are we waiting? . . .

2 Resource AllocationIssuesNetwork Models

Packet-Switched NetworkConnectionless FlowsService Model

TaxonomyRouter-Centric versus Host-CentricReservation Based versus Feedback-BasedWindow-Based versus Rate-BasedWindow-Based versus Rate-Based



Why are we waiting? . . .

Outline








Why are we waiting?Fundamentals

There are lots of examples for queuing situations:

Passport control

Supermarkets

Planes waiting to take off or land

Programs being processed by uniprocessor/multiprocessor

Packets at sending side of communication channel

Packets at receiving side of communication channel

Each of the above involves different states: waiting, beingprocessed, processed, together with transitions between eachof the states.





Waiting is a consequence of the randomness of the processingprocedure

arrival times - not known in advance

processing times - not known in advance

number of times we have to wait in a queue for either thesame or a different service - not known in advance

If these were known then we could schedule in advance andeliminate waiting altogether.

In order to model queuing scenarios

we employ stochastic processes reflecting the randomindeterminate nature of the particular situation beingstudied.




Why are we waiting?How many more times . . . ?

We explore operations of interest operating under randomprocesses in order to gain a better understanding of theoperations characteristics. We might ask

how long do we expect to wait prior to processing? -(customer question)

how long is a service likly to be idle? - (service question)

how can a reasonable balance be obtained between thetwo questions above?

We seek to identify those characteristics of a system that willallow us to measure the performance of a system.





In working with queues we need to acquaint ourselves with:AssumptionsActorsArrival and Service Times - (Modeled by StochasticProcesses)Service Discipline - (FIFO, FQ, LIFO, SIRO, Priorities)Design and Execution - (Single, Parallel, Series, Tandem,Network)Queue size - (finite, infinite)nature of Calling Source - (generates finite/infinite numberof customers)Customer and service behaviour - (processing speed afunction of length of queue; customer: jockeying, balking,reneging)



IssuesNetwork ModelsTaxonomy

Outline








Resource AllocationIssues

Resource Allocation and Congestion Control arelongstanding active areas of researchResource allocation partially implemented in

routers / switches in a networkthe transport protocol running on the end hosts

End systems use signalling protocols to indicate resourcerequirements to network nodes

Network nodes respond with information on resourceavailability





Definition

Resource Allocation is defined to be the process by whichnetwork elements try to meet the competing demands thatapplications have for network resources, by which we mean

Link bandwidth (BW)

Buffer space in routers / switches

Note:

it is not always possible to meet all of the demands placedon a resource

some users / applications may receive fewer resourcesthan they require





Throughout the following discussion

flow control will refer to practices that ensure a fast senderdoesn’t overpower a slow receiver

congestion control will refer to practices that ensure a setof senders do not send too much data into the network dueto a lack of resources at some point




Outline








Resource AllocationNetwork Models

Packet Switched NetworkMultiple links and switchespackets may encounter a bottleneck at some point in thenetwork in which, for example high speed links feed into alow speed link

Figure: A Potential Bottleneck Router




Resource AllocationNetwork Models

Figure: A Potential Bottleneck Router




Resource AllocationNetwork Models - Connectionless Flows

Assume network essentially connectionless anyconnection oriented service implemented in transportprotocol running on end hostsInternet model

Sequence of packets (datagram delivery service)TCP implements end to end connection abstraction

connection set up message traverses networkreserves a set of buffers for connection at routers (underutilisation of available resources since not available forgeneral use)

we focus on connectionless networks





What do we mean by connectionless?All datagrams are completely independent - Modeled byPoisson Distribution - car modelAlthough datagrams are switched independently usually thecase that stream of datagrams flow between a particularpair of hosts through a particular pair of hosts - train model

Definition

Model assumes a flow abstraction as a sequence of packetsbetween source and destination following the same routethrough the network

flows can be defined at different granularitiesHost to host (same source / destination addresses)process to process (same source / destination host / portpairs





Figure: Multiple flows passing through a set of routers





State information

for each flow kept at routers (soft state)

used to make resource allocation decisions regardingpackets that belong to the flow

Soft state

not always explicitly created and removed by signallinga middle ground between

purely connectionless network maintaining no state atrouterspurely connection oriented network maintaining hard stateat routers





Soft state

exists only for purpose of resource allocation

not essential for correct operation of network

however router better able to handle packets belonging toflow if soft state maintained for flow

does not imply relible and ordered delivery of a virtualcircuit




Resource AllocationNetwork Models - Service Model

In the Best Effort Service Model

each packet is treated in the same way

flows are given no guarantees

Defining a service that gives some form of guarantees

for example the bandwidth required for a video stream

is said to provide multiple qualities of service (QoS).Clearly a range of possibilities exist, regarding the optionsavailable here.




Outline








Resource AllocationTaxonomy - Router-Centric versus Host-Centric

Two broad groupsThose that address the problem of Resource allocationfrom within the network (routers / switches)Those that address the problem from the edges (end hosts)

Real issue is considered to be where does the mainburden resides




Resource AllocationTaxonomy - Router-Centric versus Host-Centric

Router-centriceach router takes responsibility for deciding when packetsare forwardedwhich packets are droppedinforming hosts generating traffic how many packets theyare allowed to send

Host-centricend hosts observe network conditions (how many packetsare getting through) and adjust accordingly

We note that these groups are not mutually exclusive, bothplay their part




Resource AllocationTaxonomy - Reservation Based versus Feedback-Based

Should we make Reservations or wait for Feedback?Reservation Based System

End hosts ask for network for a certain amount of capacityat time when flow establishedEach router allocates resources (buffers and/or % of linkbandwidth)If router cannot commit to requirements then requestdenied




Resource AllocationTaxonomy - Reservation Based versus Feedback-Based

Feedback Based SystemEnd hosts send data without recourse to networkEnd Hosts adjust sending rate subject to feedback

EXPLICIT feedback - Router sends message ’slow down’IMPLICIT feedback - end host adjusts sending rate subjectto network conditions e.g. packet loss

Reservation Based implies router centric resourceallocation since each router responsible for allocation andpolicing of its capacityExplicit Feedback-Based implies router centric basedmechanismImplicit Feedback-Based implies Host centric mechanism,routers ’silently drop packets when congested




Resource AllocationTaxonomy - Window-Based versus Rate-Based

Two general ways to express to the sender the amount ofdata that may be sent

Windows based transport protocol indicates the size ofwindow (amount of buffer space) available at the receiversendThis limits amount of data that sender can send - so a flowcontrol mechanisma similar mechanism window advertisement can be used toreserve buffer space - so a reource allocation mechanism(e.g. X.25)




Resource AllocationTaxonomy - Window-Based versus Rate-Based

Rate basedA Rate based transport protocol indicates the size ofindicates the amount of data that the receiver or network isable to absorbA rate based characterisation of flow is felt to be a logicalchoice in a reservation based system supporting differentqualities of serviceSender makes reservation for so many bits per second,each router on path determines if it can commit toreservation subject to current committments

See summary on page 464


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