SWITCHED NETKdORKS(U) NAVAL POSTGRADUATE SCHOOL MONTEREYCR H T SCHIRNTRRELLI SEP 83

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NAVAL POSTGRADUATE SCHOOLMonterey, California

DTICEECTE

,APR 17 1984

THESISMULTIPLE PATH STATIC ROUTING PROTOCOLS

FOR PACKET SWITCHED NETWORKS

by

Harry Thornberry Schiantarelli

Septebmer 1983

-J

CI hesis Advisor: J. M. WozencraftApproved for public release; distribution unlimited

84 04 16 130

GS~CONY CLASIICAYWN OF THIS 111"IE EWhm Due M8u _______________

REPOR DOCUIENTATMO PAGE REPFORZ COMPLETING FORM-1. NIEPWT2. OVY ACCER,I No MO. RECIPIENT'S CATALOG NUMBER

14. TITLE (aid 411111Me) S. TYPE OF REPORT & PERIOD COVEREDMultiple Path Static Routing Protocols Masterls Thesis:for Packet Switched Networks September 1983

V1 4. PERFORMING ORG. REPORT NUMUER

7. AITM@WJ 6. CONTRACT OR GRANT NUMBER(&)

Harry Thornberry Schiantarelli

9. 11111MFO110111 61MAKIZATION HANE AND A001111U 16. PROGRAM ELEMENT. PROjECT. TASKAREA A WORK UNIT N4U aERS

Naval Postgraduate School* Monterey, California 93943

I I- CONTROLLING OFFICE1 NAME AND ADDRESS 12. REPORT DATE

Naval Postgraduate School September 1983Monterey, California 93943 Is. NUM§60E rOPAGES

I-L NITRMI AGEICYNAM G 351I 11.3wef kn 3= 1adOtne-) IS. SECURITY CLASS. (of this eft)

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Approved for public release; distribution unlimited

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If. SUPPLIKIIENTARY OTEKS

Is. KEY W4OS (Cae e se me Of& ff ne.... OW IdwMFl 6F wle"k ..mbw)

Packet Switched Networks; Routing Protocols; Simulation;Statis Routing

20. LISTRACT (Cmfs NM aid* If nmmoee ad ldauly Ap Wleek aadee)

A central issue in the design of a packet switched comnmunica-tions network is the development of an efficient routing protocol,Es which determines the routes followed by the information as ittraverses the network. The performance of a static routingprotocol that allows for multiple path routing based on the useof routing fractions, is analyzed using computer simulation.Comparison is made between the performance of this protocol and

S/N 0 102- LL 0le 14601 1 SECURITY CLASSIFICATION Of' THIS PAGE (SIMM 36e-ertenrec

SiMON I @LAMCA,ON OF ?11111 PG (Obf "0 if bisu

that of a minimum number of hops routing protocol. Routingfractions calculated by two different methods are used andtheir relative performance analyzed. A comparative analysisis done of the performance of this protocol when usingvirtual circuit service and datagram service in the network.Provision is made to extend use of the simulation program toanalyze dynamic routing cases using routing fractions.

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Multi a. Path Static Rotinz Protocols~or Packet Switched Me works

byHarry Thrbr-LSchiant ralli

Luten nt Comm anar Paruv an NavyB.S., Naval TulecoumunictUor13 School, P-3ru,197s

Submitted in partial fulfillment of therequirements for the degrees of

RASTER or SaIncE IN TELECOMMUNICATIOSS SYSTEMS MANkGEIENT

and

RASZER Or SCIENCE IN ENGIEERING SCIENCE

from theNAVAL POSTGRADUATE SCHOOL

September 193

Author: ____-

* Approved by:__Thesis Advisor

Second Header

Chairman# Department 3f Administrative Science

Chaipm epovesfE 1041 4 crical Egineering

Dean of Info ir 4 J and Pallcy Sciences

DeA . fSciance and Engineering

3

&BSTRACT

K central issue in the design of a packet sw*tched

communications network Is the devalapment of an efficient*routing proto-ol, which letermines the routes followed by

the information as it traverses the network. The

performance of a static routing pcotocol that allows for

multiple path routing basad on the use of routinag fractions,is analyzed using computer simulation. Comparison i-s madebetween the performance of this protocol and that of aminimum number of hops routing protocol. Routing fractions

calculated by two different methols are used and theirrelative performance analyzed. A comparative analysis Isdone of the performance of this protocol when, using virt-+ualcircuit service and datagram sarvice in the network.

Provision is made to extend use of the simulation program to

analyze dynamic routing cases using routing fractions.

.4 4

TABLE OF CONTENTS

I. INTRODUCTION . . . . . . . . . .. . . . . . . .. 10

A. GENERAL a o o * a * o o * o e e e e . e o * . 10

B. COMBUNICATION NETWORKS. .. . ... .6. . 11

II. PACKET SWITCHED NETWORKS . . . . . . . . . . . . . 13

Ae GENERAL a o a o * a a o m o o a e . . o. . . . 13

B. DATAGRAM AND VIRTUAL-CIRCUIT SERVICES . . . . 16

C. NEZWORK LAYERS AND PROTO3OLS . . . . . . . . . 17

III. RO UTI Irv. .. . . .. . . 22

A . DEFINITION .......... • ....... 22

B. STATIC AND DYNARIC ROUT13 . . . . . . . . . . 24

C. DISTRIBUTED AND CENTRALIZED ROUTING . o . . . 27

D. FLOW CONTROL AND CONGESTI3N CONTROL o . . . . 30

E. ROUTING FRACTIONS ............. .. 36

F. LOOP AVOICANCE . . o . . . . . . . . . .. 39

IV. SIULATION OF A PACKET SWITCHED COMMUNICATIONS

NETWORK o e o o a a % e e . 9 . o o o o . o e o o 41

A. MODEL CHARACTERISTICS .. o . . . .. . . o 41

B. PARAMETERS OF THE PACKET SWITCHED NETWORK . o 45

C. COMPUTER LANGUAGE . . . .... . . . 49

D. SIMULATION PRORAN DESCRIPTION .. o . . .. . 50

E. SIMULATION OUTPUTS DESCRIPTION o o . .. . . . 58

1. INITIAL REPORT . .... . .. . . .. . 59

2. PERIOD REP3RT . . . . . . . . . . . .. 61

3. PERIOD DATA ............... 63

4. NETWORK REPORT . o o . .. . . . ... . . 6a

5. NETWORK DATA .R ... .. ........ 66

V. CONCLUSIONS AND RECO3MENDATIOLS . o o ... . .. 67

A. CONCLUSIONS .. .. . . . . . . . . . . .. 67

B. R0ECORBNDTIONS FOR FUTURE STUDY ....... 73

APPENDIX A: GENERATION OF GEOMETRICALLY DISTRIBUTED

NUMBER OF PACKETS . . . . . . . . . . . . . 75

APPENDIX B: LINK NAME ASSIGNMENT ............ 77

APPENDIX C: MINIMUM NMOBER OF HOPS SINGLE PATH

ROUTING TABLE ............... 79

APPENDIX D: 3RAPHIC REPRESENTATION OF DATA COLLECTED

DURING SIMULArION ......... .... 84

APPENDIX E: SIMULATION PROGRAM . . .......... 91

APPENDIX F: PROGRAM TO GRAPH GENERAL STATISTICS OF

THE SIMULATION RUN . . . . . * * .. .o. . 120

APPENDIX G: PROGRAM TO GRAPH PERIODICAL STATISTICS

OF THE SIMULATION RUN . . . . . . . . .. 129

LIST OF REFERENCES .... ......... . . ... 138

BIBLIOGRAPHY - • .• .... . ............ 141

INITIAL DISTRIBUTION LIST. .... .. .... ..... 142

6

, ? , g . ; .' ....". .-._",'-,.'.. --. '-' , ',...,",..., ,",' ., v , .. .., ...%, .-%.

.P~. .F JA "W - p-7-j. -'- . .7 '7 -.P -Y -

LIST 0F TABLES

I. GgivuLkRIT! CoKipARISON . . . . . . . . . . . . . . 68

II. PERFORMANCE CCNIP&RISON . . . . . . . .. .... 70

Ill. pERpoRgAycz COMPARIsON . e o e 73

7

LIST OF FIGURES

3.1 THROUGHPUT AND TRANSIT DELAY VERSUS OFFERED

LOAD .o. .. . ... .... . . 34

3.2 DELAY VERSUS OFFERED LOAD . . . . . . . . . .. 354.1 NETWORK rOPOLOGY . .. .. .. .. .. .. . .. 49

C.1 SINK-TREE FOR EXTERNAL VERrICES . . . . . . . . 80

C.2 SINK-rREE FOR INTERNAL VERTICES . . . . . . . . 81

C.3 SINK-TREE FOR CENTRAL NODE . . . . . . . . . . . 82

D.1 PKTS STILL IN NETWORK FOR R3UTING-FRACTION

PROTOCOL . .. .. . . . . . . . .. . . . . .. 85

D.2 PKTS. STILL IN NETWORK FOR MINIXUM-HOPS

PROT COL . . . . . . . . . . .e. . . .o. . . . 86

D.3 COMPARISON OF PACKETS STILL IN THE NETWORK . . . 87

D.4 COMPARISON OF MAXIMUM LINK USAGE FOR THE

NETWORK e a * e e e e . . . . . e . . . . .a. 88

D.5 COMPARISON OF AVERAGE QUEUE LENGTH FOR rHE

NETWORK . . . . . . . . . . .*. . . . .e. . . 89

D.6 COMPARISON OF AVG. DELAY FOR COMPLETING TRIP

PKTS .. 90

AC KNOWULEDGE SENT S

I wi.sh to express my thanks to Professor John 3.

Vozencraft for his guidance and patience throughout the

course of this thesis work. His broad knowledge on thq

subject of packet switched networks and of communications in

general made this effort a val.uable experience.

This work is dedicated to my wife Gabriela and my

daughter Gaby, whose constant supp:)rt and the atmosphere of

love they created made it al1, possible.

9.9

I. _.TRODUCZO

% A. GENERAL

In recent ys-ars wq have bs- - xpsr i-nc-na

tschnclogical conver genc.- o f compit: rs =nd

telecommunicaticns in such a way that : has bz=ccm .

difficult to s4parate what s p=ocessing and wa t S

communication. The constant imp rov mrnt i1 coaPu::rprocessing speed and storags capacity -cgether with +heirreduction in price and size, have dafinitivtely influencedthis change, making it increasingly attractive -c us .

programmable computers to control zzommunicaticn networks and

process the information transmitt d thzough them. This

allows the integration of traditional communications withcomputer networks and distributed systems, whi!.e using thesame m.ans of transmission, and thus represents a more

efficient use of the communication channels. Ihis situation

creates the necesity for the development of naw transmission

techniques thit can accomodate tha raquiremants of higher

data rates, as well as procedures to handle larger volumesof information.

A kind of network that is becoming incrasingly popular

is the Packet Switched network. Crucial to the design of

this kind of network is the development of efficient routing

procedures, which determine the routes followed by the

.aforma-ion as it traverses the network. The present studyrepresents further work in that direction and as such

involves ths analysis of a routing proc.durg that uses socalled Routing Fractions.

. . ae.1

B. COMMUNICATION N3TWOPKS

Thera are two basic types 3. communca-_oN. -. :'7c:k*' - ? architectures: Point to Pont and Broadcast. ..- :

point architectures the network normally cor--:t n=- I.i:',ischannels (we will call th-m links), waich may oz I" t

by a band of frequencies, cabl, o-.icT. -t, M - ,z

connecting a pair cf stations (w- will cn1 - .odzs) .

two nod as whc h are not ccn=-icz;ei by a I~ wv- ocommunicate, th=y must Jo so i -t v _ ce r - -

'3 intermediate cd=s. This char-=: 's- . al S

varisty 01 na-work - a n Ml

fsaturs wh.:-n trronnactll . is.: - ::each o ,- - , nv a2lcwinQ -h. ": o-- v3r-C-:'

routes in cass of link faiiu.s or u:gston s~u:--oiu.

In a point to point network, if the links s.lect.d forthe communication are used exclusiv-ly by ths twz nca s fr1the duration of the communication, the -echni~ui is callsi"line switching". In -his casa, both the nod.s an!interconnecting links must be fre.e. before th- info-ma, on

can start to be sent. A classlcal exampla of :h- use cf

this technique is the public talphaaa metwork wne.e all th--links between the caler and recip.ent cf th. -all wi- b_2held for their exclusive use, until th- snd of -hec.mmu. niatior. If one :r mcre of -- s links or the n1-1:?

called is busy, the call setup cannot be completed, and abusy tone is received at the calling node to indicate t-h

procedura must be restar-e.

If inst sad, the links can be shared )y two or mcr=K. communicaicn, and the information that is S-csivel a . inintermsdiate --ode may be stored thzre until -h requi_-:7-output link is fre ai then forwailed, th.6: ai d t e O a, - a. c n iq u s. "

called "store and forward". The aode ciller (scurce nods)does not have to wait for all the links involved in thi

,,..,. 11

0.%........................% -. '*. q *3 0* 3 ~ 3 3 ~ 3

communication, or the destination nds, to be free b-forestarting to send the information. tn most cases this allowsfor a more efficient use of resou:-es. Oth.= advantages of

point to point architectures iclude their ability to

support simultaneous transfer of information between

different stations in the network, and the use of high speedlinks to speel-up this transfer.

In broadcast archit-ect-ures, there is a sir.glecommuncation link shared by all noles, so that informationsent by any node is received by all other nodes. Satel11te

and Bus architectures are some examples of this type of

networks. Since there is only one path for all

communications, the total overall transfer rat e of

information is limited by the banivwith and speed (capacity)of that single channel, and its failure can cause complete

system failure. Another limitation of this architecture is

interference between stations requesting the use of the

channel, so that some kind of coaterBtion-resolving or

polling scheme must be used, maki.ng it more complex and less

efficient.

Broadcast architectures are used mainly in local area

networks (LAN). There the coimunication problem is

restricted to short distances and usually higher capacitylinks %1-10 megabits per second) are available. Examples ofthis kind of architecture are Ethernet from Xearox

Corporation, and Hyperbus from Network System Corporation.

In -his thesis we will concentcate on store-and-forward

nttworks and in particular on so called "Packet Switched"

networks.

12

,, --Ii i ~ i a ' ' -. . .. • , , r ., , , '., '..

-. xx. . -. ..---s 3 .3_ . 6T -7- -p.._

1. GBRUR&L

Perhaps the most popular kiai of store and forward

network today is the packet swltzhed network. In these

networks the communications, or messages, are subdividedinto fixed length parts called "Packets" (usually the packet

size is arouni 1000 bits). Packets are transmitted through

the network asing the best route selected by the routing

protocols (see Chapter I1), wich exists at the time thepacket is released into the network. Each packet traverses

the netwc-k intermixed with packets of other messages.

The main advantage of packet switched networks over line

switched networks is the conservation (reduction) ofswitching time. With line switching, a complete path of

communication must be set up between the source and

destinaticn node before the communication begins. Path setupis established through a signaling process. Before

transmission of a message, a reservation signal is sent

towards the destination. While traveling nods by node to the

destinaticn node, the signal reserves links along the path.

If at any intermediate node it caant find a free link, itwaits for a link to become free while holding the links it

has reserved so far. When a link becoms free it reserves it

and goes to the next node to repeat the same process. When

the signal reaches the desti.nation node, a path has beenreserved between source ant destination nodes. As shown by

Kermani and Kleinrock in (Ref. 1], as the input traffic

increases, a network using line switching saturates very

quickly and the message delay increases rapidly. This rapid

saturation is the result of the overhead imposed by the

13

switches to set the path, which are slow relative to the

duration of a message. Because of the reserva-ion

, operation, and the exclusive use of a path, line swi-tching

is not a good choice particularly if traffic load is high,

since it causes a substantial decrease in the networkcarrying capazity. Therefore, for communication networks

which have many nodes and require the exchange of large

number of messages, the principles used in packet switchednetworks can provide a bstter communica ion scheme.

Packet switched networks support apparent full

connectivity among the nodes by virtue of the store andforward nature of the system. Typically, packet switched

networks use fewer than (3N/2) bi-directional (duplex) links(where N is the number of nodes) , whereas a fully connectednetwork requires (N x (5-1)/2) duplex links. Packetswitched networks allow traffic to be concentrated on higher

speed or lower cost links, as raluired to reduce channel

costs and/or transmission delays. rhay also allow sendingtraffic through alternate routes and around failed orcongested links or nodes, increasiag channel utilization,

reducing trangMssion delay, and making the network morerobust and dependable.

Packet switched networks require that each node be ableto process certain information about the packet itself, and

about the network structure and status, in order to assign

the correct routing to the packet. Due to this requirement

and the further need for high speed processing to operateefficiently, each node in the network is implemented with a

programmable computer that controls its operation andregulates its participation in the network.

Packet switched networks allow for the transmission of

both data and digitized voice coamunications, but somespecial considerations must be taken when doing this.Delays in data communications ars not as critical as in

...

voice communications, and allow che storage an- fur-har

reassembly of the packets to recreate the original message

(as long as all the packets corresponding to a message

eventually arrive to the destination node). Nsvertheless,

bit errors or packet losses are intolerable for data

communications, and a procedure for error

detection/correction is required for proper operation. Incontrast, voice communications allow for s.me level of biterror and even packet loss, since the receiver (the human

brain) will in most cases interpolate and make up for the

errors. Actual experiments show that when the lost packets

constitute less than 1 of the offered voice traffic,

ccnfortable conversation can be maintained [Ref. 2]. On theother hand voice communications require near real-time

processing, and do not accept out of order packets, making

it necessary to implement some kind or priority scheme thatwill give precedence to voice packets over data packets, and

a routine procedure that will ensure the delivery of packets

in the same order they were generated. Speech packets must

meet a strict overall delay constr.aint of less than 200-500miliseccnds [Ref. 3] for comfortable conversations, this

makes it impractical to store the packets of a message in

the receiving node until the last one arrives and then toreorder them; it also ccnstrains the maximum number of linksthey can traverse. This constraint must be taken into

account, particularly when designing the network topology

and/or assigning link capacities, in order to ensure that:packet-time delay does not renter voice communications

useless.

15z . -

B. DATAGRAI AND VIRTUL-CIRCUIT SERVICES

There are two basic kinds of "service" that a packet

switched network can provide, in reference to the way it

delivers its packets: Datagram service,and Virtual Circuit

service. In datagra service the packes, which are

raferred to as "datagrams", are treated as inlependent

entities, that is, each packet of a message 4i routed anddelivered independently of the other packets of the same

message. There is no enforced relationship between the

order in which one node enters datagrams into tho networkand the order in which these same datagrams arrive at their

4: destination mode. The use of this scheme requires each

datagram to contain the whole inforzation necesary for itsrouting. Theref3re, each packet will typically contain in

its header the destination node, the message to which itbelongs, packet number, and any other information required

by the particular routing scheme implemented.By contrast, the virtual circuit is a sequenced se-vice,

that is, the order in which the packets are entered into the

network is the same order in which they arrive at their

destination node. This is guaranteed by requiring that allthe packets of a message follow the same route as the first

packet of that message. In this case each packet needs only

Sto carry in its header an identificaticm of the virtual

circuit to which it belongs, and the different nodes will

automatically route it thorough the links that correspond tothe virtual circuit.

A virtual circuit resembles the line switching technique* -. °

in the sense that all packets of a message traverses the

- same path, but differs from it in that more than ons virtualcircuit say simultaneously include the same link as part of

the route for its packets and thus share the use of that

link. Another important difference is that if a link or

16

., . .

node fails, the packet may be r.-uted through alternate

routes and communication is not lost as it would occur w4th

line switching.Each virtual circuit requires an explicit s.tup

procedure (gemerally done by the first packet of a message

or a "request-to-send" packet) whi.- establishes the route,

followed by a data transfer and an explicit shutdown

procedure. Once the "circuit" has been set, individual

packets do not have to carry their destination address,

since iz was specified during setup, allowing them to carry

more data. Packetized virtual circuits emerge as a

promising approach to pure voice pa-ket networks [Ref. 4].Virtual circuits appear to the ead users as if they were

dedicated lines; however, within the network many diff-.rent

virtual circuits share the same coimunication links. The

network modal that we chose for this study can be configuredto provide either virtual circuit or datagram service. This

characteristiz allows us to compare the behavior of the

routing algorithm for each case.*i Some examples of networks that provide these kind of

services are IBM's System Network Architecture (SNA), which

provides virtual circuit service, &ad DEC's Digital Network

Architecture (DNA), which provides datagram ssrvice.

C. NETWORK LAYBS AND PROTOCOLS

In order to simplify design complexity, most networks

are organized as a series of layers or levels, each one

built upon its predecesor. The purpose of each layer is to

offer certain services to the higher layers, shielding them

from the details of how the servi-es offered are actually

implemented. The rules and conventions that govern the

timing and forward of data exchange between layers are

called protocols, and the set of liyers and protocols are

17

% N~~S

called the network architecture. The basic aims of a network

architecture are that the network has its funstions cleerly

defined and applications and communications are separated.

At the same time, the applications interface to the network

must be as simple as possible.

There is no unique layered structure, but for this study

we will use the one adopted by the International Standards

Organization (ISO), which is a seven layer network model

called the "Reference fodel of Open Systems Interconnection"

also called 3SI [Ref. 5]. The alfferent layers cf this

model are:(1) Physical Layer

(2) Data Link Layer

(3) Network Layer

(4) Transport Layer(5) Session Layer(6) Presentation Layer

(7) pplication Layer

The Physizzal Layer deals with the actual transmission ofthe raw bits over the communication link. It is the set of

electrical or mechanical functions required to establish,

maintain and release physical conneations between the nodes

and transmisian circuits (links). Its main purpose is to

ensure that if a bit 1 was sent, the receiver gets a I and

not a 0. No consideration is tiken with the information

content of the bits, nor with charactsr or frame boundaries.

The Data Link Layer moves ase step away from thePhysical Layer, and its purpose is to present the networkwith an error free Zommunication link. This layer

establishes, maintains and releases a link connectionbetween two nodes. This involves the division of data into

frames, and the corresponding mc.hanisms to transmit themsequentially, detect any error in their transmission, and

process the azknowledgment sent bact by the receiver. Since

18

the Physical Layer merely transmits a strc.am of bits withcutregard to their meaning or structure, -- is up to khe data

link layer -o create and recognize fcame boundaries.

The next layer, the Network Layer, represents the main

concern of this thesis. It determines the mainA characteristics of the units of information, or packets, and

how they are exchanged and routed through the network. This

layer is also called the Communications Subnet layer, since

it receives messages from the origimator, divides them intopackets and ensures that they are correctly received attheir destination, and in the prop--r order. It masks allswitching and direction consideration from the higher lavel

layers. It is in this layer that the kind of service the

network will provide is determined (virtual circuit or

datagram), anI thus it contains the corresponding procedures

to handle it. Routing protocols are therefore the heart of

the network, and their effectiveness and efficiency will

affect the overall performance of the network, probably more

than any other protocol.The nex+ four layers, have to do with the way the

different processes in each node communicate betwsen them,

and with processes in other nodes (?ranspo-t and SessionLayer); and the interfaces with the actual users of the

system (Presentat'ion and kpplication Layer).

The transport layer, also known as the host-host layer,accepts data from the session layer, splits it into smaller

units if needed, passes these to the network layer, andensures that all the pieces arrive correctly at the other

end. It creates a distinct network connection for eachtransport connection required by the session layer, or may

multiplex several transport conaections onto the same

network connection, to reduce the cost. In all cases, thetransport layer makes these network connections transparentto the session layer. this layer is a true source to

19

destination or end-to-and layar, so a program on the scu.ce

node carries on a conversation w!th a similai program on thedestination node, usin; message headers and control

messages. In contrast, at lower layers the protcc,Ils are

carried out by each node and its immediate neighbors

(chained-layer).

The session layer represents the true ust.r interface tothe network. It establishes the logical connection

(session) between users or presentation-layer processes in

different nodes, and maintains and releases it at the users

request. To do this it converts naies to addresses, chqcks

for access permission, type of communicat.ion (half duplex orfull duplex), etc. It also provides connection services

such as recovery, diagnosis and statistics (mainly for

performance measurements and billinji . In some networks thesession and transport layers are merged into a single layer.

The presentation layer performs functions that are

requested sufficiently often by the users. It is then betterto have the system provide then as services, rather than

allow each user to perform them in its own way. These

services include any conversion of information that might beneeded as it is transferred between end users. Someexamples are data compaction, expansion, encryption, sending

4 and receiving formats, convertion of data types and data

representation, terminal handling and file transfer.

The application layer represents the highest level layer

in the network. Its contents usually depends on theindividual users, since they are the ultimate sources anddestinations of information passing through a network. The

application layer does not become directly involved incommunication functions, and thus the need for the end user

to know about internal communications procedures and

protocols of the network is eliainited. The presentation

layer represents the domain of the network users, while the

20

4

lover level layers represent the domain of the natwork

designers.

S21

A.- DEPIIITION

A central issue in the desiga of a Packet Switching

Network is the selection of the routing protocols which are

responsible for deciding the path to be followed by a packet

as it traverses the network. The basic concern of a routing

protocol is the efficiency of the iaformation transfer. Its

main goal is then to determine the optimal (best) routing

policy, i.e.,the set of routes over which packets have to be

transmitted, in order to optimize a well defined objective

function (like delay, cost, throu;hput, etc.). It asumesthat the integrity of this transfer is provided by othqr

protocols (error protectioan, duplicate detection, security,

etc).

In optimizing an objective faction, as for example

minimum-delay, we can use two different-criteria: retinizethe average system delay, or optimize the individual delay

for each source-to-destination traffic requirement.

Fortunately, most routing solutions obtained using these twoapproaches turn out to be similar (less than 1% difference),

especially for large networks with uniform requirements

[Ref. 6]. The system optimization approach, as we will see,is generally used in static routing problems, while theindividual or user optimization concept is most common in

1 h dynamic routing problems.

The degree of difficulty of the routing problem in anynetwork, is strongly influenced by the network topology. Ina star-connected network with full duplex links, for

example, only the control node must have the routinginformation since all traffic must go through it, and the

22

71iA . - - - v v-. .7* '~77 ~

routing will simply be a match of the destination to the

output link that connects to that node. Another simplearrangement is a single ring-connected network. If -the links

are full-duplex, traffic -an reach any destination from any

source either way around the ring, and ths routing algorithm

can be quite trivial, needing no routing table as main

component since the shor-.est path can be easily computed

from the destination node number. But networks are not

always that simple, and more and more sophisticated routing

protocols are required as the complexity of the network

topolcgy increases. Even without knowing the details of the

network traffic, it Is possible to make some general

statements about the optimum routes, based on the network

topology. One example is the Optimality Principle, which

states that if node "B" is on the optimal path from node "A"to "C", then the optimal path from "B" to "C" falls along

the same route.

r Some of the most important packet switched

communications networks in cgrrent operation ars TYSNET

(Public ccmmon carrier network based in the U.S.) , TRANSPAC

(rench's Government PTT data network), ARPANET (U.S.Department of Defense Computer Network), SNA (IBM's System

Network Architecture) and D R& (Digital EquipmentCorporations Digital Network Architecture). The routing

algorithms used in these networks turn out to be variants,

in one form or another, of shortest path algorithms that

route packets from source to destination over the least cost

path. The specific cost criterion used differs among the

networks. Some use a fixed cost for each link in the

network, and usually the cost is assigned inversely

proportional to the link transmission capacity, in bits per

second. For a network with equal capacity links,

. minimization of the path cost then generates a minimum hop

path. Links with high error rates or congestion may be

23

* M\ .< .- . ./,. . W *. V *-~* . *-

* . . . . . . .. . ." • "- . .. . . . . . . . . . . . . . . . . . . .. .. . .

assigned -higher costs to avoid sending too much traffic

through them. Other networks attapt to estimate average

packat time lelay on each link, and use this :o assign a

link cost. The resultant source-dgsination path chosen,tends to be the path with minimum average time delay. OLce

the bes- paths have been determined, routing tables set at

each node are used to route individual packets to the

appropriate outgoing link.

Shortest path with single routms turn out not to be

optimum, if0 the long-term average network delay time is to

be minimized. In this case multiple paths, where fracticnsof the packets at a node are assigned to one of severaloutgoing links (perhaps on a probabilistic basis), provide

for a closer to optimal routing. rhis kind of routing has

not yet been used in routing schemes implemented inoperating networks, although there are plans to incorporatethis procedure in future routing mechanisms for the Canadian

DATAPAC network . (Ref. 7]. In the present study we

investigate the use of a routing protocol that allows for

the routing of packets over multiple paths.

B. STATIC AND DYNAMIC ROUTING

Routing protocols can be groupa.d into two major classes:

Adaptive or Dynamic and Nonadap:ive or Stat4 - . Dynamic

protocols base their routing decisions on measurements or

estimates of the current traffic and topology of th.%.. network, and their routing policies vary in time according

to the fluctuations of these zeasurements. Static

protocols, in contrast, make those decisions independently

from the current status of the network. Their routingpolicies are determined a priori and are time invariant. For

this reason, static protocols must be designed to providesatisfactory performance, on the average, over a range of

* traffic intensities.

.4

, '.'.... ..- € € . .. ....-.- . . -€ -. .-. '€ .-.._ . .. . ..-..2. . . .

.. -.-.- . ' ' , ,- , .... , 'v,. ,,,, ,.,.', . ,,,'* . , ,,.,*. ,. .-,- -,-v. -*- . - ",.... .. ' ...-._ V*o.-.-,

If a dynamic protocol could manage to adapt perfectly tc

the changes in traffic and topology of the network, it will

naturally outperform any static protocol; but traffic loads

vary continuosly, and topology chang-s in most cases can r.ot

-be predicted, so dynamic protocols require complicated

computations which may slow the operation of the network.

Furthermore, sending thn update informaticn thrcugh the

network may itself increase the traffic. Static protocols,

. in contrast, are usually simple, and since their

implementatio is done before bringing up the network, they

do not affect the traffic lcad. Nevertheless, static routing

protocols do not react to drastic changes in traffic or

topology in the network, and since zost traffic is bursty by

nature and r-quipment malfunctions are not infrequent, they

may lead to congestion and misuse of some of the links.

Static Routing is widely used in network design. There

we are interested in determining whether a given traffic

pattern can be accommodated by the network, and if it can,

what will t.e average delay be. Network topology is

%< generally designed interaztively by producing small changes

(addition/delation of links or reducing/increasing lank

capacities) and observing the effects on throughput and

delay performance. This performance evaluation is

accomplished using a static routing algorithm. A method

that applies this process is the "Cut-Saturation" algori-hm

for the topological layout of packet switched networks

[Ref. 8].

The degree of adaptivity of a :r_:ain routing protocol

can be measured in terms of its response time, that is, the

rate of change in the traffic ani topology of the network

M which it is able to track efficiently. There is indeed a

whole spectrum of sclutions to the routing problem betweenthe two extreas mentioned (static and dynamic-). They are

characterized by different respDase times and used for

25

*% %

different applications. & comparative analysis of some

routing alternatives that combine static and dynamic routingfeatures has been done by Rudin [Raf. 9]. If the rak. of

change of conditions in a network is slow, for examp!re, a

periodically refreshed static routing (or "quasistatc")protocol, can be a reasonable solution; but if it is fast, a

dynamic routing scheme may be rsquired.In the static (or quasistatic) routing enviromer.t, e

time between traffic pattern changes is very much largerthan the avecags network transmission time, so that the

routing computation can be performed 4 thp background, at a

vary slow rats, and without increasing the load on links or

nodes mach. In the dynami- routing enviroment, on the otherhand, the tiae between traffic changes is comparable to the

time required to measure such chaages, compute new routpeand implement them. In this case we must be concerned with

the time required to arrive to in optimal solution andinstall it in the nodes, and the amount of overhead

intrqduced in both link and node usage. rhe frequency ofupdating routing tables represents a compromise between the

desire that as soon as a change is detected the information

is immeiiatsly made known in the network, and the amount ofoverhead generated by the updates.

For a fixed network topology aad fixed traffic patternsituation, the optimal static routing protocol representsthe optimal routing scheme. For daterministic steady input

then, dynamic routing protocols that use the system

optimization approach must converge to the optimal staticrouzing, that corresponds to the existing traffic pattern

and network topology.The effectiveness of different static routing protocols

rslative to dynamic routing protocols is not rsally known,

except for some suggestions from simulation. For staticrouting, a well known lower bound for d.lay has been

26

determined by Fratta, Gerla and Klainrock with their- "1Fmow

Deviation Method" [Ref. 10]. Thaza is no cor espond-ng

lower bound known for dynamic routing, but in some cases,

simple dynamic -routing schemes give delays significantly

lower than the best static routing delay for scma specific

network topologies. Examples can be found in rUM (Ref. 11].

Simulation studies at the British National Physical

Laboratory indicate that the addition of a dynamic

capability to a shortest path (static) routing rule may

increase throughput by as much as 50%. [Ref. 12].

An optimal routing strategy will then use a dynamic

protocol that behaves as a statiz one, when traffic and

topology of the network warrants it, and as a normal dynamic

one otherwise. Such a routing protocol should not be

sensitive to small variations in the traffic, and it should

allow routing through multiple paths to maximize utilization

of resources and reduce packet time delay.

C. DISTRIBUTED AND CENTRALIZED ROUTING

Perhaps the most important characteristic that

dif ferentiates the numerous routing schemes that are

currently used in packet-swithched communications networks

is the strategy used to control the selection and

.- implementatiom of the routes under different network

conditions. McQuillan (Ref. 13], defines four catqgories of

control strategies:

(1) Daterministic Control

(2) Isolated Control

(3) Distributed Control

(4) Centralized Control

Deterministic Control implies fixed routes, but nodes

have precomputed tables which can be manually selectel to

deal with line or node outages. &a example of this kind of

27

%.

,r - ; . * -' C:. , a t.L at ... :o a *: . * t -: . - ' t '. *. * - : ._.• r.

network is the SITh network. Isolated control strategies

involve decision making at each node based only on local

information. Information is not aven shared with adjacentnodes, and thus, changes are not propagated out of the node.Distributed control allows each node to make its owndecission on how to adapt to the changes in the network,

based on information obtained locally as well as from othernodes. Furthermore, this strategy tries to propagate

routing information of global importance to all the nodes.

. The last category, centralized control, assigns the

responsibility for all routing decisions to a single node,-i usually called the Network Routing Canter or NPC (possibly

backed up by alternate nodes in case of failurs). In this

case, all nodes must report their status and any networkchanges to the NRC, as wall as receive and adopt routing

decisions from it. Of these four categories, the two most

widely used are Distributed and Centralized Control. Some

examples of networks using distributed routing are ARPANET

and DATkPAC, while TYMNET uses centralized routing.

* Regardless of whether centralizaid on distributed controlis used, hsy both impose in the network a cost in time,

bandwith, buffer space and other natwork resources, to move

routing information f ro m the locations where routing

policies are selected to where they are enforced. Inaddition, if any dynamic routing scheme is used, it must

overcome a problem f undamental to them, namely, the shorttime interval available to deliv.r routing information to

and from the modes before network conditions have changed somuch that the information is obsolete.

For dynamic routing protocolIs we prefer for the

decisions to be made in a distributed fashion. The reason

is that using the centralized approach, the time it takesthe NBC tc receive information fro2 all the nodes, calculatethe routing strategy and send it back zo the appropriate

28

4%

nodes, can be so long that the routing decision may be out

of date. In this case the dynamic routing protocol way looseits adaptiveness and make what is effectively a randomchange. In contrast, distributed schemes do tot have asmuch information, since we can usually expect to have only

Athe past information of all the network (global), thepresent information of the node (local), and partialinformaticn of some other node or group of nodes. The

decision rules are usually simpler, and the propagationdelay for the exchange of status information betweenneighboring nodes, can also be smaller than if sent from acentralized center. This reduces the time elapsed betweenthe change of states and the change of the routing decision.

A distributed scheme reduces the reliance on a cental nodethat may fail. It may also diminish the effects of node and

link failure, since in a centralize! protocol, the routes tobe used by the notification of such failures may in fact bedestroyed by them. In addition it can avoid the increase oftraffic overhead in the proximity of the NRC, due to the

p.riodic collection of status reports from all the nodes,and the distribution of routing decisions from it.

Although a* mixed scheme has yet been implemented, inprinciple it is possible to combine routing strategies to

compensate for each other's defficiencies, and therefore

hope to reach reach an overall improvement of routing

characteristi-s. An example of a routing protocol thatcombines centralized with distributed routing is theDelta-Routing. In this scheme the central controller sends

-, routing tables to the individual nodes, but these are usedin conjunction with local jueue lenaths to select the routesto be taken by individual packets. Other schemes thatcombine centralized with listributed routing are discussedby Chu and Shen [Ref. 14].

29

* ,. . * . , ~ * . .- ~

ip

D. PLOD CONTROL ID CONGESTOI COU1ROL

In mo-t shared communication networks, resources are

dimensioned to meet less than the peak demand requirements,

due to cost factors. ?his underdimension introduces a

reducticn in the usual performance, which should be

acceptable to the users, plus a risk that the actual trafficload may occasionally exceed the level where acceptable

performance is obtained. The traffic load level at whichacceptable performance is just met, and where any increasein it will make performance unacceptable, is called the

overload level. By setting this level the designer ca. makethe risk of non-acceptable performance as small as he want3.Therefore, the overload level is the network's design load

level.

In a packet switched communications network, even when

% v the traffic level does not exceed the overload level, there

is a need to control the rate at which packets flow from one

node to the next and to prevent packets from arriving at the

* receiver at a rate faster that it can handle them. We mustalso make sure that the load imposed on the path between

transmitter and receiver loes not exceed its capacity. A

mechanism to allocate resources to satisfy user demands aslong as there are resources, and to settle contention whenthe network cuts out of resources, is required. This

mechanism is usually called Flow Coatrol. A good definitionof Flow-Control given by Radin [Ref. 15], states that flowcontrol is "a system of algorithms which are used in a

network to prevent a single user or a user group frommonopolizing the network resources to the detriment of otherusers",.

Flow Control may be done between neighboring nodes(local control) or between source and destination

(end-to-end control). Between naighboritg nodes the flow

.4...

30

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: : - .:: r ., , V. , " " ?" " " " -" '. ", '* . . '.. . .... -,, .,-. .:. :,-.-,.•. ;.: .I , ,....:.: ... ... ..

.R~I %1 IF. -7

control mechanism must b e design -o ensure that the

transmitter sends packets at a rate acceptable by the

receiver and thus protects the receiver node againstover-flowing its packet buffers and overloading its

* processing capacity. Consequently, it places limits on thenumber of packets at the buffers of the switching nodes.Between source and destination nodes, flow control must be

designed to ensure that the source node does not generatepackets for the destination at a rite higher than that atwhich the latter can accept then. So it places a limit on

the number of packets belonging to a source-destination

pair.All flow control mechanisms eitmar require the sender to

stop sending at some point and wait for an explicit

go-ahead, or permit the receiver to d-sca:d packets at willwith impunity. Two well known flow control mechanisms areStop-and-Wait and Sliding-Window. Some analytic models for

the study of end-to-end and local flow control can be found

in the literature [Ref. 16].When the number of packets releasad into the network by

the nodes is within its carrying capacity, they are alldelivered (except for a few that may be affected bytransmission errors) . But when too many packets are present

in part of the network, it can becoma impossible for packetsto move, because the queues into which they should beaccepted are always full, causing the network performance todegrade; this situation is called Congestion. Congestion

can be brought about by several factors. If the nodes are

too slow to perform the various tasks required (queuing,updating tables, etc), their queues can build up even thoughthere is excess capacity in their output links. On the

other hand even if the processing speed of the nodes isinfinitely fast, queues can build up if the input trafficrate exceeds the capacity of the output lines. This can

31

happen fer enapla if two or more input lines are deliveringpackets all 3f which need to be sent by the same iutput

link. Congestion tends to feed upon itself and become worseif nothing is done to control it. If the traffic increases

too far, performance may collapse completely and almost no

packets be delivered.

Many factors can cause the =crying capacity of the

network to be exceeded and cause congestion, so the network

must be able to react and take some action to control it.Flow control techniques cannot really solve the congestionproblem because traffic is bursty, so any scheme which isadjusted to restrict each user to the mean traffic rate will

provide bad service when the user wants to send a burst oftraffic, even though there is no on gestion. On the other

hand, if the flow control limit is set high enough to permitthe peak traffic to get through, it has little value as a

congestion control mechanism when ssveral users send theirpeak traffic at once. What is really needed is a controlscheme that is only triggered when the system is conges-ed;

this scheme is called Congestion Control. Congestion controlis therefore the set of mechanisms whereby the network

maintains inpat traffic within liits that are compatiblewith its carrying capacity.

In most packet switched networks, if a packet remains

queued for too long at some node before arriving to i1tsdestination, retransmission will occur until a positiveacknowledgemeat is received, this process creates ths

ability to generate traffic within the network itself. With

high volumes of traffic the generation process can create atraffic volume equal to the remaining capacity of the

network. When this critical point is reached all buffers are

full and the network fails and rumains with no throughput;

that is, it cannot receive or successfully transmit a

packet, so that all nodes are caght in a deadly embrace.

32

This extreme case of congestion is called Lock-up and is

irreversible. The only way out is to purge the locked-up

traffic.

The general strategy is therefore preventativa in

nature, and consists of controlling congestion in the first

place. If infinite buffers were provided at the nodes,

there would be no lost traffic aal the network would only

congest at infinite load, well above the overload point (the

point of acceptable delay). If to the contrary buffer size

were very small, the network will congest even at small

traffic loads, well below the overload point. Thus there is

an optimal buffer size which makes overload and congestion

cecur at the same traffic level. rhis is desirable because

it is better to have a congestion control mechanism thatrejects overloading traffic than t3 have excess buffers iniwhich traffic may spend too much time to be useful.

Without effective congestion control, packet mean time

delay will tend to infinity and throughput will tend to

zero, as the network approaches the deadlock load. With

effective congestion control, mean time delay and throughput

will increase until they reach the saturation level and then

stay the same (flatten), remaining insensitive to furtherload increases. The curves in Fig. 3.1 show network

throughput and packet transit time delay versus offered

*load, for networks with and without effective congestion

control.

It shoull be apparent that with effective congestion

control, if the network throughput and packet mean transitdelay flatten as offered load increases, -he mean admittance

delay of packets to the network by the nodes must increase.

Fig. 3.2 shows a comparison between admittance delay and

transit delay, for packets in the network, as offered load

.0, increases.

33

A = With effective congestioncontrol

B = Without congestion controlNetworkthroughput

9 'iA

___________________________offered load

J44.4 Deadlock level

Network meantransit delay

B

A

Offered load

Figure 3.1 THROUGHPUT IND TRINSIr DELAY VERSUS OFFERED LO&D.

Some common types of strategies used in packet switched

"' netvorks for dealing vith congesti~n use pre-allocat.on of

resources, choking off input (that is, requiring the node

sender to reduce its traffic by se21ing it a Choke-Packst),

packet discarding, ar.d restricting the total number of

packets allowed in the network (Isarithoic control). Theireffectiver.ess and performance are analyzed ezt*nsively by

34

Mean A = Admitance delaydela B - Transit delay

A

B

I _______Offered load

_.Deadlock level

Figure 3.2 DELAY VERSUS OFFERED LOAD.

SCHWARTZ and SAAD [Ref. 17], Ireland [Ref. 18] and Davies

[Ref. 19]. Sin.ce pcor routing algorithms often lead to

congestion prblems, and local congestion often requires at

.,., least temporary modification of routing protocols, therouting problem caLnnot be completely divorced from that of

congestion control. However, in this thesis we concentzrate

on the routing protocols under the assumption that thebetter they are, the less congestion is likely to occur in

the network.

U 35

a TW V -. 77Z- .. 777 7 7. .,

E. ROUTING FRACTIONS

Under the appropriate assumptions the optimal rou-.ing

poblem can be formulated as a nonlinear multicomodity flow

problem, so that mathematical programming techniques can be

used to solve it. All the routing protocols mentioned so

far are basel on the assumption 3f the convexity of the

objective function. A very popular analytical model of data

communications networks, which rel~tes the packet tims delay

to the flews and capacities of the links, was intrcduced by

Kleinrock in [Ref. 20]. In this iadel, the steady state- time delay in each link is calculat.l explicity as:

Tij / (Cij - Fij)

where:

i : Is the node origin of Link (iJ)

j : Is the node termination of Link (i,j).

TiJ: Is the expected delay per message experienced

by messages using Link (i,j).

CiJ: Is the capacity of Link (i,jJ in messages p.rsecond.

FiJ: Is the data flow rate in Link (i,j) '. messages

per second.

The routing assignment is then selected to minimize the

expected weighted delay "D", of messages :raversing the

network, whers:

D SUN ( riJ I ij)

(i, J)

This analysis is based on the assumptions that traffic in

each link can be modeled as Poisson message arrivals with

independent exponentially distributad message lengths, and

that queueing delays are ths only nonnegligible source of

delay in the network. The first assumption is the result of

Kleinrock's famous "Independence Assumption", that messages

3.6

.e36

,.,'A " .' t" " ,:,' ' , ., .''''.2''',.'. . . .".. : . -. .","--, / ..X ''vv v''''v.,'. ,,.,,.v .' ,

a, a -S'4 *.*-'...*

loose their indentity at each nals and are aesi.r.ed new

independent lengths. The sacond asSumption, generalized by

Kleinrock in (Ref. 21], accounts for overhead and

, propagation delays. Kleinrock's model is appropriate for

static and qusi-static situations but less appropriate for

dynamic strategies.

A generalization of this model, where the contents of

the queues at the nodes are viewed as continous quantities,

rather than as an integer number if messages or bits, is

proposed by Segall in [Ref. 22]. rhe continuous nature of

his model Is justified by the fact that the affect of any

single message on the total systea performance should be

minimal. Using this continuous mode]l the routing problem can

be formulated as a linear optimal control problem. Solution

to this problem has been approached via a feedback form,

obtained by means of Pontryagin's minimum principle, and

dynamic programming. Another solution involves replacing

some constraints with penalty functions, and uses this

formulation to investigate how to minimize the average

message delay, while disposing of whatever backlogs may

exist in the network at any particular point in time. A

comprehensive study of the feedback sclution has been

presented by Ross in (Ref. 23], and solution has been

obtained for the case in which all messages have the sama

destinaticn and the inputs are constant in time. But the

approach runs into difficulties when the general case is

considered and no solution has yet baen obtained for it.A differeat approach proposed by Wozencraft [Ref. 2]0],

involves changing the objective function while keeping the

same continuous model. Instead of trying to minimize the

average delay, the idea is to minimize the maximum delay.

This minimax approach has been extsasively researched by Ros

in (Ref. 25]. The objective is then to minimize the maximal

saturation ratio (Fij / CiJ) in the netwcrk. Subsequently

37

the next maximal saturation ratio is minimized. It :a-ion

is continued in this way until a unique solution -o thecorresponding problem is found or we have exhausted all

links. At this point we can geraerate a finite set of

fractions (we will call them Routing Fractions) that

represent the proportion of traffic from node "A" (any node)

to node "B" (1estination node) that must be routed through

lnk "C" (any outgoing link of node "Al"). We will call this

procedure: "Successive Saturation".

An alternate solution which rejuizas less computational

effort consists of doing the first iteration of the

Successive Saturation method mentioned before, using its

results to scale the capaizty of the links in the network,

and then finding the set of flows that maximize the sum ofthe exess capacity (slack) of all links. At this point we

have found a finite set of Routing Fractions, as defined

before. We will call this procedure: "Maximum Slack". Both

solutions use linear programming techniques and therefore

enjoy the trei-ndous compatational benefits that they offer.

This thesis is part of a bigger effort to analyze theuse of Routing Fractions in the routing protocols of a

packet switched ccmmunications network. As such i+concentrates on the study of their behavior in a static

multiple path routing strategy. Nevertheless, the modeldeveloped as well as the computer simulation program contain

provisions for future experimentation on their use In a

dynamic routing strategy. These provisions allow theaddition of a computer program that calculates the values of

the Routing Fractions (which is the matter of another thesisbeing undertaken at the present tile). This program couldthen be called upon to recalculate the values of the routing

fractions, when the traffic load or topology changes in the

*network warrant it.

38

Ii°.,

F. LOOP AVOIDANCE

An important characteristic that any routing prctocol

. should have is to be "loop-free". Loop-freedom iefines a*.': p--r destination partial ordering of the nodes in the

network, which is used by the routing protocols for the

propagation of packets through the network, to preven- them

" from looping. A loop-flow exists in the routing protocol%when a packet can potentially loop, that is, it can arrivs

to the same node for the second time in its way to izs

destination. A given packet may be trapped in such a loop

for a significant amount of time. If a large numbs- of

packets start looping they can cause congestion (since

retransmission will occur until a positive acknowledgement

is received) which begins at the locus of the loop and can

s.-rad throughout the network. A loop-flow may exist even

if no individual packet ever loops.

The main reason for a routing protocol to be Loop-free,

is the reduction in packet time lelay. Other important

reasons include the simplification of higher level

protocols, and to prevent some potential deadlocks.

M ost rules and procedures used to develop loop-frea!

routing scheses, are extensions of techniques used in

network graph theory and flow pattern analysis. The

following are some interesting examples of routing

principles derived from these technigues.

If we call the destination node "Sink", and if nods "A

is on a path from node "B" to the sink, we say "A" -sdownstream from "B", and "B" is upstream from "A". In a

loop-free routing protocol, no node zan be both upstream and

downstream from any other node, for a given destination. If

'"T" is a set of links that form a tree in the network graph,

and 'F" is a set of links (not in "r") going "nto node "A",

then the set (T + F) is loop-free since -he links going into

*% .*' 39o, %

Z?

.4.ir .W_ -- - -

node "A" cannot be in a loop. Furthermore the set (T + F -

(ALL LINKS NOT IN ?)) is a tree. Sums of loop-frse tree

flows are not always loop-free as might be expected

[Ref. 26].

The set of optimal routes from all sources to a given

destination form a tree routed at rae destination (such tree

is called the Sink Tree). Therefore, it will not contain

any loop-flows, and each packet will be delivered to its

destination within a finite and bounded number of hops. If

a fixed routing is contructed by zhoosing a maximal tree in

the network graph (that is using only links directed towards

the sink), then the resulting flow is nonnegative and

loop-frae, and the set of all flows determined this way is

clearly convex and loop-free.

In general, no optimal routing protocol can have

loop-flows, a fact which will tend to minimize congestion.

Some routing algorythms o-annot be said to be loop-free but

if the small number of loops whi=h they do form do not

persist (transient), and do not lead to congestion or to a

" significant increase in average network delay, they may be

accepted as efficient. An example of this case is the new.... ARPkNET routing scheme SPF (Shortest-path-first) [Ref. 27]

where a small amount of transient looping occurs while the

network is adapting to a routing change.An algorithm that does not permit looping does not

necessarily result in lower delay, higher throughput, or

- ~ less ccngestion than an algorithm which does. However

research by Gallager [Ref. 28], has proven that the paths in

a minimum distance (optimum) solution, for a network with

link distances greater thin zero is loop-free.

40

,"~ %'

•..°',.-.".. ,.. . '.2-. .....,,.'. .' D.' .- "-.'. .' ,,,.% '. "A,.''- ".",."' "" ."". '."-. "" .•.• . .-.- -•.•A

IT- RAMT11 A O1 1- ilCKI S!IC _EQ COI!UIIC ONS NETWORK

1. MODEL CHAR&CTERISTICS

In the analysis of t..e =outing protocols of a packet

switched network, simulitio has proven to be a powerful

too! to investigate their performance and carry out

comparative studies of the differeat strategies. In scme

cases, such as with distributed dynamic routing, simulation

has been relied on almost exclusively because of the time

vaying behavior of the set of i.tarac-ive queues, whose

theoretical study is still in its infancy.

In simulation the network and its protocols are modeled

in terms of a computer program. Nevertheless, it must not

be an emulation seeking to duplicate every small de-.ail ofthe network operation. & simulation model that tries to

cover every detail is an extremely expensive, wasteful, and

slow-running operation. As a genaral rule one should only

. 4 simulate the system features that are relevant. Therefore

the simulation of a routing algorithm must describe theOR nodal queue handling procedures, and the routing process

itself, in full detail.The model we chose is that of a set of nodes connected

"-' by unidirectional communication links. The number of

outgoing cr incoming links is not limited by the model; this

- allows for the configuration of the network in almost any

topology desired. Each link has a buffer (we will call it a

queue) where packets are stored if the link is busy.

Transmission of packets from the queue of each link is done

in a FIFO (First in first out) fashion. Nevertheless, some

'a packet-prioritizing scheme can be easily added to the model,

wi.hout affecting its structure.

411*.,

Our model assumes noise-free llraks, that Is, packsts

arrive at their destination without any errors and no packet

loss is experienced during transmission. Similarly,

queueing delays and transmission tima are assumed to be th?

"- only nonnegligible sources of delays in the natwork.

Message traffic in a packet switched network can be

modeled as a Poissor process, with the length of the

messages gecmetrically distributed. Accordingly, our model

uses a message gnerator that genaratas poisson distributed

messages (by using exponentially Jistributad interarrival

times), and the number of packets for each message (message

length) is generated from a geometric distribution.

Traffic load is another parameter that can be set to any

. ?.esired level in our model, and two ways of doing it are

;rovided. The first accomplishes this by setting the

average number of new messages for the network per second.

The inverse of this number is then used as the mean of the

exponential distribution used to generate the message

interarrival times as mentioned before. The second does it

by setting the average number of packets per tessage. This

number is then used as the mean of th. geometric

distribution from which the length of each message (in

packets) is generated. Both numbers are real as inputs by

the model so they can be set to any desired value.

The model accepts as inputs the probability of each node

being -the source of a message, and the conditional

probability of each nods being the destination Qiven a

- source node. With these two sets of inputs, it calculates

the probability of each possible zombination of nodes(node-pair) being source and destination of a message. When

a message is generated, the model picks a node-pair randomly

and assigns them as source and destination of the message

1-0 le respectively.

42

As indicated in chapter thras, the Routing Ftictions

represent the proportion of traffi.c from nods "A" (any "ode)

to nods "B" (lestination node) that must be routed through

link "C" (any outgoing link of nole "") . This nanrs of

the Routing Fractions make them readily available for their

use in a multiple path routing scheme.

The routing protocol procedures of the model arecontained in a separate module (see routine 'PIZK.BEST.LINK'

in the program description sections , to allow them to be

easily changel if required. values of the routing fractions

corresponding to each link are real by the model, and used

by the nodes to select the outgoing link by which to route

each packet. This selection is lone by picking a routing

fraction probabilisticly, and using the link that

corresponds to it as the selectal outgoing link. This

procedure, as mentioned before, allows for multiple paths in

the routing of traffic destined to any node.

Since our study concentrates on their use in a static

routing scheme, the values of the routing fractions do not

change throughout the simulation :an. Nevartheless, themode & allows for the addition of a Routing Fraction

recalculaticn procedure, which could be executed when -he

traffic load or topology changes i the network require it.

This addition will change the mod-L's static routing scheme

into a dynamic one.

*'.. In order to make the model more flexible in adapting to

different testing conditions, we allow the network to be

configured to provide either Datagram or Virtual Circuit

services. When in the Datagram Service Configuration, the

route in terms of links to be traversed by each packet (on

its way from the source node to the destination node), is

determined sequentially. As the pac=kt arrives to each node,

the next outgoing link to be travgrsed by it is determined

$ by the model. This procedure is -hen repeated at each node

43

until the packet arrives to its destination node. There,

data from it is collected by the model for the statisticalanalysis of the network behavior, and then destroyed by the

model. In this way, each individual packet wi1 travarse a

route specially determined for it at each node, and nodirect relationship exists between this route anl the routesof the other packets of the same message. Consequently, in

this procedure packets of the sama message car (and most

often do) follow different paths through the network ontheir way to their destination. Yhis as we saw before,

complies with the characteristics of Datagram Service.

In the virtual Circuit service configuration, in

contrast, the complete route to be followed by a message isdetermined at the moment of its creation. This route will

then be followed by all the packets belonging to that

message. No route change is therefore experienced by anypacket after it leaves the sour=3 node. 9hen a packet

arrives at a mode, the model checks its predetermined route

and sends the packet to the corresponding outgoing link.

This procedure is repeated at every node until the packet

arrives to its destination, where data from it is collected(for the same statistical purposes as in datagram) and thepacket destroyed by the model.

As it is in most packet switched networks in operation,in our model the size of all the data packets is the same,but it can be defined to be any number of bits. In order todo this the model accepts this size as an input, and fixes

the size of all the packets to it. If there were arequirement to allow packets to be of different size, amechanism .c generate these sizes could be easily added to

the model.

Another important parameter of our network model is the

link capacity, i.e. the data carrying speed of each link, inbits per second. Our model reads t~e capacity of each link

4"

Uo-

and then uses it to calculite the time required for a packet

to traverse that link (transmission time). This

transmission time is further used to schedule the arrival of

the packet at the next node. The model can therefore accept

any value of capacity for each individual link, as long as

it is in bits per second.

As mnentioned before, each liLk has a buffer or queue to

store packets waiting for transmission. In our model we have

chosen not to limit the size of these queues, in order to

allow the study of the behavior of tho routing fractions

without introducing any other process that could affect the

results of the analysis.

Most of the parameters of the model can be changed very

easily, to allow the simulation of different testing

conditicns, as we will see. As an example the number of

nodes and links do not have a theoregicai limit, but must be

set before the simulation starts, and remain fixed for the

duration of the run. Nevertheless, there ars some indirect

ways of changing the topology of tha network during the run,

such as setting the corresponding routing fractions of any

link to zero. This will prevent aaymore traffic from going

into it. In this way we can represent a link failure.

B. PARAMETERS OF THE PACKET SWITCHED NETWORK

4 The definition of the different variables whose values

must be read is inputs by the program is the following:

1) N.VODE : Number of nodes of the network, integer number.

2) N.LINK : Number of links of the network, integer number.

3) CONNECTED : Integer two-dimensional matrix that indicates

the way the links are connected in the network.

Each row represents a link and each column a node.

So position CONNECTED(A,B) must have a value of 1if link 'A' starts in node 'B', a value of -1 if

4&5

&Z* e.

link 'A' ends in node 'B' and a value of 0

elsewere.

14) PR.ORIG : Real 1-dimensional matrix, each row represents

a node and contains the probability of a message

-'' being originated in that node.

.: 5) PR.DEST : Real two-dimensional matrix, fach rowrepresents an origin node and each column a

destination nole. So position pr. dest (AB)

contains the probability that a message that was

originated in riode A his as its destination node

IBe,

6) ROUT.FRAC : Real two-dimensional matrix, 4ach row

-. represents a link and each column a node. So for

position ROUT. PRAC (k,BI , it contains the

proportion of the traffic destined to node 'B',

that should be sent by link 'A' i.e. routing

fraztion of link 'A' for node 'B'. If no traf ficfor node 'B' can be seat by link '' its value

should be zero. For our study (static scheme),these values do not change during the simulation

run. For the future us=. of this program in a

dynamic routing scheme, these will only be the

initial values of the routing fractions. During

the simulation run, their values should be

4. recalculated every time the conditions in the

network so require (see event 'NEW.ROUT.FRAC' in

section "D" of this chapter).

7) LNK.CAPACIY : Integer 1-dimensional matrix, each row

represents a link and contains the capacity of___. that link in bits per second.

8) TINE. LINIT : Real number that represents the length ofA time the simulation run will last, in seconds.

r. .. 9) REPT.TIME : Real number that r.pre.ssnts the interval of

time between 'WET.REPORT' events, in seconds.

'46I. .

a.-...

-- J VIV '.W•VV

10) UP.TIME " Real number that represents the interval of

time between 'NEW.ROUT.FR&C' events, in sconds.

11) COLL.INT : Real number that .apresents -he interval of

time between 'DAT .COLLECrION' events, in seconds.

12) LAP.TIME : Real number that rapresents the int-erval oftime between 'LAP.TOTALS.RESET' events, in seconds

(see event 'LAP. TOTALS.RESET in section "D" of

this chapter).

13) L!NGTH.PKT : Integer number zha: represents the lengthof i packet in bits.

14) AVG.MPS.NET : Real number that represents the average

number of messages per second th. n.twork will

genera te.

15) AVG.PKTS.MSG : Real nmber that represents the average

number of packets-per-message the network will

generate.

16) PBNT : Integer number that represents the printing

condition for the run. Depending on 'he value set

V. it can print the following:.

0 =a> Initial data, network topology, net rsparts,data collection messages, period reports,

collect period data messages, restart

period totals messages, lap totals reset

messages, destruction message, and end of

simulation messagg.

I -> All in 0 plus trace of all packets.

2 -> All in 0 and 1 plUs information of all links

every time it performs a 'NEW.MSG' or an

.END.XT1 event.

17) O.DE : liteger number that represen-s the configuration

of the network for the simulation. It can take th-following values:

1-> Dataaram service networkA 2 - Virtual Circuit service network

47

-' I I l I i i i I l i I I . i l -i . . . . . .

A " . : % " """". +

The 1opolcgy of the network used for our simulation :s shown- in figure 4-I. It consists of a set of thirteen nodes

connected by sixty unidirectional links. ro simplify the

drawing each line interconnecting two Lodes in, Figure 4.1represents two links, one in each direction. Each link inour model is assigned a number for its idsatification.

Appendix B c3ntains a list of the link numbers with their

corresponding origin and termination ncdes. As mentioned

before, each link owns a giaeue (or buffer) where packets are

stored temporarily while waiti ng for their transmissior ifthe link is busy. These queues have no limit in their size.

- The link capacity (the rate at which data is carried

through the link measured in bits per second) of all linkswas set to 20,000 bits per second, which is the transmission

rate that modern modems allow over dedicated lines. Thepacket length used was 1000 bits, which is approximately themaximum packet size allowed ia ARPANET (1008 bits).Transmission time is calculated by the model every time itstarts to transmit a packet .through a link. For this it ,sesthe capacity Df the link involved, and the packet length.

The probability of a node pair to be selected as sourceand destination of a message, was initially set to be equal

. for all nodes. Later a non-uniforn listribution was also

4 used to compare the behavior of the routing scheme in

balanced and unbalanced traffic situations.

The mean 2umber of messages per second for the network

-- and mean packets per message where set to different valuesto analize the response of the network to different traffic

loads.

Two sets of routing fractions were used. The first setwas calculated by the successive saturation method and the

second set was calculated using the maximum slack approach.

as explained in chapter II1. Both sets where tested underthe same network and traffic conditions.U 48

.'- F * *"9,, 'q'2':',** ,.'.'*,'... . ..... . .. ,...*'.- ...- ,.'..*:':-.2."'. .-. . . . . . ." ...:"..;-z . -. , . -.. .. . _

-'f

-.PI IL

.113

Figure 4. 1 NETVORK rOPOLOGY.

-" C. CONmPUTER LANW/&GE

The siulation of our packet switched natwo-rk model was

dons using the SIMSCRIPr 11.5 Zo~mputer Language. This'.language was selected bkcause it pcov-6des an -_zc,%llent means

for discrete-event simulation. Another important

characteristi of this language is that it allovs the use of

Fortran subroutines. This feature makes it possible to take

49

U% ? ' . . . . .. *.* . f. .

. • -t ame

(m.e e ee ee ~ . q a e o. ee'

"e" em~ *e" ° • m -

• e e

q ' -

.-J

advantage of existing subroutines or programs, rather J-han

to waste time reprograming them in SIMSCRIPI 11.5.

SIMSCRIPT 11.5 language uses e.glish-like statements and

allows for the insertion of some ax -a words, that mak- it

•_ f."easier to real (sven by someons wi-4: little przactice in this

lanquage). fhese characteristics make a program writ-aen in

Simscript 11.5 almost self-documented and only some short

comments are needed. Nevertheless, care was taken to make

the program as modular and structured as possible, to make

it easier to change and understand. in additior. .c the

simulation p-ogram, two other programs where written in

Fortran language for the display and graphinq of data

collected from a simulation run, using the Disspla graphics

software package.

D. SIMULATION PROGRAM DESCRIPTION

In writing the program one of the main objectives, as

mentioned before, was to make it flexible so as to adapt to

possible variations in the network topology or rsquirements

of -he simulation. Consequently the values of the input

parameters can be set to adipt to most simulation

requirements, as seen before.

The program is divided in three major parts, the first

part is called the PREAMBLE, the second is called the .AI.,and the third contains all the Subroutines and Events.

The preamble contains mode and limension d.finit-ons of

Global Variables, declaration of Events and Event

priorities, and definition of Statistical Variables and

program Functions.

The main program is the drive; of the simulation, it

calls and schedules the initializing Rcutines and Events,

and starts and ends the simulation.

50

p..

:1° AL .. !.6

The modularity in this program is mainly accomplished by

dividing the rest of the -ode into subroutines and Even-s.

The main difference between a Subroutine and an Event, is

that a Subroutine is called upon to perform a function (orprocedure) by another Subroutine or Evant, whereas an Event

is scheduled to occur (perform its function) at a certain

point in tima. While Subroutines return control to their

caller an Event returns control to the timing mechanism of

the SINSCRIPT 11.5 system (we will call it the Timing

]Routine) .

The different Subroutines and Events contained in the

program, and the functions they perform, are t-he following:

- ROUTINE NETWORK. CONSTRUCr ION

This routine reads the number cf nodes aid links, andconstructs the network based on those parameters.

- ROUTINE INIrIALIZATION

This routine reads the values of the initial conditions

chosen by the user and ititializas all Global Variables

for the simulation run. It thin finds the probability

of each possible pair of aodes being source and

destination of a message, by using the input variables

'PR.ORIG' and 'PR.DEST' using probability's General

Multiplication rule. After that it stores these values

and the corresponding node names in the matrix

'P1IRS(A,BC)', where "A" is the probability of the

pair, "B" the source node, and '." the destination node.

- ROUTINE PRINT.INIT.CONDIIONS

This routine prints the initial setup of the network,

and values of the initial con'.itions chosen for the% simulation run.

- ROUTINE SELECT.MNODESThis routine selects & node-pair by picking a razdom

number uniformly distributed from 0.0 to 1.0, and

comparing it with all the node-pi-r probabilities listed

51

in an a ccummulat iv a fashion. Thea node roa:

corresponding to the probability range where the random

number falls, is selected. I: then assigns the numbe:

corresponlig to the row of tie matrix 'PAIRS' that

" contains the aode-pair selected, to the variable 'LOW'

and returns this value.

- ROUTINE TO PICK.BEST.LINK GIVEN N).DE, DE.ST

This routine selects the best outgoing link, given the

node where the packet is (I3.DE), and the packet

deszinatian (DE.ST). It first finds the value of the

routing fraction of each outgoing link of 'NO.DE' that

corresponds to the destination node 'DE.ST'. Selection

is then done by pizking a random number uniformly

distributed from 0.0 to 1.0 and matching it to the

values of the routing fractions found, listed in an

accummulativs fashion. The routing fraction that

corresponis to the range where the number falls,

determines the link to be used. The name of the link

chosen is returned as the value of the variable

B'ST.PCK'.-,ROUTINE TO SET. VIRTUAL .CIRCUII GIVEN START.NODE AND

END.NODE YIELDING IY' AND 'BE.LI'

This routine finds the Virtual Circuit for a message,

given its origin node (START.NDDE) and destination node

(END. NODE . To do this it calls the routine'PICK.BESr.LINK' with the values of 'START.NODE' and

'END.NODE', and sets a counter to 1. When the value of

'BST.PCK' is receiv ed back, it compares the

termination-node of that link with 'END.NODE'. If they

- do not coincide, it calls 'PICK.BEST.LINK' again, but

this time with the name of the termination-node of

IBST.PCKI and 1END.NODE1. It then increases the counterto 2. The process is repeated until the termination node

of 'BST.P::K', and with 'END.N3DE' are the same. The

52[-.

a. ' - ." ,- ,- ,- .- • - , -, o - , . • • . . ,. . . . - . . .- . . . .. . ... .4.4 , % . . .. . . - . - - . . - . . . . . . . . . . . . . .

number of links in the Virtual Circuit is then reur-- rcu-: -6-urned

as the value of the variable 'I', and the name of hs

succesive links cn the Virtual ircuit, as the values of

the array 'BE.LI'.

- ROUTINE PERIOD.REPORT

This routine calculates and prints th4 status and

statistical data of ths network, collected by the system

during a period. The starting time of a period is taken

from the variable ,LAST.PERIOD' (which is reset every

time this routine is sxecuted), and the ending time from

'TIME.V'. The ro utine 'RESTART.PERIOD.TOTALS',

reinitializes all the totals an variables used in each

period, so status and statistical data collected during

each period is independent of the rest.

- ROUTINE COLLECT.PERIOD.DATA

This routine calculates and outputs some period data to

'UNIT 9', for further graphing and/or analysis. The

starting time of a period is taKen from the variable

'LAST.PERIOD' (which is reset every time this routine is

executed), and the ending time from 'TIME.V'. The

'. routine 'RESTART.PERIOD.TOTALS', reinitializes all thetotals aad variables used ia each period, so data

collected during each period is independent of the rest.1'Unit 9' must be defined as one of the system units

(printer, tape, mass-storage, etc.), before the program

can run.

- ROUTINE RESrIRT. PERIOD.TOTALS

This routine reinitializes the totals and global

variables used in a period, and sets the period starting

time, every 'UP.TIME' seconds.

- EVENT NEW.MSG

This event calls the routine 'SELECT.NODES' and using

the value of 'LOW' returned by it, finds the origin and

destination nodes for the message from the corresponding

53

...

:'I., : . . . ... ..; ..:/ 4. :.;; . <.<:;::}. . . .,-,;.;,:-.-.-...-.- -.:...:.:

".. .. . . ...,

row of the matrix 'P&IRS'. Oaa= this is don- ths eveInt

picks a geometrically distributed random number,

following the procedure indicated in appendix A, and

uses it as the number of packets for this message.

If 'MO.DE = 1' has been selztad, the evert calls'PICK.BEST. LINK' (giving the source and destination

nodes of the message), to find the best outgoing link

(from the source noda). It -. en finds the number of

packets ia the Propagation Queue (queue where packets

are stored for a period equal to their transmission-timeover that link, to simula-e that they are been

transmitted) and the Status (c=lition that indicates if

a packet is being transmitted by the link) of this link,

and saves this information for further use. After doing

+his, it generates the packets indicated by 'NUM.PKTS',

and for each one, it creates a record wirh the name of

the scurce node and files it in the 'TRIP.RECORD' of the

packet. The event then files the packets in th. queue

of the outgoing link selected.

If 'MO.DE - 2 has been sel-cted, the event calls

S'SET.VIRTUAL.CIRCUIT' (giving the source and destination

nodes of the message), to fiad the Virtual Circuit for

the packets of the message. It than uses the first link

of 'BE.LI', as the the best outgoing link (from the

source node). rhe event then finds the number of packets

in the Propagation Queue and the S-.atus of this link,

and saves this information for farther use. After thisit creates each of thq packets indicated by 'INU.PKTS',

records the rest of their Virtual Circuit 4n their

'TRIP.RECORD', and files them in the queue of the link

selected.

When the process is completed, for any 'MO.DE' selected,

the event recalls the values of the Status and

Propagation Queue size of the link selected, and only if

54

I'.,' -. ,,-...' X ',, ;v,- ,-.-',.'..:-," * , ."-' '- -. -- -. •" - - .. . . . .- - - - .. . . ..'4', ,= ; -,., "gnA,,M ,, 2 .. _ :,., .. ,-, . , . , ,.. .. . ,. .; . o .,., .. , . . . .

*.

they were both zero (which meias no packet is currently

being transmitted by it or link is idle), schedulss an

event START.XMT for this link to be executed "NOW". It

..&s important to mention that events scheduled to be

executed NOW, within an event, are executed as soon as

. the event returns control to the timing routine. They

preceed events having the same avent-timu (time at which

they must be execu:ell, that may have been scheduled

before.

The event NEW. MSG then picks a random number

exponentially distributed as the new message

interarrival-time, ani schedules another avent NEW.•SG

at that time from now, if there is enough time before

. the end of the run. If there is not enough time left it

does not scheduled it. after this the ;event returns

contrcl to the Timing Routine.

-. EVENT START. XT GIVEN LI. NK

This event removes the first packet from the queue of

'LI.NK' and finds out its destination node. If this

node coincides with the termihation-node of 'LI.NK' It- schedules an event 'ARRIVAL' for this litk, in

transmission-time seconds from now. If they do not

coincide, it schedules an event 'XMT.END' for this link,

in transmission-time seconds froa now. After scheduling

one of these events, it files the packet in the

Propagation Queue of ILI.NK' a.d returns control to the

Timing Routine.

- EVENT END.XHT GIVEN XMT.LINK

This eve.r removes the packet from the propagation queue

of 'XMT.LINK'. If 'O.DE = 1' has been selected, itchecks if the termination-node 3f 'IXT.LINK' is equal to

any of the records of the packet's 'TRIP.REZDRD'. If so,

the packet has looped, ana the event collects

information about it, destroys the packet, and returns

.55

-.J

K. W-

control to the timing routine. If not, the event calls

'PICK.BEST.LINK' with the termination-node of 'XMT.LINK'

and the destiation node of the packet to find ths newbest cutgoing link. It then finds the number of packets

in the Propagation Queue and Status of this link, andsaves this information for furthar use. After doing

this, it creates a record with rha name of the

termination-node of OKKT.LINK', and filas i t in the

'TRIP.REC3RD' of the packet. rhe avent then files the

packet in the queue of the outgoing link salected.

If 'MO.DE = 2' has been selectad, the event reads the

next lirk of the pazket's Virtual Circuit from its

'TRIP. REMORD'. It then finds the number of packets in

the Propagation Queue and the Status of this link, and

savas this information for further use. After this, it

files the packet in the queue of that link.

When the process is complsted for any 'HO.DE' selected,

except fcr the case when the packet loopel in 'NO.DE =1' (in this case control has already bz.en returned to

the timing routine, and no furthar action is taken by

the event), the event recalls the values of the Status

and Propagation Queue size of the link selected, and

only if they ware both zero, which means no packet is

currently being transmitted by it (or link is idle),schedules an event START.Xmr for this link to be

executed "NOW". Finally the avqnt returns ccntrol to

the Timing Routine.- EVENT ARRIVAL GIVEN ARR.LNK

This event removes the first packet from the PropagationQueue of 'ARR.LNK', reccrds information about it and

destroys the packet.

- EVENT NEW.ROUT.FRkC

This event was added to allow for the further use of

this program, to investigate the behavior of the Routing

56

I. .. , , . ' '¢ ' .. : .',-' , . .. _"...- .. .. . .. .,. . . . . . • . .. .. . -. . . .

47

Fractions in a dynamic routing scheme. This can be

accomplished by inserting in this event, or calling from

it, a subroutine to recalculate the Routing Fractions.

To aid in this recalculation of the Routing Fractions,

this event collects information of queue length,

utilizatin per period (percentage of time the link is

busy per period) , and utilization per lap (percentags oftime the link is busy per lap), of every link.

The new subroutine can then use the information

collected by this event, and any of the global variables

of the prDgram like 'LNK.CAPA:-I]Y ° and 'CONNECTED', to

find the new routing fractions. By setting the value of

the variable 'UP.TIME', the event INEW.ROUT.FRACI can be

executed at any time 5uring the simulation run, when the

conditions in the network require it.

- EVENT LAP.TOTALS. RESET

This event reinitializes lap totals of the simulation,

every 'LLP.TThEI econis. The purpose of the lap totals

is to allow the simulation to keep statistics of link

utilization for arbitrary periols (laps) to be selected

by the user by setting the value of the variable

'LAP.TINR'. The ability to calculate link utilization

per lap was added to allow its use by the event

,NEW.ROUT.FRAC' when the dynamic case is analized.- EVENT N!T.REPORr

This event calculates and prints status and statistical

data of the simulation, up to the time it is performel.

Since variables and totals involved are rot reset duringthe run, every time this event is performed its

calculations are done for the period from time z4ro up

to the time of execution. This event is executed every

'REPT.TIME' seconds.

- EVENT DATA.COLLECTION

*4. 57

%.

.. This event calculates and outputs some simulation data

to 'UNIT 8' for further graphing and/or analysis. Since

variables and totals involved are not reset during the

. run, every time this event is performed its calculations

are done for the period from tixe zero up to the time of

.4 execution. 'Unit 8' must be defined as onq of the

system units (printer, tape, mass-storaga, etc.) , before

the program can run.

-EVENT DESTRICTION

This event cancels all events that rqmain scheduled for

execution in the Timing Routine. So after execu-ion of

this event, control of the program retu_-ns to statement

following 'START SIMULATION' in the 'MAIN' (or driver of

the program) , and the simulation can be ended.

1. SIMULATION OUTPUTS DESCRIPTION

The main purpose of any simulation is to provide a maans

tc observe and measure different parameters of interest, of

a process that resembles the actual bahavior of a specific' system. Thus an evaluation of its performance and other

important characterist-ics can be obtained, without the need

for a physical implementation of the system. To accomplish

this, five modules of our program whare designed to collect,

calculate and output information aboat the simulation run.4 They are:

-Routine ' PRINT.1NIT.CONDII:NS'

-Routine 'PERIOD. REPORT'-Routine 'COLLE-.PERIOD. D&Tk'

-Event 'NIT.REPORT'

-Ev ant 'DATA.COLLECTION'

- The following subsections describe the contents of outputs

generated by these modules, and include a brief explatation

of the names used in them (which zust be complemented byinformation given in previous sections of this chapter).

I FZj 58

'"In addition to these modules the program of Appendix F

was written to allow the graphing of data collected by the

event 'DATA.C3LLECTION' using the Disspla Graphics Software

. package. Sisilarly, the program of Appendix G allows

graphing of data collected by routine 'COLLECT. PERIOD. DATA'.A sample cf some of the plots these programs can produce is

shown in Appendix D.

The routine 'PEINT.INITIAL. CONDITIONS' performs two

functions. First, it prints a report of the network s9tup

and initial conditions of the sinulation (we will call it

"Initial Rsp rt "). Second, it outputs most of this

information to 'Unit 81 and 'Unit 9', for its further uss in

the graphing and/or analysis of ata collected by Evqnt

'DATA.COLLECTION' and Routine 'COLLECT.PERIOD.D&TA',

respectively. Units 8 and 9 can be any unit of the computer

* system used, previously defined by the user.

The report printed by this rouzine is divided in

four sections, which contain the following information:

a) A list of the following variables -hat control the

simulation indicating their values read by the program:

- NUMBER OF NODES

Number of nodes of the network, as indicated by the

input variable 'N.tIODE'.

- NUMBER OF LINKS

Number of links of the network, as indicated by the

input variable 'N.LINK'.

- DURATION OF SIMULATION

Time in seconds when the rua will stop, as indicated

by the input variable 'TIME.LI4IT'.

- REPORT GENERATION INTERVAL1W

Time interval between 'NET.REPORT' events inseconds, as indicated by the i.put variable

'REPT. rINE'.

59

42.

- ROUTING UPDATE INTERVAL

Time interval between *IEW.ROUT.FRAC' events in

seconds, as indicated by the input variable

'UP.TINE'. This is a provision for the future use

of the program in the analyisis of the dynamic case.

- DATA COLLECTION INTERVAL

Tim interval between 'DATA.COLLECTION' events in

seconds, as indicated by the input variable

-. 'COLL.INT'.

- LAP INTERVAL

Time interval between 'LAP.TOTALS.RESEV' events in

seconds, as indicated by the input variable

*LAP.TIBE'.

- PACKCT LENGTH

Length of packets in bits, as indicated by the input

variable 'LENGTH.PKT'.

. - AVG. MESSAGES PER SECOND FOR NETWORK

Avera;e number of messages-per-second for the

network, as indicated by the input variable

§¥VG.dPS.NET'.

- AVG. PACKETS PER NESSAGE FOR NETWORK

Average number of packets-per-message for the

network, as indicated by the iaput variable

". -. ' kVG.PKTS. BSG'.

-'PRINT CONDITION

Print condition for the run, as indicated by the

input variable 'PRNT'.

M"BODE SELECTED

Type of service to be provided by the network, asa,.

indicated by the input variable 'MO.DE'.

• b) A list of all the links in the network including theirF7 name, node origin, node destination, and capacity (in

bits per second) , as indicated by the input variables

'CONNECTED1, and 'LNK.C&PACITY'.

60

c) A list of the Routia; Fractions that have non-zero

values, influding the nodes to which they correspond, as

indicated by the input variable OROUT.FRALC'.d) A list of ths node pairs that have non-zero probability

of being selected as origin and de.stination of a message,

as calculated by the program frot the values of the input

variables 'PR.ORIG', and 'PR.DEST#.

Data output by this routine to 'Un it 8' of the system

includes the folloving:

- NUMBER OF NODES (same as Initial Report).

- NUMBER OF LINKS (same as Initial Report).

- NODE SELECTED (same as Initial Raport).

- PICKET LENGTH (same as Initial Report).

- AVG. MESSAGES PER SECOND FOR NETWORK (same as Ini-ial

Report).

- DURATION OF SIMULATION (same as Iaitial Report).- ROUTING UPDATE INTERVAL (same as Initial Report).

- LAP INTERVAL (same as Initial Report).

- DATA COLLECTION INTERVAL (same as Initial Report).

.. - AVG. PACKETS PER MESSAGE FOR NETWORK (same as Initial

Report).

Data output by this routine to 'Unit 9' of the system,

includes the same information indicated for 'Unit 8', except

for "DATA COLLECTION INTERVAL" which is not included.

"_a :'2 . L _U 9. J .R 21 T

The routine 'PERIOD.REPOar' collects sta-us and

statistical information during a period of -he simulaticn,

and prints it in a report-like format (we will call it"Period Report") . As mentioned before, information of each

period is independant from the rest, since the routineh -'. 'RESTART.PERIOD.TOrALS' r2.initializgs all the variables and

totals involved. This report is divided in thq following, P4three sections:

61

% .. ....

a) A list of all the links In the network (including -heir

origin and destination nodes for ease of identification),

indicating their period utilization (proportion of time

being involved in transmission or "busy") ; the mean,

maximum value, and standard deviation of their "queue

size" for the period; and the present size of their queue

and propagation queue.

b) A list of the status and statistics of the network, which

includes the following information:

- AVERAGE LINK UTILIZATION

Average calculated using the "1in k utilization"

values of all links, for ths period. Its worth

noting that a value of 'MAXIMUM LINK UTILIZATION' isnot included as a periodical statistic, because for

any useful analysis the traffic load usel will cause

this quantity to be 1.0 for most periods, and

therefore it loses its significance.

- AVERAGE QUEUE SIZE

Average calculated using the "mean queue size" of

all links (in packets) , for the perio4.

- MAXIMUM QUEUE SIZE

Is the largest value observed, of the "queue size"

of all links (in packets), during the period.

- STD.DEV. OF QUEUE SIZE

Is the average value of the "standard deviation" of

the "gueug size" of all links, for the period.

- NUMBER OF MESSAGES GENERATED (For the period).

- NUMBER OF PACKETS GENERATED (For the period).

- AVERAGE PACKETS PER MESSAGE (For the period).

- NUMBER OF PACKETS COMPLETED TRIP (During the period).

- NUMBER OF PACKETS THAT LOOPED (During the period).

- TOTAL NUMBER OF PACKETS STILL IN NETWORK (At the end of

the period).

62

po"e

c) A list of statistics of the packets that arrived tc their

destinatiom during the periol which includes the

following information:

- AVG. LENGTH OF TRIP

Average of "trip length" values of all packers that

arrived to their final destination during the

period, .In "hops".

- AVG. TOTAL TRIP TIME

Average of "trip time" values of all packets that

arrived to their final destinalicn during the

periol, in seconds.

- AVG. TIME SPENT IN QUEUE

Average of "mean time spent in queue" values of all

packets that arrived to their final destination

during the period, in seconls.

- AVG. TIME PER HOP

Average of "mean time per hop" values of all packets

that arrived to their final destination during the

period, in seconds.

3. PERIOD 2A&

The routine 'COLLECT.PERIOD.DATA' collects status

and statistizal information during a period of the

simulation (we will call it "Perial Data"), and outputs it

to 'UNIT 9', for its further graph and/or analysis. As in

the case of Period Report, information of each period is

independent from the rest. Data collected and output by

this routine corresponds to the following information:

- Time of execution of the routin (or end of the period),

in seconds.

- TOTAL NUMBER OF PACKETS STILL IN NETWORK (Same as Period

Report).AVERAGE LINK UTILIZATION (Same as Pariod Raport).

-AVERGE QUEUE SIZE (Same as Perlol Report).

-MAXIAum QUEUE SIZE (Same as Period Report).

63

- AVG. LENGTH OF rRIP (Same as Period Report)

- AVG. TOTAL TRIP TIME (Same as Period Report).

- AVG. TIME SPENT IN QUEUE (Same as Period report).

A - NUMBER OF P&CKETS THAT L3OPED (Same as Period Report)

4. NEWORK REPORT

The event 'NET.REPORT'• when execu t ed, collects

status and statistical information about the simulation and

prints a report (we will call it "Network Report"), that

rasembles the Period Report. The main difference be ween

this two reports is the time frame used to compute the data

used by them. While for Period Report variables and totals

used are reset at the end of each period, for Network Report

they are never reset. In consecuenze, each Network Report

% ccntains information for the "period" from time zero (start

cf simulaticon , up to its execution time.

The Network Report is divided in thres sections,

which contain the following information:

a) A list of all the links in the network (including their

origin and destination nodes for ease of identification)

indicating thei.r u-ilizition up to now; th. me-an, maximum

value, and standard deviation of their "queue size" up to

now; and the present size of their queue and propagation

queue.

b) A list of the status ani statistics of the ne.twork, which

includes the following information:

- AVERAGE LINK UTILIZATION

Average calculated using the "link utilization"

values of all links, up to now.

- MAXIMUM LINK UTILIZATIONLarges. value observed, of the "Link Utilization"

for all links, up to now.

- AVERAGE 2UEUE SIZE

I6

:- ,. .-%:.- -.-. .. ,.-'%"-" ..- ,. .' .', -. -'. ",.,, . " "%"% % .- .- ,-., . . ,- . -, -%-. . . .- -.. . .- -

A' vera~e calculated using the ,,imean queue si zq,, of

'--p .-

-- all links (in packets), up to now.i - MAXIMUM QUEUE SIZE

" The largest value obs.erved, of hro "queue size" of';:'all links (in packets) , up to now.

9 .

. - .- STD.DEV. OF QUEUE SIZE9.m -The average value of the "standad daviaio " of sihze

"lueu siz " of all links, p to now.

, - NUMBER OF MESSAGES GENERATED (Up -to --ow)•T .- NUMBER OF PACKETS GENERATED (Up to now)•.

- AVERAGE PACKETS PER MESSAGE (Up to now).

-", '- NUMBER OF PACKETS COMPLETED TRIP (Up to now)•% - NUMBER OF PACKETS THAr LOOPED (Up to now).

- TOTAL NUMBER OF PACKETS STILL IN NETWORK (Up to now)

w - AVERAGE PACKETS IN THE NETWOORK (Up to now).c) A lis of statistics cf the packts that arived to thei_

destination up to now, which includes the following

' ;"- information:S- AVG. LENSTH OF TRIP

/ ',Average of "trip length" values of all packets that• .arrive.d to their final destination up to n.ow, in

.4.

- . "ho ps"'- AVG. TOTAL TRIP TIME

he"Average of "trip time" values of all packets thae

.9-

aerived to hair final dsinaa.ion up to now, in

': second s.

. - AVG. TIME SPENT IN QUEUE. ,..Average of "1mean time spent in queue,$ values of all- " packets -hat ar.-ived to their final !c-stiration up

- N"Bo now, in seconds- AVG TIME PER HOP

; Average of "mean time- per hap" values of all packe.ts-NMERthat Oarived -o thAir final destination up 3 now,

°"" 65

-9,.. >i ,.- ', 'i ,.- ''''',,';,,, .. ' ... ,..,.,. - , " . ' " .-,-".-•-"-•-"-"-", . ,.'. - . - - .... , . : , . - ,.-. . -. -.-. . . .: .- . . . .-. . '."

5~~. _NETWORK DATA

As in the case of the Natwork Report, the event

'DATA.COLLECTION' when executed, collects status and

statistical information of the simalation (we will call it

"Network Data") , for the "period" from -time zsro (start of

simulation) , up to its ex'cution tize. It then outputs this

data to 'UNIT 8', for its further graphing and/or analysis.

Data collected and output by this routine corzesponds to the

following information:

- - Time of exe-ution of the event, in seconds.

... - TOTAL NUMBER OF PACKETS STILL IN NETWORK (Same as Network

Report).

- AVERAGE LINK UTILIZATION (Same as Network Report).

- AVERAGE QUEUE SIZE (Same as Network Report)

- MAXIMUM QUEUE SIZE (Same as Network Report).

- AVG. LENGTH OF TRIP (Same as Network Report).

- AVG. TOTAL TRIP TIME (Same as Network Report).

- AVG. TIME SPENT IN QUEUE (Same as Network Report).

- - NUMBER OF PACKETS THAT LJOPED (Saie as Network Report).

- MAXIMUM LINK UTILIZATION (Same as Hetwork Report).

- AVERAGE PACKETS IN THE NETWORK (Same as Network Report)

* % .-

-a

p.-%. .6

-4 e

. . . . ~ i -A , ' [ ? ,r+ + , + , +" , , T -

,... . . .. . . . . . .

-.

T. CONCLUSIONS iND REC3MENDTIOIS

A. CONCLUSIONS

The simulation was run at diffr ent traffic loads, which

allowed us to determine the maximum load that the

routing-fraction protocol could handle with this network

configuration before saturating (we will call it satura-ion

load). As shown in Figure D. 1 of Appendix D, for the

uniformly distributed traffic case with all link capacities

set to 20,000 bits-per-s.cond, saturazion load was found to

be 440 packets-per-second into the network. This load was

then generated usin difeen egrees of traffic_granularity, i.e., differEnt combinations of

messages-psr-second and packets-per-message (both for the

network).

As shown in table 1, for -ha different degrees of

traffic granularity tested (fo: the saturation load

maintained at the same level) the _anning average of packets

in the network, total time delay of packets that completed

trip, average time spent in queue of packets that completed

trip, and average queue size, where found to increase

proportionally with the number of packets-per-message.

The maximum link utilization for the aetwork was

observed to decrease by a very small amount as we increased

the number of packets-per-message. This reduction in link

utilization is caused by the time fiztor that is included in

its calculation (link utilization represents the propor-ion

of time a link is involved in trzasmislon of packets or

"busy"), and the lower average namber of messages received

by the nodes for the same period. As we increase the number

of packets-per-message while keepi.ng the same saturation

67

*.--°- -* --- * & iIi~ ii:::

ABLE I

GRANULARITY COMPARISON

ROUTING FRACTIONS

(440 msg/sec 223 msg/sec 110 msg/secpkt/msg 2 pkt/msg 4 pkt 'msg

RUNNING AVERAGEPKTS IN 116.17 252.04 468.06NETWORK(in pkts)

TOTAL TIMEDELAY PKTS 0.260 0.562 1.056

COMPLETING TRIP(in secs)

AVERAGE TIMEIN UUEUE PKTS 0.164 3.466 0.962COm LETING TRIP

(in secs)

AVERAGE QUEUESIZE 1.22 3.48 7.09

(in pkts)

level, we reluce the number of messages-per-second into -.he

network. These changas will inzrease the message

interarrival-time which is exponentially distributed with

mean: ( 1 / messages-per-second ). In addition for the same

period, fewer nodes will receive new messages. The final

effect is that on the average, there will be an increase inthe time queues will be empty waiting for a new packet to

%arrive, aid maximum link utilization will be slightly lower.

The running average number of packets in the network at

the saturation level, for the different degrees of

granularity, was found to be apr ximatelly equal to the

theoretical value given by Little's formula [Ref. 29], which

states that:

E(N) - E(T) x L

where:

E(N): Average value of packets i the network.

68

•.

E(T) : Average value of time delay.

L : Average packets per second entering the network.

This results zonfirm that the proto.-ol behaves correctly for

different traffic situations and conforms with the

theoretical values expected.

A series of tests where perforaed using unbalanced

traffic generation patterns, to investigat e protocol

performance under these conditions. The results of cours-

showed that for unbalanced traffic situations performance

degraded, due to the use of routi.ng fractions which where

calculated for a different (uniforaly distributed) traffic

load.

For the static routing case, than, an estimation of the

traffic distribution is of primary impcrtance if routing

*fractions are to be used, since the procedure used for their

calculation will render a set of routing fractions which areoptimal only for that traffic distribution. This result

4allows us to anticipate that for the dynamic case (where

recalculation of the routing fractions to be used by the

protocol will oe done when variations in traffic

characteristics or topology in the network warrant it), the

protocol should render as good r.esults as for the static

case, since this recalculation prcDedure will maintain the

routing fractions suited for existing conditions in the

network. The main consideration will then be to determine

when this routing fraction recalculation should be done.

A minimum number of hops (minimum-hops) , single-path,

static routing protocol was also calculated, as indicated in

Appendix C. Simulation runs where performed for the

minimum-hops and routing-fraction protocols under the same.S- conditions to determine their relative performance. Results

showed that the maximum load that the minimum-hops protocol

could handle before saturation was 335 packets-psr-second

69

- % 6 9

into the network (see Figure D.2 of Appendix D) . This load

is 23% lower than the one found for the routing-frac-on

protocol.

As shown in Table II and Figures D.3 to D.5 of Appendix

D, performance of the routing-fraztion protocol for the 335

packets-per-second load was found to be significantly better

than the performance of the minimum-hops protocol with the

same traffic load.

'p

TABLE II

PERFORIA CE COMPARISON

.4.'

ROUTING MINIMUMFRACTION HOPS

335 msqs-=z 335 msg/sec1 pktl.-msg 1 pkt/meg

RUNNIN3 AVERAGEPKTS IN 50.31 102.34PETWOR K(in pkts)

TOTAL TIMEDELAY PKrS 0.148 0.301

COMPLETING TRIP(in secs)

AVERAGE TIMEIN QUEUE PKTS 0.052 0.211CO LETING TRIP

(in secs)

AVERAGE QUEUESIZE 0.297 .198

(in pkts)

From the different status ani statistical infora-.ion

gathered by the events and routines of the simulat ion

program, the "Running Average of Packets in the Network",

"$Average Total Trip Time", "Average Time in Queue", and

"Average Queue Size", where found to give the b-st

indication of the way the protocol handled the -raffic

70

. ." .-.* v..,*. . , ..*',%

**7o -. 6 - .v

during the simulation, and therefore were prefsred as

performance measures and for comparison between pro-occis.

In a similar way "Maxiaa m Link Utilization" and "Tozal

Number of Packets Still in the Network", gave us a better

indication of the maximum traffic loads the routing protocol

could handle.In addition "Number of Packets that Completed

Trip" when compared with "Number of Packets Generated"

indicated the protocclfs throughput performance.Throughout our research the use of the graphing programs

of Appendix F and Appendix G proved to be extremely useful

since they provided an excellent means of visualizing and

comparing large amounts of information. A sample output ofsome of the plots these programs can produce is shown in

Appendix D.

A comparison was done between the virtual circuit

service and datagram service configurations. For thiscomparison we used the successive saturation set of routingfracticns, uniformly distributel traffic and link capacities

set to 20,000 bits-per-second. Results showed that there isno significant difference between th.3 two. This similarity

is explained by the fact that the routing fractions usedremain fixed throughout the simulatior, run and thus no

difference is introduced by select-.ag the complete route of

the message at the time it is generated.

All the tests mentioned previously where done using a

set of routing fractions generated by the Successive

Saturation method. As indicated in Chapter III Section E,

another way of calculating routing fractions is the Maximum

Slack method. In order to determine their relative

performance, several simulation tests where performed using

routing fractions calculated by the Successive Saturation

method, and then repeated under the same conditions using

routing fractions calculated by the Maximum Slack method.

71

% %'..

Results showed that for a networkwith excess carrying

capacity, i.e., traffic load much lower than the satu-aion

load, the Maximum Slack set of routing fractions performed

equally to the Successive Saturatioa set. For the case of

traffic load near the saturation load, the SuccessiveV..-Saturation set performed better, and even gave a higher

level of saturation load. This difference ia performance is

explained by the fact that when calculating the routing

fractions using the 3aximum Slack aethod, we maximiz- tho

sum of the slack saturatioa-ratio 3f all links, which tands

to saturate more the links with higher capacity. In

contrast, in the Successive Saturation method we tend to

distribute saturation more uniformly among the links.

The maximum-slack routing fractions will therefore tend

to use the excess capacity of the network, when there is

some, and its performance then approaches that of the

successive-saturation set. When there is no excess capacity

in the network (near the saturation load) , the routing

fractions calculated by th- successive-saturation method

make better use of the available capicity, by spreading the

traffic more uniformly over the network, ani thus have a

V better performance.

Comparison was also made between the maximum slack set

of routing fractions and the miniaum-hops protocol. The

saturation load of maximum-slack routing fractions was 420packets-per-second, while for minizuam-hops protocol it was

335 packets-per-second, which is 191 lower than the former.

Is shown in Table III, for the 335 packets-per-second load

we found that the maximum slack set of routing fractions

also rendered a much better performance than the

minimum-hops protocol.

From thase results w ma Y conclude that the

routing-fraction protocol is a much better alternative for

static routing applications than :he minimum-hops, single

72

%:; /

T& BLE III

PERPFORMA CE COMPARISON

MAXIMUM MINIMUMSLACK HOPS

335 usg/saz 335 sg/sec1 pkt/msg 1 pk'.Zmsg

RUNNINE AVERAGE 123PKTS IN 49.77 102.34.ETWOR K

(n pkts)! TOTAL TIME

S. DELAY PKTS 0.146 0.301COMPLET ING TRIP(n s sCS)

9~~ AVERAGE TIMEIN QUEUZ PKTS 0.052 0.211CO PLETING TRIP

(in s cs)

AVIRAGE QUEUESIZE 0. 297 1. 198':>2(in pkts)

path routing protocol. In ailition, the successive

. saturation method should always be used when working with

. traffic loads that are close to the saturation load, and themaximum slack method shoald only be used when there is

enough excess capacity in the network (compared to the

. saturation load), or when simplicity in the calculation isrequired.

B. RECOMMENDaTIONS FOR FUTURE STUDY

The present study was done kepiag in mind the futurg

use of some of its contents for the investiga'!on of the

performance of routing fractions in a dynamic routingapplication. additicns have been made, when possible, of

'A mechanisms that will facilitate this future work.

Furthermore, provisions have been made in the simulation

73

program, to allow for the insertion of a subprogram to

recalculate the values of the routin; fractions.For the analysis of the static case, status and

statistical information was obtained mainly from events

IET.REPORT ° and 'DATA.COLLECTION', which use a time basis

V." f-om the start of the simulation up to event execution time

("total-time") . In contrast data from routines

'PERIOD.REPORE' and 'COLLEZT.PERIOD.DATA', which use a time

basis from the start of period to tie end of the same ppriod

("period-time") , was used mostly for validation of

total-time data. Nevertheless we 4ave designed the latter

with similar capabilities for gathering status and

statistical information about the simulation as the former.

This is because we expect the periol-time data to become the

preferad scurce of information for the analysis of the

dynamic case, given the periodical nature of its process.

we can also anticipate that tha jueue size and link

utilization measurements will play an impcrtant rol in the

decision cf when to recalctlate the values of the routing

fractions, since their values directly reflect when a link

is being saturated.

The built-in capability of the simulation program to

configure the network to provide virtual Circuit service

should also become an important subject of investigation for

the dynamic cise. This aspect bezomas more evident if we

recognize that for this case routing fractions will change

their values.from time to time, and thus mixtures of virtual

circuits created using different sets of routing fractionswill exist qimultanecusly in the network, the interactions

among which should be studied.

rem

744

-S.j

.- ..

GENlERAIONI OF GBOHBTRTCALLY DISTRIBUTED NUMlBER OF PACKETS

The Geome3tric distribution is closelyv rela-ed to the

Binomial distribution. The variiole in the Geometric

distribution is the number of triils preceding the first

success, in a sequence of indepealant. Binomial trials with

probabilityv Df occurence equal to "1pit. I -s probability

densityv function QPDF) is:

X-1

p ( 1 - p) for x = 1, 2, 3...

0 otherwise

The mean of the Gecmet-iz distribation is (1/p) and the

variance (1-p) /p2. A G eometrical ly distributed random

number can be generated diractlyv from a standard

un~iformly-distributed numb-er, byv mappiag It to the Geometric

cammulative distribution function (CDP). 1 he CDP of the.

Geometric distribution is:

1 - (1-p) for x = 1, 2p 3,r...

0 for x < 1

Let "y" be a number uniformly ditribu-ted between 0.0 and1.0, then:

x

-0a0

lr(1 -Y)- x ln(I- P)

x l n (1-y) / ln(1-p)

75I~L

GEI LSIQ OF~ N1v Gj"TIAL ITItJE ~BRO AKT

Since "y" is uniformly distributed from 0.0 to 1.0, then

(1-y) will also be uniformly distributed from 0.0 to 1.0,

therefore:

, x = in(y) / ln(1-pI

We must then round "x" to the closest integer that is higher

or equal to it (since the Geometric is a di screte

distribution), to get the value of the random number we are

looking for.

To determine the number of pik.ts fo- each message

generated during the simulation run, we follow this

procedure, and assign the value of the number obtained to

the variable 'NUM.PKTS'. This variable is then used by the

program, to zontrol the number of pdckets generated for the

message.

-A.

.7

: -76

_'I..-...x

.. LINK ILE SSIGINEIT

LINK NO DE NODENAME ORIG rERMINATION

2 1 33 1 44 1 55 2 16 2 37 2 68 2 99 3 1

10 3 211 3412 3 613 3 71l4 4 115 4 316 4 517 4 718 4 819 5 120 5 421 5 822 5 1223 6 224 6 325 6 726 6 927 6 1028 7 329 7 430 7 631 7 831 7 103 ~ 7 1134 8 435 8 536 8 737 8 1138 8 1239 9 240 9 641 9 1042 9 13413 10 644 1 0 7

4- 6 10 11, r,, 47 1 0 1 3

4:: 9 11 850 1 1 10: : :51 1 1 1 2

., : . .5 2 1 1 1 3. ,.5 3 1 2 5

,a54 !12 855 12 11

;...v56 12 17

Moov

57 13 958 13 1059 13 1160 13 12

o. .

.8

,..

-a

',

N...

% r .%

-4'8

.4%.,. . , , .- ,€:''"o ."... .% r:.,.,,,.., ,..,,.,,,.. .% . . ... ,(. -"-% . -". '. ."." '. ,"-"." '.' . .",

KII5MNMBRO HOPS SINGLE PATH ROUTING TABLE

To calculate the values of -a min.imum number of hops

*(minimum-hops) single path routing table for the network of

our study (sea Figure 4.1 of Chapter IV) , where all links

havs equal weight, we used the networks symme-ry to SiMD1±fy

the procedure. We therefore diviled the process into ohe

f llowing 4 steps:

1) Find the sink-tree (sezt of rcares for packets from all

nodes to the node selezcted) for one of the nodes

located at the external ver-tices o-f the network. The

resulting sink-tree shown in Figure C.1, can then be

transformed into a sink-tree for the rest1 of the nodes

located at external vertices of t-he network, by simply

rotating

2) Repeat the procedure mantioned before bu this time for

nodes located at internal vertices of the network. The

resulting sik-tree is shown at Figure C.2.

*

3) F.Ind the sink-tree for the node located at the center of

the network. The resulting tree Is shown in Figure

C.3.4l) Using the foregoing sink-tres construct the

corresponding routing table. rhe resulting table is

shown in Table IV The left column indicates the

- sending node, the upper row indicates the destination

node, and the contents of the table indicates the nodevia which traffic has to be sent.

79

"""lctd. 5enlv.tie ft ntok ysml

roatn iv

*:,- .r.. .., * r . - ..-. ,.-, .. .. .... .. -., .*_ .,.. ,. , . - .. .;.o-;,- _ . -? >_..X -. . .t 3 .. t. ._. .?

NETWORK

95-

%*4,

Figure C.1 SINK-TREE FOR EXTERN&L VERTICES.

80

,S.. ,> "",' ; IX ,",", , , .' .,.> '',,. ,,. . . . , . .. ". ," . . ' .. v v "... . . .,,' ,".

-NETWORK

FLOW

FiueC2 SNaTE O NERA ETCS

-'S1

NETWORK

SFLOWS

.- -

Figure C.3 SINK-TREE FDR CENTRAL NODE.

82

*~~~~~k ?U...S

dWI -f * . W7* A7 I 2 . ~2. :, .- - T7. -7

ABLE IV

ROUTING TABLE

FROM TO NODE

NODE 1 2 3 4 5 6 7 8 9 10 11 12 13

1 - 2 3 4 5 2 3 5 2 2 5 5 2

2 1 - 3 1 1 6 6 1 9 9 9 9 9

3 1 2 - L 4 6 7 4 6 6 7 4 7

4 1 3 3 - 5 3 7 8 7 7 8 8 8

5 1 1 1 4 - 1 4 3 1 12 12 12 12

6 3 2 3 3 3 - 7 7 9 10 10 7 10

7 4 3 3 4 8 6 - 8 6 10 11 11 10

8 4 7 4 4 5 7 7 - 11 11 11 12 11

9 2 2 2 2 13 6 10 13 - 10 13 13 13

10 6 6 6 7 7 6 7 11 9 - 11 11 13

11 7 10 7 8 8 10 7 8 10 10 - 12 13

12 5 5 5 5 5 13 8 8 13 13 11 - 13

13 12 9 9 12 12 9 11 12 9 10 11 12 -

83

W4 PP IEDT

GRAPHIC REPRESENT&TION OF DATA COLLECTED DURING SIMULATION

The following plots where obtained using the graphing

programs of kppendixes E and F. Due to space constraints

only the most important data is shown plotted.

-"-1 Figure D. 1 shows the number if packets st ll in the

. network for '440 packets-per-second (satuzation load), and

460 packets-per-second (highe- than satu-ation load) for -he

routing-fraction protocol.

Figure D.2 shows the number of packets still in the

network for 335 packets-par-second (saturati-on load), and

350 packets-par-second (higher than saturation load) for ths

minimum number of hops (miaimum-hopsi protocol.

Figures D.3 to D.6 represent a graphic comparison of

data collected during simulation of the routing-fraction and

minimum-hops protocols, for the 335 packets-per-second load.

The upper plot of each figur. corresponds to data from the

routing-fraction protocol, and the lower plot to data from

the minimum-hops protocol.

6% %

. 84

i* V

-<.4-.*.\., ,,,

P=cKET STILL IN NETOR

I 4 - - --t CONOITIONS 07 SIMIJLTION

- M.e-' Ors . NODES : 13

NL*OWE 0r LINKS ' 60-RVG MESS PER S C: 440.00

". - RVS PACKETS PER MSG.: 1.00f. PA K T LENGTH s 100 BITS

SERVICE t ORTRGtM

ORRT0ON Or RUNt 170.0OESCS

- - UPORTC NTRVAL -20.OOSCCS

0.0 11.0 ;.0 S1. . 0 wl 0. 0 18. 0 l a. ix I . 0,! TtI (SECS)

P...CETS STILL IN NETWORK

I i[ N PKBO'NI or SIUATO

r MAW L' Or LINS t60

.. , /PACKET L[NG;. , tI O aeI S

-- : OUDMI CN OF guNt 170.O0 5E"S

-do-

S1.0 * .0 64.0 n US 0.0 10.0 111.0 33.0 13.0 IM0.TIME ISCCS)

NIP. -% Figure D.1 ~~PROTS STILL IN NEWOKFOTOUIG-RCTO POOCL

.% tJWR-NOES11

°GAGCTP.n,. 20

- --. PAKTTENOT a 000SIT

.85Cp'G

",---ll-

"" ." , , ." " " -" . ." -" ." " " ." . ' , .- ' " " , " " " " , , " - " . . ," " " -" ", ' . " - - -, ." . . .-a- -• ' . . . . # " "5- - - - - - -'- .., . '. -' .. . .. . , , -' -. -" , --: - . ." , " -- . , • .- . , , ., .'

Pfl*CTS STILL IN NCTNM

- - - . - - OMITIONS Or SIMULATION

KM oNU r' N0 0C5 s 13

• ~IMBR OW INKIS : 60o' - -G M'SSGES PR SCCz 335.00

a~V PACET p Fxr ER t SL: 1.00

K - -- - - PAOCCT LENGTH i 2000 8173

S* E ScRVIC

0IMAIGN Of RUDt 170.OOSMC5

- -UPD INTRVAL t 20.005=ct LAP INTERVAL a10.0 .OSCCS

0.0 7.0 34.0 13.0 U.0 n.0 10.0 li.G 11.0 153.0 170.0TIME ISEC

- - - - - OWOTIONS Cr SILtLATION

K-------------------------- ------- ------------

NU W Or LIP NS t 60

--- -I -VG MESSAGES PER SM. 350.00* AVS PACKETS PER M1SG., 1.00

too PACKET LENGTH : 1OO1ITS

* SERVIC t DATAGRR"DURtATION Wr Rul: 170.005C05LR INTERV. I0.0OSCCS

.. 0 37.0 4.0 S 0. 05.0 t0.0 111.0 L.0 353.3 ' .o

Figure D.2 PKTS. STILL IN NETWORK FOR MINIMUM-HOPS PROTOCOL.

":". .

Q.74

86

%.-*

rpo1E STILL. IN ICT5MM

'.5.~ --------------------------

S. MISCR Or LINKS s 60I - -- - - MVISIAGCS PER SM 335.00

AMG PACKCTS PER HI.i t1.00

PCT LENTH : 1000 BITSSERVIM ORTAWMI

- - --- ------- ---- DURTION Or "s~ 170.00SMC

AM I~nA - .0'

TIMC (MM~I

at CODTOSOr3qLT

£~~~~ - ------ - -------- WEOTOES£1

a NUMBER Or* LINK~S 60I ~ ~ ~ ~ ~ ~ t -- - - - VSSfaGsP" scca 335.00* AVMG PACKETS PER 115.t 1.00

.5 PACKET LDNGTh & 1000 BITS

V.,DURATION or RUta 170.00WEC

UPOATC INTERVALt 20.OOSCCSLAP INTERMI. 10I.O0SEES

'%

3.3 3.0 $@.a 51.40 .0 M.11 20.0 111.0 330.0 13.0 1M.6

Figure D. 3 COMPARISON OF PACKETS STILL IN THE NETWORK,

5 87

L.Pq

<.1w

CMQITIOM 7 SIILTIO4

NOW Of LINKS s6W-r6 AiI55 C5 PCRtSEC: 35.00

gF114 PFIKETS PER M. 1 1.00* PftxcT LDWTh I Iwo0 BITS

too OKTION Or RUN: 170.00WMIPCATE INTERVWI. s 20.00WEC

- - -- - - - - - - IP INTERVFL. 10:.oosccs

0.6 11. 240 1.0 0.0 *. l34.0 11.0 3:1.0 353.0 Me0

TINC tsccSI

lInimtLINKJSUraRt VC NCTWeORK

-O Or LIS t 60

%AVG PrCKETS PCR WA5.: 1.00

4. - PKICET LNGTHs 1000 BITS

- - 1 UNAITION OrRI"s3I7O:OO0SS- - ifM IkTRVL s 2O.OSCM

0. t3 0 34.0 13.0 U0.0 E-0 12-00 11.0 133.0 133.0 10.0

FiguIre 0.4 COBPABISOK OF HAZINUMr LINK USAGE POR THE NETWORK.

Los

88

''a T

~~CONDOITIONIS O1r S]IMTION~

'9L O F" or ("WES 13

ISER Or LINKSC W6NVPiAKETS PER mSS.I 1.00

pfo= a tO00 t O TS

SERVICE I tTFA1W- I oION or RNU 174.30.M0 C!

OtTIR Ivt.A 20.coSL INTERVALI 10.QO0sm

L . . . . i I -.-- _B ar2 C

,.,..O* . 0 1 1 .0 B a a M ,IS m a~ I . O 11 l.0 I5 . , 31 3.0 l iS A l

TIMC ISEcl

.. wmam Q=u LW"m ral tcMcM

i ] COMN Or IITLAN

-. ,.-.. W Nooc : 13

MR W Or LIKiS 60- -- - - - - -CSSfacs PERSCC: 35-5.

M'G PACKTS PER MA.: 1.00PAKET .LW M 9 1000 ITS

S-, . .SERVICE a OfiTAGANI

U.JATION or UttNS 170.OOSC!- -- - - -UPDATE INTEVAL s2.SCCS

LI? INTERVAL 3 10.005SCS

.. I

- " so al a If. e 11 51 A IL .0 102.0 &11.0 35. 113.0 I1.rem TilE SC I

Figure D.5 COHP&RISON OF AVERAGE 2UE5E LENGTH FOR THE NETWORK.

89

. , ; ... - .. ,., .. ,;- . . . . , , ,, . , .-.- . . . . . . . . . . . .". - .:-" - :- -* .. * ,,, 'a *'-a, ,.-,. ,.,-..'.;,'.,-,&.,'a. " - ;.",-, .;, . .. , .'/ .. .-. -..- ,.-..,,.-

RVEC ELR MW rl LCPI-TR1IP PrICCIS

WSW Of LINKCS t 60

- - - - - VIPCSSNCS PCR SMC 335.00N - -- --- ----- --- AW PRCETS PCRt WA5.s 1.00

-. POCT LCNMT s 1000 BITS

oDrR10 Or RUN. 170.OOSCCSS- - LFRIMt INTMRWW : 20.OOSMO

~- -- - - UP INTCRVFIL s 10.OOSCCS

---- - --------

e- 3WWkw11

0 J rLNSs6

0W ESGSPRSC 3.

64 ~ ~ ~ ~ ~ ~ V 174CT PERg MG.0 1.00SI. 160 4 r.@ :

4l~ UPCLA? INTRVA 2OL.CaSEPPWICE

V - - INERM 10.00SC3

8.4. 17gCU 34A 11.0 U.:600. 1. 110 I-~~~~TM - GNSGCmcSC:330

FiueD6 CMAIO fAG EA O OPEIGTI K

-LA~T 19IICi20

90OTL~&hm200BT

APPENDIX E

SIMULATION PROGRAM

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AD-R148 166 MULTIPLE PATH STATIC ROUTING PROTOCOLS FOR PRCKET 2/2SWITCHED NETI4ORKS(U) NARIR POSTGRADUATE SCHOOL MONTEREYCA H T SCHIANTARELLI SEP 83

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Dissertation, Naval Postgraduate Scbhol, Monterey, 1981.

14

INITIAL DISTRIBUTI39 LIST

Sl No. Copies

1. Defense Technical Informatioa Center 2Cameron *tati n 22314Alexandria, Virginia 22314

2. Library, Code 0142 2Naval Postgraduate SchoolMonterey, California 93943

3. Department Chairman, Code 62 1D~partmEnt of Electrical EngineeringNaval Post raduate SzhoclMonterey, California 93943

4. Prof. o. M. Vozencraft, Code 62Wn 3Department of Electrical EngineeringNaval Post graduate SchoolMonterey, California 93943

5. Lieutenant Commander Harry Tharnberry 2Peruvian NavyClemente X 135 San IsidroL ma, Pru

6. Lieutenant Colcnel Knon Sik Bak 1Korean &rmySHC Box 1328Naval Postgraduate SchoolMonterey, California 93943

7. Lieutenant Petros Magoulas 1Helenic Ai: Force41 Kilkis Street,Patras, Greece

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