BSTJ 60: 8. October 1981: Design and Optimizaton of Networks With Dynamic Routing. (Ash, G.R.; Cardwell, R.H.; Murray, R.P.)

16.9 MB·English

Design and Optimization of Networks With
Dynamic Routing

By 6. RASH, FL H. CARDWELL, and FP. MURRAY
(atanuserit osived Marah 6, 1981)

{The grout of electronic siting systems and the high capacity
Inceroffce signaliny network prove on opportunity fo exten flee
howe netzark routing rules beyund the voneeniional hierarchy

‘Network mestets are serie Yo! naira he savings inherent
‘designing networks for demcie, nombinrarehial muting. An alg

‘thin for engineering suck networks tn discard, and the compara:

thw adonnteer of aroun pa routing ane progressive routing th:

niques urn iustrated. A particularly simple implementation of dy

namie eating called tus-litk dmamnie routing with erankback és
‘isenssrl 0d is shun t0 yield benefits comparable fo much more
complicated routing schemes. The efficient solution of embedded
linear programming ‘LP; rowing problems isan essential ingredient
{or the practicality ofthe design alyorisn. Wr introkece an efficient
heuristic optimization meth for sulation nf Ue mauling probleme,
think preadly improves computational speed with minimal love of
faecarary. Wr alsa project eomputattonal requivements for a 200-node
ddengn problem, which 1s the estimated size of the intercity Bell
Sytem dynamic routing netiork in the 19808

| INTRODUCTION AND SUMREARY

“The rapidly growing stored prosrant cunts isPe) network, cate
ing of electronic awitehin syeoms incervonnected by common ehinnel
intaroffce (ers) ngrnliny, links, proven signin apporcaniy 20
tauend the (lephone etre routing rules beyond the conventional
‘erarchy. In due arc network, there arene retriction co hievarhienl
route ehoices or ta routing rules eich remind i ie, I we
tay rationally consider nctwork configurations which use dst,
snonlerarehieal routing (PWT), The term dynamic eeribes ein
techniques which are time-tencitive, az oppowed Lo preaenladay Hier
sarchicel routing rales which are time fixed, An importa surible in
the dynamie routing straleny Hs the foanueney with which network.
outing rules are updated

11 Savings possible with dynamie routing

"There are two major opporconties :o improve the pled nek
sign {ororaniy with tore advaneed routing techniques. Firs, ee
fenuse of ie Txed nature, prasent hierarchical routing cannot really
take much advantage of load variations which ais from Insness/
zrstonee, tne res, seasonal variations nd other reasuns, By allow
ing tine varsing, or dynamic routing, some of this pendlty can be
reduced. Second, the present hierurebva! routing has gid path
‘Shiees, pun Tow Blocking on final Tinks which lini flexibility and
reluce eliceney. Ewe choose paths based primarily on cust and ela
the preven rg in network stuctare, a more efieient notwurk
thon real. The ope Tilson iropravement in these Heo arous are
duced frst

Te ivenimated foun & 28-nadl intercity network model (Fig. 1} hae
out 20 peroent of the networks Rat naa cat be stbuced 10
designing for time varying los wring ner erent tate hierarchical
routing techniques, ‘To shew thin, we frst designed a hierarchical
fetwork using 4 conveninmal cluster buss-hour approach, ‘Then,
‘quantify the extra capacity being prvi, we alno derigned the 2.
todo model for the imfividhal hourly Inads. These hourly networks
‘were obtained by xing ence bury Toad, and ignoring the other hourly
Tadeo dimnrsio hierarchical netic chat would perfectly match
thachonr's Ind This procedure results 17 separate network eign
fe fora oe:

igure 2 plor of te normal newest (inling siting
and faciicy cose) equired for the caster sy honrand hourly network.
designs, On the topline, the cluster buy hour solution had a network
capital coo of une wnt sulisfy all 12 hous of load with ed,
Ierarehieal routing. The 17 hourly cetworks, sla on the lower
‘curve, repent the normabod enptal cost of the circuit idee and
‘trunk aetually sore rah hor stn the load. Threenerwark
‘buey pariods ae exe: moraing,alleranon an evening. We ean aso
soe auun hour drup is loud azn an saey-eveuig dtop aa the bariest
‘ay ends and residential eaing begins in the evening, The hourly
hetwork curve separates che eapacisy provided in the clisler Ina
gut elution into two components: below the curve ie the capacity
artoally needed at exch hour to meet Une lou: wows the rave i che
‘caparty mbich ia avilable but ie not needed ac thot our. This
‘ANdLional eapacity exceeds 2 percent of the total neoworks capacity

1785 THE AFL SYSTEM TECHNICAL JOURNAL, OGTOER 1981

‘rough all hours of the day. This wap reprenente the eapeciey pat in
the network lo meet noneoineident los and suggests a maximum
Tinton necwork reducion which might he achieved through improved
routing techniques.

1.4.2 Limited path ralection effects

Addicional benefits van ie provided in necwork design by allowing
‘sore Gexble intercity muting plan that 2 not reseieced to hiorar-
‘hice router, Our approach llows the selection of shortest (nonhies-
frchicl) paths, Applied! tv each hourly load, this approach yields an
‘overall savings of abou 5 percent in comparison ln the hierarchical
hourly networks, Figure 2 clio displavs Unewe real and shows that
the 2 percent bound discussed above has increased to a total of 25,
percent. This addivional savings polenta! anslates into actual bene-
Fits by introducing nonhierarchieal shorts path routing into the
dosgn, at done in che DSI network design algorithm.

‘Figure 2 lastrtes the limitation thatthe hierarchy imposes in the
2enode network between San Diego al Riningham. The alterate
paths between thee” points go through two regional centers, San
Bernardino, Ca. and Hockdnle Gu, providing relatively long paths.
Selecting more direct paths, ur example the Tucson, and Phoonix, Az
‘and Montgomery, Al paths, would provide design benefits. Allowing

4790 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1981
the optimum choice of intercity eustes beyond the hinaachical chaives
lis, nonbieraebical tack) vilda design savings. This inhides
sllwing the present final paths ta use alternate routing, which in
‘many eaeen would further improve the notwark efficiency.

1.2 summary

I Section 8.2, we describe the route formulation of the unified
sevith (04). In tia formulation the alowed tac pattern (routes)
tae fhrned for exch point-to-point demand prior to traffic asignment
in the roming optimisation step. Three routing methode are considered
in designing netsrerks using the route formulation method:

G) Progrossive routing in which « call progresses through the
network ono avitch at a time without retracing its path unl ether
euch ils cetinion or arrives at an intoeredint site fom whic
‘thas no out,

U2) Multilink path routing in which a cll blocked by a busy trunk
froup on a path may use the capabilities of the sec network (o be
cranked back" to the originating node and attomp: the acst path in
the rove

(Gl) Toon yah eoating ich ig enti to rltink routing,
tecenl that path Trom origin to deatination may have al mat Lo
ins

"We find that design savings on the order of 10-15 percent are
parse when using these routing methods an compared to present
‘Berarchieal rechnigues, From the savings remlte and implementation
considerations, we conclude that bwo-lik routing is preferred.

‘We next consider apother formulation of the ua called the path
formulation, which ie specifically cilored to examine two-line ring
options. This method does not preseloct allowable roulas bu alles
the trafic alloasion step to msi tific dirty to phe i under te
vninimiar aetna. Rates ave formed after the optimization step
Wor veales the esr ws, flow feasibty algorithm je deneibed

NETWORK DESIGN 1791
which forces the reslkicy pls ows to he realizable, The twink
fhuting methods for realising It optiawum path Hows are thon consi

ted earping in cranplexity a avery Menible seth, om fouling
(developed Uy Chun etal, Wo. very staple method called sequential
rotting, The latter method consist of offering al traffic to on ordered
Lit of olin pale with Ihe eveeflow Tram one path being affered 2
the next lh; the onder Tis may change by time-ot day to tale
ssdvantage of trae noncoincidence

“We tint that the eouring techniques investigated using the path
fornulotion achieve at last 1-2 percontage points additional savings
ver the routing techniques sual airy te mate formulation, We
‘than find that sequential routing ince sn ewigrican cost perl
‘when compared to moro flexible routing schemes and, because of ict
implicit, we eon that sequential vauing is che preferred routing
method.

Tificiant optimization ccbniques ave considered in Section 1V
‘These mothots flow the flsign of wry large networks for dynamic
‘outing using rewnable coropter resources, nally, potecral Bell
Syscem applications ave dscuazed in Section V.

1 DYNAMIC ROUTING CONCEPTS: DESIGN, SERVICING, AND

CONTROL,

igure 4 illuntrtne che thre primary componencs of the network
design and tminiiration Tunctions a8 three interaccing feedback
Toop stound the necwork, The coor offer Id in shown to
couaiz of predictable, avcrnge demand components, unkown forecast
terrors, and day-io-ly variaian components. The feedback controls
function to reyulile Ihe rerview provided by the network through
capacity an renting adjusanents. Necwork design (or planned serv
icing) operates over a year-long inverval, drives the nctwork capacity
expan, and preplans routing patterns ve minimize netork costs,
Themand! servicing accounts for te exiting ewpaelty an, on a westkly
Tne, Finecunes ink sizes and routing patlcrns to accoua for fers
trrur iherent inthe yast-long design loep. Teal-time eontrol males
Timited adjuscmenta to the preplann routing ers ls necoune for
normal daly shifts in lood patterns.

‘Networi provisioning for dynamic routing depends primarily on
‘performing olin ealuluions fur network desgh and demand cer
Jeing, The of linersleulalioneerlecttheoplienal eucing pattem tm
very lange autaber of possible alternative in ander to minimive Loe
Cranking mvtvork net. Phe tert dmamie routing requently euggests
tuneatensive sear fr te nptinal enoring aesignment cabs performed
‘mn veal time, This extensive search i infact being made hut mose of
the senaehiny is porfarmal in denn ising an off Tine design system

1792 WE RELL SYSIEM TEGHMIGAL JOURNAL, OGTOBEN 1B
(ciate)

re Je wets}

find an of-line dean servicing aystent, The effectiveness of the
Alesgn depends on how accurecely we cua forecast the expectad load
fom the network, Exzare soci wit thy fenurnst are camrected in
the demand servicing process deseribed in the cornnion stile The
‘only routing elections necesary in veal time involve conditions that
flso become known in teal time: ay-o-day Tol vurintons, network,
failures, and network overlonds Prceshros for ral ine routing
also described inthe companion article

3.1 Overvow

In thin section, we describe the algorithm used to design near
‘minimum cost nonbierarchieal nenwor uring dymamie routing. ‘This
llgorthm is termed 4 because # combines $nto one systematic
procedure various network dign concepts. auch as

(i) Using time-eenative syramic rowing 1 tke advnntage of
‘waffc noncoincidence,

(ut) Routing trae slong the least cori pacha,

(ii) Raworing large, move efficient crank groupe,

NEIWORK DESIGN 1789.
(ie) Using efficient trunk uroup blocking levels determined by the
economic hundred call seconds (ee) nethod, and

{0 Minimizing inert network cost.

‘The fiat two concepln were deerihed in Section 11. A bref descrip
tion ofthe other Unre concepts incorporated in the a is given below.

2.1.1 Fovorng lage trunk group

Figure 6 iluraates the nurbor of uunks, N, roquired to carry a
particular eared load, a, at constant blocking. From the shape ofthe
furve comes the well-known fact tha at constant blocking tho number
of additonal crunka required to carry an increment of offered load
creas as the trunk group size increases Honco, its advantageous
{o combine sveral trafic parcels into one large pare vo be routed
‘ver large trunk group since one large rank group inherent more
‘ficient chan several smaller unk xroups-

In the va, larger trunk groups are favored through the usw of a Tink
incremental cost metric proportional tothe slope (V/2a) ofthe trunks
‘eros loa curve, Thus he ink melee indicates the attractiveness of
this ink to camry addtional trae.

8.1.2 Use afictent blocking lvele

igure 6 illscrates the cos! rude off herween caring traffic onthe
“iret erunke group between A and Hand the alternate network that
‘overflow calls wil se, The problem is ¢o find the optimum value of
blocking (or, usuivalently, che nomber of cack) lo handle the offered
Toad att minimum costs Thia question was first answered by Tet?
who derived the coucept of an zecs hasod on the dict path to

1794 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1881
eon BET ea) ayers

Neon |

2 t % a

alternate path vost ratio and the marginal capacity of the alternate
path, Trult's cece method is commonly used today in both intercity
land metropolitan network design. "This methed is also used in the Us

34.9 Minimize incremental network cost

[Network cost and performance are nontinesty related. Hence, the
_netvork design problem js inherently a nonlinear programming prob-
Tem. To avoid the complerties asvocintd with aonlinearity,¢he nel
work cast function can be Lieatiged around the present operating
Point and che linearized ineremencal) coc funetion minimized co yield
‘uuinunur, cost network

"This approach of minimising Use incremental network et hak ben
sucosflly used iy other investigators. Vaged haa used thie tech-
rique to find a near minimum cont facility network to satisfy trunk,
‘lemande when the facility links diaplay a concave facility cost versus
‘channel capacity relationship. For his pblem, Yaged demonstrated
Phat thie eehnique saisied the Kuhn: Tucker conditions which are
necessary (but not sufficient) for optimality. An analogous approach
teas used by Kneples* who applied the minimal incremental cost
concept to the deaign ofthe automatic voice network (AUTOVON)

igure 7 shows the iverative loop forthe ruute formulation of the
‘od. Base input parameters include trank cost, point to pin offered
Toads, al required point to.point grate af service (cos)

"The router finde the abortetpathe (aequences of links) between
points in the network, Using ascumed link blocking levels, the router
then forms The paths inco ean rons Ganquencts of paths) and
Aletermines the proportion uf Me appwsrng un each path i ve role
for each unit of effored load. This method of forming routes from
auH as

sesame link blorkings ic 2 Rey feanure of the tt, Tt eliminates the
fonlinese relation bet ween tink blocking, amber of run, and ofered
load frum the optimization step, and it also permits investigation of

‘wide varity of routing schemes

"The an then assigns Dow to the celine routes to. minimize
‘netmork cont, The output from the router isthe oprimam routing plan
Consiting of the routes vo be wwe in cach hour. This routing is
provided to the engineering prugrnn which determines the flow on
frch link and gies the Link to meet the design Level of blocking usd
inthe router step, Onee the groupe have been engineered, the ost of
the neework can be evaluated and entspazed tothe Tas tration.

Ifthe netvork cot is sill decreasing, che wpante module (2) com
putes the sie of che capacicy versis load curve on each link nnd
Updates the link coat uring thas slope as a weighting factor, and)
fomputes «new level of ink blocking wing the recs method. The new
Tink tongs and blockings are fil to Ue router which again selects
shortest paths, and 39 on

12.2 Dotaed deserpton
An initial ot of link blockings and metres are ealeulated based on
the woos method. Lita ine Mocking are determined assuming that
the overflow path isthe shortest te fink path between the endpoints
with a marginal eapacity of 8 cos
‘Tho router consists ofboth w route generator and an uP, The route

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