gavish&hantler-ieee-1983-an algorithm for optimal route selection in sna networks.pdf

8/10/2019 Gavish&Hantler-IEEE-1983-An Algorithm for Optimal Route Selection in SNA Networks.pdf

1/8

1154 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-31, NO. 10 ,CTOBER983

[ 141 J .

K.DeRosa,

L.

H. Ozarow,

and L.

W . Weiner,

Efficient packet

satellite communications, f E E E

Trans . Comrnun.

vol. COM-27,

pp.1416-1422,Oct.1979.

[ 151

T .

Suda,H.Miyahara,

and

T. Hasegawa, Optimal

bandwidth

assignment on up- and downlinksf satellite

with

buffer capacity,

IEEE Trans. Com rn u n .

vol. COM-28, pp.

1808-1818,

Oct. 1980.

[

161

J .

F. Chang,

Packet

satellite

system

with

multiuplinks

and

priority

discipline,

IEEE Trans. Com jnun .

vol.COM-30,

Part 11,

pp.

1143-1 152, May 1982.

[

171

J .

F.

Chang nd

L.

Y.

Lu,

Highcapacity

low

delay

packet

switching via

a

processingsatellite,

in

Cot

R e c . , f n t . Con

Commun. , Philadelphia, PA, June 1982, pp. 1E.3.1-IE.3.5.

[

181 R.

V.

Churchill,

Complex

VariablesandApplications,

2nd

ed.

New

York:

McGraw-Hill, 1960.

An Algorithm for Optimal Route Selection

Networks

BEZALEL GAVISH

AND

SIDNEY L. HANTLER

in SNA

Absrract-The problem of selecting a single route for each class of

service and each pair of communicating nodes in an SNA network is

considered.Thenodes, inks,sets ofcandidateroutes,and raffic

characteristics are given. The goal is to select a set of routes which

minimizes the expected network enld-to-end queueing and transmis-

sion delay. Queueing is modeled as network

of M / M / I

queues which

leads to

a

nonlinear combinatorial optimization problem.

UsingLagrangeanrelaxationandsubgradientoptimization ech-

niques, we obtain a tight lower bound on the minimal expected delay

as well as sets

of

feasible solutions for the problem. An experimental

interactive ystemhas beenused Ito evaluate heprocedure; very

favorable results have been obtained on a variety of networks.

C

I. INTROD.UCTION

OMPUTER communicationnetworksare a vitalpart of

manyndustrial,overnmental,inancial,nd service

institutions.Theysupportan ncreasingvarietyof services.

Backbonenetworks odaycancontainfrom a few nodes o

hundreds of nodeswithmanyhosts upporting housands

of users.Most of thecommercially available networksand

network architectures such as DATAPAC [51

, [

28

1 ,

SNA

[2 2] , [2 5] , NPDN [3 4] , TRAIVSPAC [81, TELENET [351,

andTYMNET [3 0] , [3 6] have adopted a staticorsemidy-

namic routing method

in

which routes are defined at system

gene ration or at ession initiation for each pair f communicat-

Paper approved by the Editor

foI

Computer Communication

of

the

IEEE Communications Society for publication without oral presenta-

tion. Manuscript received October19, 1982.

B.

Gavish is with the Graduate School

of

Management, University

of

Rochester, Rochester,

N Y

14627.

S. L.

Hantler is with the

IBM

T.

J.

Watson Research Center, York-

town Heights,

N Y

10598.

ing nodes. The selection of these routes is o f p rime importan

in determining the response times experienced y users and has

a majorignificanceneasonable tilization f etwork

resources (nodebuffersand inkcapacities)whileproviding

reasonable service

to

users.

We consider theproblem

of

optimal oute election n

computerommunicationetworksnwhichhe

nodes

(hostsndommunicationontrollers),inks,inkrans-

mission speeds,ndxternalrafficnputharacteristics

are given. Messages origina te and erminate at nodes (source

and destination, respectively) and are transmitted from source

todestination hrough ntermediatenodes nd inks long

fixed outes,determinedat he ime of networkdefinition.

(Theroutesarestatic.) Messages in the netwo rk are charac-

terizedby class of ervice (e.g., inte rac tive ,batch, ecure),

and the set of messages of a pa rticular class of service at e ach

source/destination pair comprise a c ommodity. Givena sub-

set of all possible routes n he network, we select for each

commo dity one route over which all messages fo r tha t com-

modity will be routed. (The routing is nonbifurcated for each

commodity.)

The problem we are studying is tha t of selecting the opti-

mal set of routes for multicommodity

flow

in a network with

static, nonbifurcated routing. (Our motivation for concentrat-

ing on this case i s that most operational networks use a static

nonbifurcated routing.)

Messages entering the ne twork encoun ter delay due to the

finite transmission speed of the links and the resultant queue-

ing at intermediate nodes. The delay encountered by messages

depends

on

the hoiceof outes, ndourobjective is

to

selecthoseouteswhichminimizehe averageelay

of

messages in the network.

Following Kleinrock [2 6] , th e links are modeled as single

server queues with exponen tial service time distribution. The

0090-6778/83/1000-1154 01

.OO

1983 IEEE


2/8

GAVISH AND HANTLER: OPTIMAL ROUTE SELECTION

network is a set of such queues at which messages arrive with

aPoissonarrival rate and whose engths are chosen from an

exponentialdistributionwhich is identical for all ueues.

Nodes re ssumed to have infinite uffers ndinks re

assumed to have negligible propagation delay. The network de-

lay in such a model is a nonlinear function of link utilization

and he outing is assumed t o benonbifurcated.This eads

to an optimization problem whose formulation is a nonlinear

zero-one programming problem.

Previousresearch on routing n computer communication

networksbyFrankandChou [ lo ] , CantorandGerla [ 4 ] ,

and Bertsekas [3 ] has concentrated on th eprQblem of optimal

route selection n networks with bifurcated routing. This re-

sults in the formulation

of

a continuous programming problem

with a nonlinear objective function over a convex polyhedral

set.Theproblemhasbeensolvedusing echniquessuchas

thegradientprojection lgorithm, lowdeviation, nd he

extrema1 flows method. Gallager

[

121 proposed a distributed

algorithm

for

optimal outing

of

messages inanetwork n

which the traffic input character istics are slowly varying over

time ndnwhich messages of a single commoditymay

traverse different routes at any time. (This s quasi-static bifur-

cated routing.)

There is no published research which attempts to solve the

nonbifurcated oute election roblem ptimally.Courtois

and Semal

[6]

apply a modified version of the Cantor-Gerla

flow eviation lgorithm as a euristicn etworkswith

nonbifurcatedtaticouting.Theyestedheir rocedure

on avariety of networksand were able to generategood

solutions

for

lightly loaded networks.

In SNA networks,up oeightroutesareselectedatnet-

work definition time for each commodity. For each commod-

ity, hese outes reordered ndbecome he outesover

which llraffic orhat ommodity will travel. When a

conversation (session)of a oarticular class

of

service

is

initiated

by

a

user, the first active route in that list (Le., route whose

nodes and inks are working and available) s selected as the

route for all messages

of

tha t session. In this paper, we restrict

our attention to the problem

of

selecting the first rout e for

each commodity from a set of given candidates.Thisset of

candidatesmay nclude all legal SNA outesbetween he

source and destination or may be a suitably chosen subset.

The problem we address is combinator ial in nature, as can

beseen romasimpleexample.Suppose hereareat east

r routes n hecandidateset oreachcommodityand hat

there are

c

commodities in our example network. Then there

are

r c

possiblechoices for selecting the first route for each

commodity. In a typical small SNA network, we can expect

r

to

be about five and c

to

be about

200.

The problem con-

fronting the route planner in such a network is t o select the

optimal 200 routesrom monghe pproximately lo4'

choices

of 200

routes.

InSections I1 and 111 therouteselectionproblem

is

for-

mulated as a nonlinear zero-one integer programming problem.

In Section

IV ,

we ntroducea Lagrangean relaxationofour

problem.The elaxation

is

obtainedbydualizing ubset

of

theconstraints,and nSection

V

weshowhow t o use a

subgradient optimization procedure to move from one relaxa-

tion

to

another naneffort o mprove he esultant ower

bound for theprobl em. We show, inSection VI, how o

solve the elaxations, nSection VI1 weshowhowwe have

implemented his echnique n a system for network design,

and in Section VI11 we present some results of computational

tests. inally,weonclude y discussing openroblems

and suggesting further research.

11. PROBLEM FORMULATION

In order omodel heend-toenddelay n henetwork

we use assumptions that are commonly used in modeling the

queueing phenomena in computer networks. We assume that

links have a finite capacity for transmissions, that nodes have

unlimitedbuffers to to re messages waiting for ree inks,

and hat he arrival processof messages to he netw ork has

aPoissondistribution.To implify he exposition we also

assume that links have a negligible propagationdelay, hat

nodes have no message process ing delay , and hat here isa

single class of service for each pairof nodes.

The queueing and transmission delay of messages are mod-

eled as a network of

MIMI1

queues, in which links are treated

as servers whose service rate is proportional to link capacity,

messages are reated as customers whose waiting area is net-

worknodes. Using the ndependenceassumption Kleinrock

[ 2 7 ] ) , the ueueing ndransmission elay on link

is

l/(pQl

f l , where Q l is thecapacity of link 1 inbitsper

second, { l is th e arrival rate of messages to link 1 and /p

is the expected message length. This formula is used as a basis

for estimating the expected end-to-end delay in the network,

which is the weighted sum

of

the expected delays of the links

in the routes.

We introduce the following notation for the route selection

problem.

n Thendexet of theommunicatingource/

destination pairs (commodities) in the network.

Typically, this is a subset

of

the nodepairs.

L Thendexet

of

linksnhe etwork.

R Thendexet of candidateoutes.heet of

candidateoutesanerovidedysers,

generated by a route generation algorithm or a

combination

of

theseechniques.

A

route

is

characterized by he ordered set

of

links (from

source to destination) in the route.

used in router and is zero otherwise.

The

index set

of

candidate routes

or

commodity

p .

We assume th at if

p

hen

S,

n

S

=

qj.

6, l

An indicatorunctionwhich is one if link

1

is

S

z

The apacityofink inbitsper econd.

f r (or

{

The message arrival rate of the unique commod-

1 P Themean of thexponentialistributionrom

ity p associated with route

,

where

r

E S,.

which the lengthsof the messages are drawn.

selected for message routing and zero otherwise .

Xr Aecisionariablehich is one if route r is

Using theabovenotationweconclude hat he otalbit

arrival rateon ink

1

equals . ~ f r h r l x r / p . rom his,we

observe that the expected network delays

where

T =

ZpEnf, is th e otal arrival rat e of messages in

the network.

The route selection problem (problem IP) is t o find binary

variables x which satisfy

ZI P

= min

subject to


3/8

I156 IEEERANSACTIONSNOMMUNICATIONS, VOL. COM-31, NO.

10,

OCTOBER 1983

, = I

r E S p

x r = 0 or

1 V r E R.

The first constraint ensures hat he flow on each link does

notexceed tscapac ity, while theselection of exactly one

route per commodity is ensuredby he second and hird

constraints. Problem IP is a nonlinear combinatorial optimiza-

tion problem with constraint set identical to that of the multi-

ple choicemulticonstrained napsack roblem Sinha and

Zoltners [ 3 3 ] , Gavish andPirkul

[

18 ]) , which

is

known

to

be NP-complete.Theouteelection roblem has the

additional complication of having a nonlinear objective func-

tion, thus leading to a more difficult problem.

Research t o date on nonlinear combinatorial optimization

problems is quite limited to special cases such as the quadratic

assignmentproblemor to verysmallproblem sizes.Present

networkscontainup o 200 nodeswith housands of com-

munica ting node pairs tha t select routes from sets containing

from a few thousand to hundreds of thousands of candidate

routes, eading to very arge problem sizes. Future networks

will require the solution f significantly larger problems.

Several methods have beenconsidered as candidate s oi

solving problem IP. Takingadvantage of the act hat he

objective function in (1) is separable over links, y e can relax

the integralityconstraints, replacing themwith

0

< x r < 1

for all

r E R .

This eads to a very argenonlinear optimiza-

tion problem of a separable objective function over a convex

set. Based on the state of the art in the computational ability

to solve the relaxed problems, the idea was rejected. The idea

of using piecewise linearization of the objective function and

solving the inearprogrammingproblem was lso rejected.

The main reason was the fact hat he relaxed problems are

very large and solving them would have required a significant

computational ffort nd would ave generatedractional

solutions, orcing

us

to use abranch-and-bound Garfinkel

andNemhauser [ 131 ) procedurewhichwould have made

matters even worse.

111.PROBLEM EFORMULATION

In thissection we transform herouteselectionproblem

formulation ntoanequivalent ormulationwhich is better

suited ora Lagrangean relaxa tionprocedure.Letting

f i

be

the utilization of link I (i.e., heproportionof he links

capac ity consumed by the actual message flow), the objective

function can be rewritten as

where

and

o r

=

r

V r E R a n d I E L .

P Q I

Since the objective function n

(2) is

strictly increasing with

f i we can replace the equal ity in

3 )

with an inequality leading

to

subject to

V l L

r = l

r E S p

x r = 0

or

1

V r E R

where p is the index set of routes that support comniodity

p ,

and nd L I are upper ndowerbounds, espectively,

on the utilization of link 1. When the prob lem has a feasible

solution, UI is less thanone.Tosimplify heexposition we

will assume that LI

= 0

and

i =

1. Once a feasible solution

to heproblem has been dentified, hosebounds can be

significantlyightened by using informa tion enerated by

the feasible solution.

IV.

LAGRANGEAN ELAXATION

By multiply ing the constra ints, in

3 )

by a vector of rion-

positiveLagrangemultipliers, X I

I E

L,andadding hem

to the objective fu nction, we obtain the Lagrangean relaxation

of problem IP:

L(h)

=

min

subject to

O < f r < l

and

x r = 1

r E S p

and

x,

=

0

or

1

V l E L

V r E R .

The set of feasible solutions for problem IP is a subset of the

setof feasible solutions orhe Lagrangean relaxat ion of

problem IP. The nonpositivity of

h

ensures that in any feasi-

ble solutionor roblemP,he xpression

Z, lELXdf i

2 r E ~ . x r ~ y ~ }s nonposit ive and thus, the value of the objec tive

function in 4 ) is never greater than t he value of the objective

function in .problem IP. Thus, whenever problem IP hasa

feasible solution,

L(h)d

Z I P .For each vector of multipliers

A,

L(h) is a lower bound for

Z I P .

The best possible bound for

such a procedure s given by the vector of multipliers

A *

which

satisfy L(h*) = maxAG oL(h) . Thus, to have tight bounds we

need a procedure for computingh*.

V. THE

SUBGRADIENTPTIMIZATIONROCEDURE

Several methods have been suggested n the iterature for

computing a vector of optima l Lagrange multipliers for com-

binatorialptimizationroblems. Thesencludeolumn

generation procedures

[ 2 3 ] ,

dual ascent and multiplier adjust-

mentprocedures [91 , andsubgradientoptimizationproce-

dures

[ 2 4 ] .

Subgradientoptimizationprocedures have been

shown o be ery ffectiven ariety of combinatorial

optimization problems such as the traveling salesman problem

[ 2 3 ] ,

the multiple traveling saleman problem

[

191

,

opologi-

cal design of computer communication systems [ 15 ,

[

161 ,

and ot sizing in BOMP based systems

[

1

.

This

was

the


4/8

GAVISH AND HANTLER: OPTIMAL ROUTE SELECTION

1157

motivation or hedecision o oncentrateon ubgradient

optimization techniques.

Let xr(h),

f l X )

be an optimal solution to the Lagrangean

problem for a fixed vector h. A subgradient is the vector with

coordinates

70) = O xr(h)arl 'J L. 1

rER

Poljack [29

1

has shown that when the multipliers are updated

using the iterative formula

X;+ = hk

+ tkYf

( 5 )

then x converges to h* provided that tk converges to 0 and

ztk

diverges. Held and Karp

[ 2 3 ]

and ater Held et al .

[24

have suggested substituting

-

Z I P m k

0 y k 112

tk

=

6p

They have shown that if 0

< 6,

< 2-and

ZIP

L(h*) this itera-

tive computation of t k has been used in most successful appli-

cations of subgradient optimization procedures.

The teps involved n the ubgradientoptimizationpro-

cedure are as follows.

1) Initialization:

-

a ) Using aheuristic,computeanoverestimate

ZIP

of

L X * )

or set

ZIP

o an arbitrarily large value.

b) Select an initial set of multipliers ho and set

k ,

the

iterationcounter, o

0,

the mprovementcounter to

0, X*

to

ho,

the current best value of

L(h)

to

0,

and 6 , a parameter

for adjusting he stepsize, to 60 (an arbitrary positive nitial

value, e.g., 2) .

2) Solving the Lagrangean problem:

a

Increment he mprovementand terationcounters

5

Go to .2.

Extensivecomputationalexperiencewith hisprocedure

has shown that it s very stable and converges in a few hundred

iterations oa olutionwhich is very lose to L(h*). The

procedure has een found o bensensitive to he nit ial

multipliervalues nd to he nitialoverestimate.However,

:,.&he rate of convergence and uali ty of bound enerated

'hepends to a large extent on the limits set on the improvement

and iteration counters. Low settings terminate the procedure

before

it

reaches a good solution, while high settings consume

excessive computing resources. Good settings of these param-

etersrequirecareful balancing between hese woconsidera-

tions, which seems to be obtained most readily by experimen-

tation.

VI.

SOLVING

HE LAGRANGEAN PROBLEM

The computational efficiency of the subgradient optimiza-

tion procedure depends on our ability to solve efficiently the

Lagrangean problemwhich is generated nstep2)b) of the

subgradient optimization procedure. Fortunately, for a fixed

setofmultipliers, he Lagrangean problem is separable into

subproblems which a re readily olved.

The Lagrangean problem can be rewri tten as

L(h)

=

min

z

I+

X f I I

Z r {

EL

-

1

with no change in the set of constraints.

Since there reno oupling onstraintsbetween he f r

and the

x,

variables, L(X) can be written as

L h )

= L l ( A ) +

L , ( X ) where

by 1. Subproblem

b) Solve the Lagrangean problem using

X k

as the Lagrange

t

multipliers. Thus, obtain

L ( h k )

and xk fk.

3 )

Testing and updating parameters:

a ) If

L ( h k )

isgreater han hecurrentbes t value of

L h ) then eplace hecurrentbest value of L(h) by

L ( h k )

and et

h*

to

hk.

Also reset he mprovement ounter o ubject

to

-1.

of

its associated objective func tion for that prob lem. this

value s less than hecurre nt value of

Zip,

thenset ZIP toand

this Subproblem 2

C ) f the mprovement counter has reached a prespeci-

fied upper limit, then set 6 to 6/2,X k to h*, the improvement

counter to 0, and go to 2)a).

d) If theterationounter has exceededespecified

b) If

x k

is feasible forroblemP,omputehe value 0

r l

1 'J I E L

limit ;

f

6 is less than a prespecified limi t, or if t i is less

thana prespecified limit ,or if ( Z I p - L X*))/L h*)s less

than a prespecified error to lerance , then stop.

4)

Updating the multipliers: Compute a new subgradient

Compu te the new stepsize

Z I P

L O k )

Compu te the new multipliers

h f + ' = m i n ( - l , h f + t k y f ) J Z E L .

Set k to k + 1.

subject to

r = l Y P E n

rESp

x I = o o r

1

J r E R .

Subproblem 1 can e eparated int o J L subproblems,

one for each link, where the subproblem associated with.the

kt h link is


5/8

I158

IEEERANSACTIONS ON COMMUNICATIONS, VOL. COM-31, NO. 10, OCTOBER 1983

subject to

O < f k < l .

The solution to this subproblem s

This gives us the value of Llk and, hence,of

L l X ) .

Subproblem

2

canbe separated nto

In

subproblems,

one oreachcommodity,where he ubproblem oreach

commodity

p

is

~5 =

min

2

xrar

,ESP

subject to

x , = 1

, E S P

x r = O o r 1 v r r E S p

where a, = X I E ~

-Alarl .

index 0 which satisfies

Thesolution o hissubproblem is toset xp = 1 oran

ap = min a,.

r E S

VII.

PROCEDURE

MPLEMENTATION

To est heapplicability of thesubgradientoptimization

procedure to network design problems and to obtain estimates

on the rat e of convergence, he quality of bounds, and solu-

tionsgenerated, we have implemented heprocedure nan

APL-based system.

The

system

has

a user-friendly nterface

and nables the user to conveniently efinehe etwork

characteristics, raffic patterns, and optimization goals to be

achieved.Thesystemprovides acilities to analyze he gen-

erated olutionsand allows th e user to revise thedataor

optimization goals and redesign thenetwork.The process

is initiatedbyentering henodesandhosts n henetwork

anddefining thecommunicatingnodepairs. Links and heir

capacities redefined next.The user is thenprompted to

specify t he oute generation equirementswhich re used

in a route generation procedure for generating a set of candi-

date routeswhich could be additions to the users predefined

set. Next, he user is prompted o specifysession character-

istics which are used to compute the matrix

{a,l}.

The system

uses a full screen display and is menu driven by the user who

has flexible options and escape procedures. It allows the user

toefine,ptimize,ndefinearge,omplexetworks

easily and quickly.

After specifying the problem parameters, the user initiates

an optimizationprogramwhich he ightlycontrols. This s

done by means of a menuof parameters that the user provides

and can be changed easily depending on the optimizati on re-

sults.

Two ypes of iterations,major ndminor, redefined

in he ystem.Amajor teration onsists of manyminor

iterations, each of which is an evaluation of the current value

of

the objective unction,achoice of subgradientdirection

andmodification of the value of X Theminor terations

terminatewhenone of thestoppingconditions is satisfied.

For example, he difference between a feasible solution and

the Lagrangean is small, the subgradient is small, or an upper

limit on the number of iterations has been reached.

Throughout he optimization process, he system updates

the best Lagrangeanvalue, themultipliers,generated neach

major iteration, and the besteasible solution yet generated.

Based on the output generate d after

a

major iteration, the

user mayerminate,eenterheubgradient ptimization

procedure with new parameters, or modify he optimization

problemby changing inkspeeds, traffic, sessions, or routes

andhenesumehe ptimization. Thisterativerocess

continues until a satisfactory solution has been reached.

Thesuhgradientoptimizationprocedurerequires anover-

estimate Z1p on L(X*) used toupd ate he Lagrange multi-

pliers. This overestimate can be a feasible solution generated

byaheuristic

or

a large numbergreater han L(X*). The

following heuristic is used to generate good feasible solutions.

In eachminorteration of theubgradient ptimization

procedure, Subproblem

2

is solved. We select, fo r each com-

modity, he owestmodifiedcost oute as thebest et of

rout es for the Lagrangean problem. If this routing is feasible

forproblem

IP

and esults in ashorterdelay han hebest

previous easible solution, t replaces theprevious olution

andbecomes he bestnew easible solu tion . In mall and

medium size problemshis rocedure as erformed wel

and has quickly led to near-optimal solutions. This, however,

has not been the case in large problems. Here most selections

have been nfeasible.Carefulexamination of theprocedure

has evealed tha t in arge problems hereweremany cases

in

whichdifferent outes had an dentical educedcost. In

those cases, possible ties exist for selecting the primary route

in the Lagrangean subproblem. herocedure haseen

modified

so

that tgeneratesup to K differentcandidate

solutions neach teration.Each olution is determinedby

selecting a single route per commodity. The routes are selec

with denticalprobability rom heset of routes hat have

identical educedcost or hatcommodity.Routesare as-

sumed to be identical if the difference between their reduced

costs n he Lagrangean procedure is sufficiently small. The

solutions are evaluated and the best feasible solution generated

is picked as the new bestfeasiblesolution. In the extensive

computationalxperimen ts we have conducted,we have

found

this procedure to

be effective and

efficient

in quickly

generating very good feasible solutions.

One of the prob lems with Lagrangean optimization proce-

dures s that hey cangenerateabound even if there

is

no

feasib le solution for he original problem. When this occurs,

the user is notifi ed ha t no feasible solution has been gener-

ated.He is thenexpected omodify he design toaccom-

modate the required traffic. In early states of system develop-

men t, he userhad noguidance n making themodification

andwasted onsiderableimewithruitless ttempts.To

assist theuser, he ystemnow ecords good nfeasible

designs. If, in the ull designcycle, no feasible solution is

discovered, the ystem provides the user withdata bout

these infeasible designs which enables him to identify problem

areas in the designs. Such information includes solutions with

the minimal number of saturated links and solutions in which

themaximallysaturated linkhas minimalutilization. Using

these data , the user can modify link capacity or routesso that

a feasible solutionexistsand hen eenter heoptimization

phase.

VIII. COMPUTATIONAL ESULTS

Thenetwork design systemdescribed nSection VI1

has

beenused to est a variety of simulatedand real-world net-

work design problems. It has performed weli without excep-

tion on all the problems tested. In this section we present the

results of a few computa tional experime nts w ith the system.

Figs. 1 -4, which are labeled ARPA, OCT, RING, and USA,

define the topologies of four networks, in which every node

communicateswith every othernode. The irst hreeare

networks tested in

[6]

.) Each ordered pair of nodes consists

of a host node communicating with a terminal node.


6/8


7/8

1160

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-31, NO. 10 OCTOBER 1983

TABLE I

SUMMARY

OF

COMPUTATIONAL RESULTS ONTHE NETWORKS

IN

FIGS. 1-4

Generate

AKPA

ARPA

A R P A

A R P A

A R P A

A R P A

A R P A

A R P A

A R P A

O C T

O C T

O C T

O C T

O C T

O C T

O C T

O C T

O C T

RING

RING

RING

RING

RING

RING

RING

RING

RING

USA

USA

15

15

I5

2

2

2

1

1

2

2

2

2

4

4

8

16

1

I

1

2

2

2

3

4

4

Y

8

2809

2809

2809

420

420

420

210

210

210

325

598

598

598

598

1195

1195

2294

2886

496

496

496

992

992

992

1481

1984

1984

2762

2762

I

I

Mean

Message

Length

0

60

65

50

60

65

50

60

65

I80

200

210

21

220

200

220

220

220

100

I80

183

183

190

200

200

200

210

32

35

T

I

B C

Lower

7.420

11.946

15.790

7.432

11.985

15.913

8.040

16.070

206.980

102.200

81.276

108.035

128.250

155.890

80.912

154.970

150.780

152.070

13.929

77.256

330.750

44.443

49.874

59.563

55.556

53.322

62.831

6.418

7.288

Percent

7.575

0.189

.446

2.306

6.162

0.715 12.032

0.733

0.000

6.070

0.000

.040

0.254

5.954

0.167

2.005

206.980 0.000

102.200

0.000

81.456 0.220

108.459 0.390

128.765 0.398

159.010 1.958

81.720 0.996

158.280 2.090

153.370

0.847 153.370

1.690

13.929

0.000

77.256 0.000

330.750

0.000

45.100

1.456

51.232 2.650

61.608 3.319

56.817 2.220

54.805 2.705

64.006

I .

836

6.502 1.290

7.712 5.496

whichourmethodscan be extended onetworkswith dif-

ferent models

of

delay, e.g.,

M M m

ueues.

The ideas that were presented in

this

paper can be applied

to rela ted network design pToblems. Work is

now

in progress

[

171 on developing modelsnd ptimizationechniques

for hesimultaneous outingandcapacityassignmentprob-

lems n omputer ommunicationnetworks.Thesemodels

incorporate inks, raffic,anddelaycostdata oselect ink

capacities and route the traffic,

REFERENCES

P.Afentakisand B.Gavish, Optimal ot-sizingalgorithms for

complexproduct tructures,Grad.SchoolManagement,Univ.

Rochester, Rochester, NY, Working Paper QM-8318, 1983.

V . Ahuja, Routing and flow control in systems network architec-

ture,

IBM Syst.

J . ,

vol. 18, pp. 298-314, 1979.

D.

P .

Bertsekas, A class of optimal routing algorithms for com-

munications networks, in P r o c .

1980

In t . Conf . C ircu i t s Com put . ,

Atlanta, GA, Nov. 1980.

D. G . Cantor and M. Gerla, Optimal routing in a packet switched

computer network, IEEE Tr ans . Comp ut . , vol. C-23, pp. 1062-

1069,1974.

P.M.Cashin,Datapac networkprotocols, in Proc .3rd n t .

C o n f . C o m p u t . C o m m u n . , Toronto, Ont., Canada, 1976, pp.

15

155.

P. J . Courtois and P . Semal, An algorithm for the optimization f

nonbifurcated flows in computer communication networks, Per-

f o r m . E v a l . , vol.

1,

pp. 139-152, 1981.

A. Danet, R. Despres, A. Le Rest, G . Pichon, and S . Ritzenthaler,

The Frenchpublicpacketswitchingservice:TheTRANSPAC

network, in P r o c . 3 r d In t . Comput . Commun. Conf . , 1976, pp.

25 1-260.

R. Despres andG .Pichon, The TRANSPAC network status report

and perspectives , in Proc.OnlineConf.DataNetworks-De-

velop. Use London, England, 1980, pp. 209-232.

M .

L. Fisher, Lagrangean relaxation method for solving nteger

programmingproblems, ManagementSci. , vol.27,pp. 1-18,

1981.

H

Frankand W. Chou, Routing in computernetworks, N e t -

w o r k s , vol.

1

pp. 99-122, 1971.

L.Fratta, M.Gerla, andL. Kleinrock, Thelow eviation

method: An approach to store-and-forward communication network

design,

Networks ,

vol. 3, pp. 97-133, 1973.

R.

G .

Gallager, A minimum delay routing algorithm using dis-

tributed computation, IEEE Tran s . Commun. , vol. COM-25, pp.

73-85, 1977.

New York: Wiley, 1972.

R. S . Garfinkel nd G . L. Nemhauser, IntegerProgramming.

B . Gavish, New algorithms for the capacitated minimal directed

tree problem, in Proc . IEEE In t . Conf . C ircu i t s Comput . , 1980.

-, Formulations and algorithms for he capacitated minimal

directed tree problem,

J . A s s .

C o m p u t . M a c h . , vol. 30, no.

1,

pp.

118-132, 1983.

Topologicaldesign of centralized omputernetworks:

Formulationsandalgorithms, Networks, vol.12,pp. 355-377,

1982.

B. Gavish and

I .

Neuman, A system for designing the routing nd

capacity assignment in computer communication networks, Grad.

SchoolManagement,Univ.Rochester,Rochester,NY,Working

Paper, 1983, to be published.

B.Gavish and H. Pirkul, Efficient algorithms for solving multi-

constraint zero-one knapsack problems to optimality, Math . Pro-

g r a m . , to be published.

B. Gavish and

S .

K. Srikanth, Optimal solution methods for larg

scale multiple travelling salesman problems, submitted for publi-

cation.

A. M. Geoffrion, Lagrangean relaxation and its uses in integer

programming, Math . Program. S tudy , vol. 2, pp. 82-1 14, 1974.

M .

Gerla, The design of store and forward networks for compute

communications,Ph.D.dissertation,Dep.Comput.Sci.,Univ.

California,

Los

Angeles, 1973.

J . P . Grayand T. B . McNeill,SNAmultiple-systemnetwork-

ing, IBM Syst.

J . ,

vol. 18, pp. 263-297, 1979.

M. Held and R. M. Karp, The ravelling salesman problem and

minimumspanning rees,Part

11,

M a t h . P r o g r a m . , vol. 1 pp.

6-25, 1971.

M. Held, P. Wolfe, and H. Crowder, Validation of subgradient

optimization, M a t h . P r o g r a m . , vol. 6, pp. 62-88, 1974.

V . L. Hoberecht, SNA unctionmanagement, IEEE Trans.

Commun. ,

vol. COM-28, pp. 594-603, 1980.

L. Kleinrock, Commun ication Nets: Stochastic Message

Flow

and

D e l a y . New York:Dover,1964.

-

Queueing ystems,

vols. I 2. New York:Wiley-lnter-

science,1975,1976.

C.

I .

McGibbon, H. Gibbs, and

S .

C. K. Young, DATAPAC-

Initial experiences with a commercial packet network, in Proc .

4 th In t . Conf . Comput . C o m m u n . , Kyoto, Japan, Sept. 1978, pp.

103-108.

B.

T.

oljack, A general method f solving extremum problems,

S o v . M a t h . D o k l a d y , vol. 8, pp. 593-597, 1967.

A. Rajaraman, Routing

in

TYMNET, in Proc . Euro . Comput .

C o n g . ,

1978.

M.

chwartz and T.

E.

Stern, Routing echniques used in com-

puter ommunication etworks, IEEE Trans.

C o m m u n . ,

vol.

COM-28, pp. 539-552, 1980.

A.Segall,Optimal outing orvirtual ine-switcheddatanet-

works, IEEE Trans. C o m m u n . , vol. COM-27, 1979.

P . Sinha ndA.A.Zoltners, Themultiple hoiceknapsack

problem, O p e r .

R es . ,

vol. 3, pp. 503-515, 1979.

H. Svendsen, The Nordic public data network (NPDN),n P r o c .

Onl ineConf .DataNetworks-Deve lop .

U se ,

London,England,

1980, pp. 189-207.

TELENETCommunicationsCorporation-PacketSwitchingNet-

w o r k (AuerbachComput.Techno]. R ep. ). New York: Auerbach,

1978.

L.

R.

W. Tymes, Routing and flow control in TYMNET, IEEE

T r a n s .

Commun .

vol. COM-29, pp. 392-398, 1981.

T. Yum, The design and analysis of a semidynamic deterministic

routing rule, IEEE Trans. C o m m u n . , vol. COM-29, pp. 498-504,

1981.


8/8

IEEE TRANSACTIONSN COMMUNICATIONS, VOL. COM-31, NO.

10,

OCTOBER 983 1 1 6 1

Combined Random/Reservation Access for Packet

Switched Transmission Over a Satellite with

On-Board Processing:

Part

I-Global Beam

Satellite

Absrmcr-A combinedandom/reservationultiple access

(CRRM A) scheme fo r packet-switched communication over a global

beam satell ite with on-boa rd processing is proposed and analyzed.

Channel ime s divided nto contiguous slots; each slot contains N

minislots or ransmission of requestpacketsand N minislots for

data. With N substantially smaller than the number of earth stations,

collisions will occur in requestpacket ransmissions. Two channel

access algorithms for the CRRMA model a re proposed: uncontrolled

channel acces s (UCA) and controlled channel access (CCA). UCA is

simpler but has an inherent stability problem particularly when the

number of minislots N is small. TheCCAalgorithm estricts he

transmission of request packets for new arrivals to take place only

when the slot is in the FREE state. With N =

3,

the CCA algorithm

exhibits good delay-throughput characteristics. As N increases, the

UCA algorithm offers stable operation. For N 5 the simpler UCA

algorithm is prefe rred over CCA.

Paper approved by the Editor for Computer Communication

of

the

IEEE Communications Society for publication without oral presenta-

tion. M anuscript received July 20, 1982; revised December 10, 1982 .

This workwas supported by the Natural SciencesandEngineering

Research Council of Canada under a Postgraduate Scholarship and

Grant AIII9 .

H. W. Lee is with the Department o f Electrical Engineering and the

Computer Communication Networks Group, UniversityofWaterloo,

Waterloo, Ont., Canada N2L 3G1.

J,

W. Mark is with Department

of

Electrical Engineeringand the

Computer Communication Networks Group, University

of

Waterloo,

Waterloo, Ont. , Canada N2L 3G1.

The performance of the CRRMA scheme is compared to those of

slotted ALOHA, reservation ALOHA, and split reservation multiple

access (SRMA). In all cases the proposed CRRMA scheme exhibits

good delay-throughput performance over a wide range of channel

utilization.

A

I . INTRODUCTION

l a rgenumbe ro fpa pe r so nmul t ip l e c c e ss e c hn ique s

ra ng ing f rom pu re r a ndom a c c e ss o o t a l l y c oo rd ina t e d

dynamic assignment access have appeared in the l i te rature . As

t h e y a r e t o o n u m e r o u s t ois t them a l l , only those whichareper t i -

ne n t to t he p re se n t pa pe r a re l i s t e d in t he Re fe re nc e s .

A primary concern in packe t swi tched da ta communica t ion

ove r a b roa dc a s t c ha nne l i s t he p rob le mf organiz ing the access

o f ma ny u se r s w h ic h sha re t he c ommon c ha nne l . Tw o impor t a n t

performance me a su re s nse lec t ingasui tablemul t ip leaccess

s c h e m e a r e 1 ) m a x i m u m a t t a in a b l e c h a n n e l u t i l iz a t i o n a n d 2

me a npacketde lay .The seperformanceme a su re sde pe ndon

t h e s y s t e m p a r a m e t e r s s u c h a s t h e s i z e o f t h e u s e r p o p u l a t i o n ,

thebu rs t i ne sso fda t a r a f f i c , a nd he p ropa ga t ionde la y . n

th is paper we consider a very la rge user popula t ion wi th bursty

t ra ff ica ndac ha nne lw i tha ongp ropa ga t iondela y, e .g., a

satelli te channel.

The a ssum pt ion o f a a rge popu la tion

of

bursty users ex-

c lude s a ny c ons ide ra t ion of f i xe d a ss ignme n t sc he me s suc h a s

frequency d iv ision mul t ip le access (FDMA ) and synchronous

t imedivisionmul t ip l e c c e ss STD MA )w hic hpermanent ly

assign a por t ion of the channel capac i ty to an indiv id ua l user ,

0090-6778/83/10004161

01

OO 1983 IEEE

gavish&hantler-ieee-1983-an algorithm for optimal route selection in sna networks.pdf

Documents