A Delay Constrained Minimum Hop Distributed Routing Algorithm using Adaptive Path Prediction

Transcription

1 46 JOURNAL OF NETWORKS, VOL., NO. 3, JUNE 007 A lay Constraind Minimum Hop istributd Routing Algorithm using Adaptiv Path Prdiction A. R. Mohd Shariff Univrsity of Bradford/partmnt of Computing, Bradford, Unitd Kingdom a.r.mohdshariff@bradford.ac.uk M. E. Woodward Univrsity of Bradford/partmnt of Computing, Bradford, Unitd Kingdom m..woodward@bradford.ac.uk Abstract W propos a nw dlay-constraind minimumhop distributd routing algorithm (CMH) for unicastrouting. CMH uss a novl path fasibility prdiction (PFP) modl that is abl to prdict th fasibility of a tntativ routing path, and mploys a crankback facility. It is a hybrid algorithm whr it uniquly intgrats th us of local-stat and th global binary connctivity information maintaind at ach nod to comput routing paths. Simulation rsults show that avrag mssag ovrhad is modst with good connction succss and low nodal storag. Indx Trms distributd algorithm, routing, quality of srvic, path fasibility prdiction I. INTROUCTION Th prvasiv dmands for connction-orintd raltim multimdia applications ar vr blooming. Ths applications ar bandwidth hungry, impos strict dlay guarants, stabl jittr and low packt loss probabilitis, which constituts th notion of Quality-of-Srvic (QoS). On major lmnt in th provisioning of QoS srvics in th Intrnt is QoS-routing [1], [19]. QoS-routing algorithms can dynamically dtrmin a fasibl path basd on crtain constraint optimizations of a rqustd flow. Two most important schms studid ar sourc routing and distributd routing. Thy xhibit prformanc trad-offs in trms of computational and protocol ovrhad. In sourc routing whr path computation is don at th sourc nod, an updatd global link-stat databas of th ntwork is kpt at ach nod using linkstat protocols (or distanc vctor). Protocol ovrhad is xpnsiv du to frqunt triggring of link-stat updat packts spcially whn a ntwork is larg and traffic is dynamic. For low call-blocking probability, th globalstat maintaind must b accurat, particularly for dlayconstraind routing [3]. Thr is a clar trad-off btwn Basd on A istributd Algorithm for Unicast QoS-Routing using Path Fasibility Prdiction, by A. R. Mohd Shariff, and M. E. Woodward which appard in th Procdings of th IEEE Intrnational Workshop on High Prformanc Switching and Routing 006, Poznan, Poland, Jun IEEE. protocol ovrhad and imprcisnss of routing information, influncd by diffrnt triggring policis for ntwork stat updats [0], []. In addition, th storag siz of th global-stat databas incrass xponntially with ntwork siz and th numbr of ntris, ach rprsnting a diffrnt QoS mtric. In distributd routing, path computation is distributd amongst intrmdiat routrs btwn sourc and dstination. istributd routing is catgorizd into two tchniqus. First, routing that rlis on th global-stat and scond, routing that dpnds only on th local-stat. istributd routing algorithms (RAs) basd on th global-stat rquir ach nod to comput a forwarding tabl using ijkstra s algorithm (or Bllman-Ford) with ntry spcifying th nxt-bst hop to th dstination. A routing dcision is mad locally at ach nod on a hopby-hop basis. Although computationally fficint, ths algorithms inhrit th sam problm of stat information imprcision and high protocol ovrhad as in sourc routing. Flooding [1] is th most studid distributd routing schm that dos not rquir th global-stat. A connction-rqust packt is floodd ntirly or slctivly [18] in th ntwork whr it travrss on a link-by-link basis whilst QoS rquirmnt is mt until it rachs th dstination, or is droppd at th particular link whr it is violatd. Sam connction-rqust packts taking diffrnt paths may arriv at an intrmdiat nod or th dstination spcially in lightly loadd ntwork conditions. Pruning of rdundant paths ar ncssary for th bradth-first-sarch schms of flooding. On limitation of RAs is th computational burdn (i.. mssag ovrhads) of finding optimal paths for multipl additiv constraints (.g. a dlay-constraind last-cost problm), particularly if th RA is dpndnt on th local-stat alon. On th contrary, computing optimal paths using sourc routing algorithms (SRA) for th sam problm is found to b NP-complt. Although a study suggstd that NP-compltnss is rarly found in practical xcpt for four conditions [1], th prsistnt problm is maintaining an updatd global-stat for xact (loop-lss) QoS-routing. W strongly bliv that RAs

2 JOURNAL OF NETWORKS, VOL., NO. 3, JUNE ar holistically scalabl compard to SRAs whn prformanc masurs of protocol ovrhad, nodal storag and scalability ar considrd. A RA that is abl to comput a dlay-constraind minimum cost path with modst ovrhad and using minimum stat information can b an attractiv solution for QoS-routing in th Intrnt. W prsnt in this papr a nw RA for unicast routing calld lay Constraind Minimum Hop (CMH). W considr CMH as a spcial cas of lay Constraind Last Cost (CLC) problm whr CMH computs a dlay-constraind path with minimum hop in a distributd fashion. W dvlopd a novl inquality modl calld th Path Fasibility Prdiction (PFP) that is adaptiv to path dlay variations whr it allows CMH to prdict and mak an a priori dcision as to whthr a link should b accptd or othrwis. Th inquality modl of th PFP combins pr-computd Shortst Path (SP) hop count information to all nods as potntial dstinations and on-dmand local-stat into a singl function. CMH is a guidd dpth-first-sarch algorithm as th RA is always guidd towards raching th dstination by th SP hop counts. CMH uss a crankback procdur to rtrac to a good path whn a path dlay violation is dtctd. Th concpt for CMH was originally dvisd from a squntial dcoding tchniqu introducd by R.M.Fano [1]. This papr is an xtnsion of [] whr th basic PFP modl and som gnral rsults wr prsntd. In this papr, w provid a dtaild analysis of th proprtis and charactristics of th proposd PFP modl. W commnt on its strngths and limitations, and practicality for QoS-routing. W prsnt two nw rsults from th simulation for th prformanc masurs of infficincy and computd path dlay variation. Th rst of this papr is organizd as follows. An ovrviw of th squntial dcoding procdur of Fano is givn in Sction II. In Sction III, a thorough xplanation of th PFP modl is prsntd focusing on its proprtis and charactristics, and path adaptability. Th routing tabl structur and information of CMH is dscribd in sction IV. Th routing control mssag rquirmnt is prsntd in Sction V. W xplain thoroughly CMH huristics and discuss its complxitis in sction VI. Simulation rsults ar givn and discussd in sction VII. Finally, sction VIII concluds th papr. II. THE SEQUENTIAL ECOING OF FANO On of many issus of QoS-routing is scalability. For a RA, scalability is tantamount to computing QoS-basd paths with modst stat information, computational (i.. mssag) and storag ovrhads. With no global-stat dpndncy, th combination of an intllignt routing computation modl and fficint huristics is crucial. Thr xists a squntial dcoding procdur for rror control coding that is somwhat similar in th contxt of path computation and prformanc objctivs to QoSrouting. Squntial dcoding has a primary advantag ovr maximum liklihood dcoding of Vitrbi [13] whr it can dcod convolutional cods with larg constraint lngth with arbitrarily small rror probability. Of particular intrst is th storag fr, sub-optimum but computationally fficint squntial dcoding algorithm of Fano [5], [1]. For QoS-routing, this corrsponds to computing QoS constraind paths using only th localstat with minimal ovrhads. Fano s algorithm xamins a squnc of nods in th k cod-tr from th start nod to th nd nod making dcisions to mov forward or backward dpnding on th Fano Tiltd istanc (T) dnotd by (1). Th T is th diffrnc in masur btwn th Hamming distanc d[c(l), r(l)] and pnl dtctd by th dcodr at any l th lvl in th k cod tr. Th bhaviour of λ(l) fundamntally indicats whthr th Fano dcodr is tracing a corrct or an incorrct path, which is th c(l) path. Th Hamming distanc d[c(l), r(l)] is th total diffrnc in bits btwn th transmittd cod squnc c(l) and rcivd cod squnc r(l) of th l th lvl in th k cod-tr, p is a dsign paramtr chosn btwn th Binary Symmtric Channl (BSC) probability p 0 and ½ i.. p 0 < p < ½, n is th output bits in a block of th convolutional cod and l is th branch lvl in th k cod-tr. λ(l) pnl - d[c(l), r(l)] (1) A corrct path (i.. c(l)) is dtctd by th dcodr whn λ(l) incrass as l incrass. This implis that th Hamming distanc d[c(l), r(l)] is zro and nondcrasing. If c(l) is an incorrct path, thn λ(l) will dcras with incrasing l bcaus of th growth in th Hamming distanc d[c(l), r(l)]. Whn an incorrct path is dtctd, th dcodr must locat th nod whr th corrct path divrgs. Fano s algorithm provids a simpl yt intllignt sarch procdur for th nod of divrgnc. This is anothr ky stratgy of Fano s algorithm in addition to th T. A λ-mtric is assignd to ach l th nod, which is qual to th T (i..λ(l)) of th ntir path from th start nod to that l th nod in th k cod tr. Th dcodr compars this mtric against a squnc of dfind thrsholds T k t along th tntativ computd path. It ithr movs a branch forward to a (l +1) th nod or backwards to a (l 1) th nod dpnding on whthr th valu of th mtric at that currnt l th nod is largr or smallr than th thrshold T. Ths ar th two main concpts (i.. th T and forward/backward movmnt) adoptd in th proposd CMH []. III. THE PATH FEASIBILITY PREICTION (PFP) MOEL A point-to-point ntwork G is rprsntd as a collction of nods V connctd by dirctd links E dnotd as G(V,E). Each dirctd link E from nod v m to nod v n whr v m,v n V has an associatd nonngativ dlay ) and cost c( ), ) : E R + and cost c( ): E R +. A routing path from a sourc v s to a dstination v d, v s, v d V is dfind as an altrnating squnc of nods and links P(v s,v d ) (v s0,v 1,v,, v d, s101, 1, 3,, id ) that can also b xprssd ithr as; a subst of dirctd links E(v s,v d ) ( s101, 1, 3,, id ) or a subst of nods V(v s,v d ) (v s0,v 1,v,, v d ).

3 48 JOURNAL OF NETWORKS, VOL., NO. 3, JUNE 007 Th nd-to-nd dlay of th routing path is th sum of all link dlays in P(v s,v d ) P sd and is givn as ( Psd ) ) () P sd Givn a dlay constraint, th problm of dlayconstraind QoS-routing is to sarch for a suitabl path whr th sum of link dlays dos not xcd. Assum that such a routing path xists is th P sd path. ( P ) d sd ) P sd ( (3) Equation (3) indicats that at any nod v j whr th routing is currntly locatd, th accumulatd dlay so far whn subtractd from yilds th rsidual-qos dlay to rach dstination v d from that nod v j. Th rsidual-qos dlay is dnotd by r j(d) as indicatd in (4). ) rj( d) P sj Each nod must know th cost of th last-cost-path (LCP) from itslf via ach of its adjacnt nighbors to v d. This LCP valu to rach v d from any nod v j via link jk (or adjacnt nighbor v k ) is dnotd as C jk(d). (4) C min c( ) (5) P Givn C jk(d) (5) and (4) is known, a basic inquality in (6) is dfind whr th lft-hand trm is a prdictor and th right-hand trm is th rsidual-qos dlay. Variabl w is th prdictor multiplir fundamntally includd such that (6) holds. Th multiplir w taks a singl nonngativ link dlay valu at any nod in P sd, [w )] : E(V s,v d ) R +. C prdictor rsidual QoS w ) (6) Psj Rarranging (6) into (7) and xprssd as a function of ), thr proprtis ar attributd to (8). f ( w) ( ) ) d jk d Psj ( C w) 0 ( (7) Not that f(w) f( )) sinc [w )] : E(V s,v d ) R + f )) ) ( C w) 0 ( ( ) jk d P sj Proprty (1) Th function f( )) provids a gnral solution for th CLC problm. Th function f( )) is a dlay maximization function and an optimal solution is attainabl by optimizing (C jk(d) w). Assum Ω (P 1, P,,P n ) is th st of routing paths from v s to v d whos (8) nd-to-nd dlay satisfy. Thr xists a path P i Ω such that th total costs is optimum (i.. min C( P ) ). P Ω At ach nod in P i, f( )) is maximizd if; 1. Th costs to rach v d from any nod in P i is optimal and dcrasing sinc P i is an optimal cost path.. Path P i is th optimal dlay path, P ) min ( P ), thrfor th prdictor multiplir w: i ( i i P Ω a. Has th smallst dlay from Ω, ) Ω: ) min w or; b. Has th smallst dlay statistics (.g. man link dlays of P i ). Proprty () If all link costs hav unit valu and ar qual, E: c( ) 1, thn C jk(d) H jk(d). Th LCP is transformd into th Shortst Hop Path (SHP). Th quantity H jk(d) is th optimum hop count to rach dstination v d from any nod v j via link jk (or adjacnt nighbor nod v k ). Equation (9) prsnts a problm for dlay-constraind last-hop that is a spcial cas of th CLC problm. Equation (9) is th original T routing inquality of MFA [7]. In this work, w propos a nw distributd algorithm for th QoS-routing problm of dlayconstraind minimum-hop. f )) ( ) ) d jk d Psj ( H w) 0 i i ( Proprty (3) Undr optimal conditions dfind in proprty (1), (9), which is a by-product of (6) is picwis linar and monotonic dcrasing with gradint H jk(d). Proprty (3) holds whn only all link dlays ar constant. Assum P i : ) d. lim d ( ) d lim d ( ) d lim d ( ) d lim d ( ) d lim d ( ) d f f )) f ( d) ) d (9) [( )) ( H ))] [( d) ( H d) ] ( H H ) H ) ( H ) d ) d )) + ( H ) d) ) d )) + d + ( H d) ) d d)

4 JOURNAL OF NETWORKS, VOL., NO. 3, JUNE H ab(f) sourc a h d ab d H ab(f) b c d bd d H f) H df(f) d d df 3d d d d d g d f dstination d gf d g Claim A: incras f p ab p bd )) < f p d p g p gf )) 3 d > d < 3d > d > d Claim B: Figur 1. A dirctd topology f r ab r bd r d r g r gf )) A. Monotonic Charactristics of th InqualityFunction It is imprativ that a monotonic analysis is givn as computation of CMH is dpndnt on th monotonic charactristics of (9). Bfor procding with th analysis, w assum proprty () holds. Undr optimal condition 1 and as dfind in proprty (1), (9) is always monotonic dcrasing. composition of (9) producs two linar indpndnt and pic-wis subfunctions with asymmtric monotonic charactristics. A. That f p ( )) (H jk(d) w) and xhibits ithr monotonic dcrasing or incrasing bhavior. B. That f r ( )) r j(d) is always a strict monotonic dcrasing function. To guarant clarity, a simpl routing topology in Fig. 1 is considrd with routing paths P 1, P P af, P 1 ( ab, bd, df ), P ( ab, bd, d, g, gf ). Analysis 1: Proprty (1) conditions 1 and ar valid. Th path P 1 is an optimal dlay and optimal cost path. Claim A: f )) p ( ab p ( bd 3 d > d > d p ( df Claim B: f )) r ( ab r ( bd - d > - d > - 5d r ( df Both sub-functions ar monotonically dcrasing functions. A dlay-constraind hop optimizd routing path is fasibly found whn all conditions of proprty (1) ar obyd. Nvrthlss, du to inxistnc of th global-stat for th proposd CMH, it is vry unlikly that condition in proprty (1) is ncountrd during any routing procss. ( P P af Analysis : Proprty (1) condition 1 dos not hold whn a divrsion is rquird from th optimal path P 1 to nonoptimal path P. For xampl, a brokn ntwork link is dtctd or if f p ( )) is highr than f r ( )) at link df. Thrfor, C P ) min C( P ) whr path P is nonoptimal. At nod d whr th divrsion is ndd, f p ( )) rvrss its ordr. - d > - d > - 3d > - 5d > - 7d Finding a dlay constraind optimal hop path is unviabl bcaus of th incrasd routing costs at th divrsion point. Howvr, it is fasibl to find a routing path that satisfis th dlay constraint with minimum hop. It is worth mntioning that a divrsion can also occur whn f p ( )) rvrss its ordr whn its valu is abov f r ( )). Th incurrd highr cost du to routing path divrsion dos not chang th monotonic dcrasing ordr of f r ( )). Analysis 3: Proprty (1) condition (a) and (b) ar unrachabl. Path P 1 is not an optimal dlay path but a dlay-constraind path. Thr is no prior knowldg that P 1 is th optimal dlay path and w is th smallst in P af. Anothr drawback with condition is w varis with dynamics of ntwork traffic. Assum d df is doubld to 6d. Claim A: Condition (a): w ) min d f )) p ( ab p ( bd 3 d > d > d p ( df Condition (b): w i(av) Σ )/h i, hnc w a(av) d, w b(av) d and w av).67d Claim B: Incras f p ab p bd )) < f p df )) 3d > d <.67 f r ab r bd r df )) - d > - d > - 8d Variations in link dlays has no ffct on th ordr of f r ( )). It is always strictly monotonic dcrasing. Subfunction f p ( )) xhibits an ordr dcrasing and incrasing with minimum and man dlay valu of P 1. A routing path that satisfis th dlay-constraint with optimal hop is still achivabl providd f p ( )) is maintaind lowr than f r ( )) valu at ach computation point. Finding th non-trivial valu of prdictor multiplir w guarants a solution to f p ( )), and thrfor (9). Th T inquality (9) is satisfid whn th prdictor is lowr than th rsidual-qos. This is tantamount to finding a suitabl w as dfind in th non-trivial condition of Proprty (1). Nvrthlss, satisfying Proprty (1) condition or using any minimum valu to rprsnt w

5 50 JOURNAL OF NETWORKS, VOL., NO. 3, JUNE 007 d 3 H -3 d 01 d sourc H -4 d dstination Figur. A simpl ntwork for path fasibility prdiction analysis only guarant routing computation succss but would not limit ovrhads. Thr is an inhrnt wak satisfying capability of th inquality at initial computation phass sinc th prdictor product would b considrably lowr than rsidual-qos (i.. r jk ( d) >> H jk( d ) w ). Links with larg dlays hav highr tndncy of bing slctd rsulting in an arly ovrspnd of th dlay-constraint (or rapid draining of r jk(d) ). Consquntly, routing byond suffrs multipl divrsions du to frqunt failurs that ar wastful of mssag ovrhads and hop counts. In addition, th dual monotonic bhavior of th prdictor coupld with wid varianc of link dlays du to ntwork traffic dynamics could also triggr divrsions. On solution to limit th waknsss of (9) and its vulnrabilitis to ntwork dynamics is to us w drawn from th constraints (hop count and dlay) that is adaptiv to changing routing bhavior and ntwork traffic. B. Analytical Modl of th Path Fasibility Prdictor Equation (9) is furthr xtndd in rtrospct to its limitations as discussd in sction A. Two diffrnt variabls ar dfind furthr, Fix as dnotd by (10) and I. Fix is th a priori man link dlay distributd qually ovr th links on th optimal path (shortst path) from any routing nod v j to dstination v d. It is not th actual dlay, rathr Fix givs an artificial projction of th maximum allowabl man path dlay if v d is to b rachd via th optimal hop path (i.. H jk(d) + h). is th dlay constraint and h is th travrsd hop count to rach v j on th tntativ routing path from sourc v s. This Fix is a varying quantity computd onlin at ach nod. I is an initial valu also dtrmind from (10) only onc at v s whr h 0 whn v j v s Fix I H H sk( d ) Fix H + h jk( d) h 0 v j + h jk( d ) h 0 v j v s v s 6 (10) Assum in Fig. that a routing path xists as P sd (v 0, v 1, v, v 3, v 5 ; 01, 1, 3, 35 ) whr sourc is v 0 and dstination is v 5. At ach nod in P sd, th tru man link dlay is calculatd and dnotd as T,v in (11). Mor spcifically, T,v is th tntativ man link dlay from v s to any slctd adjacnt nighbor nod v v of currnt routing nod v j. T, v P ) + sj h + 1 Exampl of T,v squnc in Fig. v 0 d 1 01 v d01 + d 1 1 jv )... (11) If link dlays in P sd ar quiprobabl (i.. 01 ) 1 ) 3 ) 35 ) d), thn T,v Fix. Whn this condition occurs, P sd is a dlay-constraind path (i.. accumulatd dlay always satisfis ). If th link dlays ar not qual, which is normal for ntwork links du to dynamics of ntwork traffic, a mismatch xists btwn T,v and Fix (i.. T,v Fix ). u to this mismatch, thr is no guarant that accumulatd dlay on routing path P sd would satisfy th. This mismatch is rprsntd as a ratio φ and is xprssd as Fix T, v ϕ (1) Th φ, whn is subtractd from unity (on) yilds a factor k (13). For th quiprobabl cas as is P sd, k 1 bcaus φ 0. Th algorithm will potntially travrs th optimal hop path from v s or any nod v j to v d via any outgoing nod v k (i.. H sk(d) or H jk(d) ). Whn φ R +, k > 1, a path pnalty condition ariss, and whn φ R +, k < 1, path gain condition ariss. k Fix k ( 1 ϕ) (13) ( 1 ϕ) 1 T, v Fix quiprobabl ( 1 ϕ) > 1 T, v > Fix pnalty ( 1 ϕ) < 1 T, v < Fix gain Th factor k is insrtd into (9) as (1-φ) yilding a lfthand path prdictor as dnotd in (14) that is adaptiv to varying link dlays. This k factor is uniquly rfrrd as th path fasibility prdictor factor. H w (1 ϕ) ) (14) jk( d ) P sj Th prdictor multiplir w is rplacd with I in (14) to giv a final routing inquality of Eq as such that consistncy is rachd for (10) (i.. T,v Fix whn h 0, indicating that th dlay-constraind path is an optimal hop path). Equation (15) is trmd as th Path Fasibility Prdiction (PFP) inquality for diffrntiation with th T inquality (9). H prdictor rsidual QoS jk( d ) w (1 ϕ) ) (15) P sj

6 JOURNAL OF NETWORKS, VOL., NO. 3, JUNE Thr ar two primary strngths of th PFP inquality ovr th T inquality. First, th inclusion of th apriori fasibility prdictor factor k (1-φ) transforms th T inquality (9) from a blind computation modl into a prdictiv basd computation modl (15). Scond, substituting w with I stms from th inhrnt wak satisfying critria of th T inquality. In addition, th casual or random charactristic of th T inquality is rducd whr slction of links on a routing path is logically influncd by th initial man I, drivd from an application s hop count and dlay-constraint rquirmnt. On potntial us of I in (15) is found in routing of hard ral-tim communication channls [3]. Without making spcific linkag to ithr rat-basd or schdulrbasd schduling policis [4], I can b mappd as th targt dadlin or worst-cas dlay that can b offrd to a connction on ach link in th routing path P sd. Link dadlins [6] can b calculatd by knowing: th sourc and dstination ndpoints (assuming hop counts on th optimal path); th traffic modl consisting of minimum intr-arrival tim, maximum packt lngth and maximum burst siz; th nd-to-nd dlay bound. Th calculation for th link dadlins is inhrntly influncd by th rquird rsourcs of a connction. Thy ar link bandwidth and buffr spac rquirmnts. By substituting link datlins in (15) as I, routing would aid jittr control [4], thus potntially minimizing som buffr spac rquirmnts by computing a path with a low link to link dlay variations. C. Path Gain and Path Pnalty Proprty of th PFP Modl W laborat furthr in this sction th adaptability and influnc of th path fasibility factor k to variations in link dlays and rout corrctiv capability for th proposd CMH. Two mismatchd cass ar considrd in Fig. 5. for link d 01 whr d 01 > d 1 and d 01 < d 1. Cas 1. d 01 > d 1 ; assum d 01 d and d 1 0.5d T,1 d 01 + d Fix ϕ Fix 1 T,1 k (1 0.5) 0.75 d + 0.5d 0.75d d 0.75d 0.5 d Cas. d 01 < d 1 ; assum d 01 d and d 1 d T,1 d 01 + d 1 d + d 1.5d As dlay on link d 1 dlay is incrasd to d, th xact man T,1 riss abov th maximal allowabl fixd man Fix rsulting in th mismatch factor φ to hav a ngativ valu. Th nt valu of th prdictor is hnc highr bcaus of th up-scaling of th k factor from 1.0 to 1.5. For cas d 01 > d 1, whn d 1 0.5d, k Th nt prdictor product is down-valud by a factor of 0.75 (or 75%) yilding a path gain of 0.5. Subsquntly, if thr is an incras in th dlay of th nxt link by about 5% of th Fix (i.. d 3 1.5d), th PFP inquality (15) will still hold. Anothr intrsting aspct of th k factor is adaptability to routing path divrsions. A divrsion causs a routing computation to vr from an optimal to a non-optimal rout rsulting in a fin-graind tuning of Fix. Byond this divrsion point, routing computation must find a path with a tntativ man T,v lowr or qual to that nw lowr tund Fix. Th variabl Fix has an invrs proportional rlationship with th quantity H jk(d) + h. Equation (16) shows th cost offst dnotd as h div du to routing divrsions at any routing computation point. H sk(d) is th optimal hop cost from sourc s to dstination d via outgoing nod v k. h div H H (16) jk( d ) sk( d ) As mor routing divrsions ar ncountrd, h div incrass making Fix smallr. Th mismatch ratio φ is mor ngativly biasd thrfor inflating th lft-hand prdictor product. This condition is howvr an advantag sinc it could prvnt routing computation from bing rratic saving prcious computational mssags. Any slightst variation btwn Fix and T,v ithr du to larg fluctuations in ntwork link dlays or routing path divrsions is capturd by φ that ultimatly affcts th prdictor. Th dsird objctiv is to always maintain k 1 (unity) on th tntativ routing path as th algorithm travrss th path. It is important to mntion that a divrsion can only happn du to a mismatch btwn Fix and T,v so significant that th PFP inquality is violatd. Th k factor is infrrd to b ffctiv for finding a balancd distribution of ntwork link dlays on any optimal routing path, and to limit or prvnt routing computation from going astray du to divrsions on th non-optimal path. IV. ROUTING INFORMATION AN TABLE STRUCTURE In this sction w discuss routing information that must b availabl for th xcution of CMH. Each nod owns a routing tabl containing routing information for th computation of th PFP inquality and on th dlayconstraind connction sssion. Assuming many sssions xists with distinct sssion idntifir S i. Th ntry in th routing tabl for a S i at any nod i is shown in Tabl 1. Fix ϕ Fix T,1 k (1 ( 0.5)) 1.5 d 1.5d d 0.5 H(S i, i, j) LINK_LY(i,j) PATH_LY(S i) TABLE I. ROUTING TABLE INFORMATION SP hop count to rach th dstination via ach adjacnt nighbor nod j from nod i Th updatd dlay of links conncting nod i to ach adjacnt nighbor nod j Th accumulatd path dlay to rach nod i from th sourc

7 5 JOURNAL OF NETWORKS, VOL., NO. 3, JUNE 007 A global-stat databas that rprsnts th topological connction (binary connctivity) of th ntwork must b kpt. Each nod uss this global connctivity map to comput th SP hop counts to all othr nods (all possibl dstinations) using ijkstra s [17] algorithm. It sorts th H(S i, i, j) ntry giving prcdnc to adjacnt nighbor nods with th fwst hop counts to rach th dstination.g. H(S i, i, m) < H(S i, i, n) < H(S i, i, k) whr m, n, k ar dirct nighbors of i. This mans that adjacnt nighbors with th fwst hop counts ar always givn priority for valuation. W rfr to th spcification of OSPF [10] that xplains th procdur of stat updat and maintnanc of th global-stat databas. Nvrthlss, th only global information that CMH nds to stor is binary topological information (i.. for calculation of th SP hop counts) and, addition and failur of nods and links that changs th ntwork topology is xpctd to b infrqunt. Th SP hop counts can b pr-computd and kpt in a global SP hop count tabl providd ntwork topology is intact. Th storag cost and protocol ovrhad for maintaining this global topological databas is minut compard with algorithms that dpnd on global-stat of dynamic link mtrics (.g. dlay). Th proposd CMH is oblivious to th problm of stat information imprcision as this is particularly rlatd to th stalnss of global-stat [], [0]. Routing tabl xplosion is instantanous and fficint whr th siz is a function of th numbr of ongoing connction sssions. A connction rqust is squntially passd from on nod to anothr if only th a priori condition of th PFP inquality is mt. This implis that th routing tabl is not a forwarding tabl. Basd on routing information rquirmnts of Tabl 1 and th PFP inquality (15), CMH is considrd as hybrid, whr rout slction is basd on a pr-computation (i.. H(S i, i, j)) and on an on-dmand (i.. LINK_LY(i, j)) approach. V. ROUTING CONTROL MESSAGES In distributd routing algorithms, routing path computation and stup ar don ithr by xchanging a control mssag in a squntial mod or many control mssags in paralll. Ths control mssags ar madto-masur whos siz and information is dpndnt on th rquirmnts of an algorithm. Th standard critria in dfining a control mssag is by dtrmining how much information nds to b communicatd, and communication bandwidths and nodal buffr spacs should not b ovrly consumd. For xampl, in [18] th control mssag siz is limitd to th siz of an ATM cll for samlss and fficint mssag procssing in th routrs. For many prominnt RAs [14], [18], a standard fail-saf approach is to rcord routing path information at intrmdiat nods so that small control mssag siz is utilizd. An opposit stratgy is adoptd for CMH using biggr mssag spac primarily for routing loop dtction. This implis that no mchanism for routing loop rmoval is ndd for CMH. Thr control mssags ar dfind to implmnt CMH. Thy ar PATHRQST, CRANKBACK and PATHACK mssag. PATHRQST is a connction rqust passd from th sourc to th dstination squntially travrsing any intrmdiat nods to build th routing path. CRANKBACK is passd in rvrs to th prdcssor nod from th nod whr th routing instanc is currntly at on th tntativ routing path. Assuming that routing instanc is at v, as in Fig., th succssor and prdcssor of v is v 3 and v 1 rspctivly. Nod v can ithr forward a PATHRQST to v 3 or rturn a CRANKBACK to v 1 dpnding on th outcom of tntativ path dlay tsts. Whn a dlay-constraind routing path is found, PATHACK is snt in rvrs along th succssfully computd routing path to rsrv th rsourcs and admit th connction. PATHRQST(S i, src, r{ },, I, acmly, h) CRANKBACK(S i, src, r{ },, I, h) PATHACK(S i, src) Hr, src is th sourc addrss, dst is th dstination addrss, r{ } is th list of nodal addrss that formd th partial or complt routing path, is th dlay constraint, I is th initial dlay, acmly is th accumulatd dlay from th sourc and h is th distanc in hops th mssag has travld from src. Th control mssags ar only activ during th path computation phas. For any connction sssion S i, th control mssags ar discardd onc a path is found (whn PATHACK mssag rachs src) or whn no fasibl path xists (whn CRANKBACK is rturnd to src). Th control mssags can only travl a maximum distanc of on hop at any computation instanc. VI. ELAY-CONSTRAINE MINIMUM-HOP (CMH) ISTRIBUTE ROUTING ALGORITHM In this sction, th huristics of th proposd CMH algorithm is xplaind. Upon rcipt of a connction stablishmnt rqust to a dstination dst, with a dlay constraint. A sourc src, initiats CMH by issuing a uniqu connction sssion idntifir S i. Th src builds th routing tabl, initializ h 0 and acmly 0, and is now th activ routing nod rfrrd to as th had. Any nod rciving a PATHRQST or a CRANKBACK also assums th rol as had. Th had slcts an adjacnt nighbor nod dnotd as succssor succ from H(S i, i, j) tabl ntry (had i and succ j) and calculats th tntativ path dlay dnotd in (I). Th tnt_dly(src,succ) is th tntativ path dlay up to th slctd succ. tnt _ dly( src, succ) acmly( Si,had) + LINK _ LY( had, succ) LINK_LY(had, succ) is th local link dlay conncting had and succ. Th acmly(s i, had) is th accumulatd path dlay from src to had xtractd from th PATHRQST rcivd by th had. Th had valuats. (I)

8 JOURNAL OF NETWORKS, VOL., NO. 3, JUNE BEGIN _ dly( src succ) (II) tnt, If (II) is satisfid, th had valuats (III). It tlls th had how many hops it is locatd away from dst via th succ. H ( S i,had, succ) 1 (III) Whn (III) is satisfid, th had is on final hop from dst whr succ dst. Th had snds a final PATHRQST to dst. Th dlay-constraind routing path is found. stination dst rturns PATHACK towards th routing path in rvrs to confirm th connction thrby rsrving rsourcs. H ( S i,had, succ) > 1 (IV) If othrwis (IV) is rachd, routing must travrs mor than on hop to rach dst. It indicats that succ dst. This condition calls th had to valuat th PFP inquality (Eq. 5.15). Using (I) and h from th rcivd PATHRQST, th had calculats Fix (Eq. 5.10), T,v (Eq. 5.11) and φ (Eq. 5.1) to valuat th PFP inquality. If th PFP inquality is satisfid, th had stors acmly(s i, had) in PATH_LY(S i ) tabl ntry. Bfor fowarding PATHRQST to th succ, th had updats PATHRQST contnts (i.. acmly(s i, had) tnt_dly(had,succ), incrmnts h by 1 and appnds its addrss in r{ }). Th succ bcoms a nw had subsqunt to accpting th PATHRQST. Whn ithr PFP inquality or (II) is violatd, th had slcts anothr succssor from H(S i, i, j) tabl ntry. If all succssors ar slctd and individual valuation fails, routing computation at had trminats. Th had snds a CRANKBACK to its prdcssor. Prdcssor addrss is listd in r{ } containd in th PATHRQST snt arlir to had. Th had omits this prdcssor addrss from r{ } and dcrmnts h by 1 bfor snding th CRANKBACK. Routing tabl ntry cratd arlir is hnc dltd by th had. Th prdcssor bcoms th had upon rciving th CRANKBACK. This rappointd had utilizs th formrly stord PATH_LY(S i ) as acmly(s i, had) and rvisits th valuation. CMH routing computation is trminatd if CRANKBACK is rturnd all th way to src. A had must slct a succ according to its sortd list (i.. prcdnc for succ with lowst SP hop count), a had cannot slct a succ that has alrady bn slctd, a had must nsur that a slctd succ is not listd in r{ } to avoid routing loops. Th distributd huristics for CMH is givn blow. A. Routing Loops Avoiding or limination of routing loops is important for QoS-routing algorithms. Routing loops ar prvalnt in a RA that dpnd on th global-stat whn th routing tabls ar outdatd. Most RAs gnrally xprinc forwarding loops whn a connction rqust snt by a nod is ithr rturnd to itslf or forwardd to any nod in th st that alrady formd th partial routing path. A larg majority of RAs liminat ths frquntly occurring forwarding loops using additional. gt a succ from H(S i, i, j) ntry 3. switch (CASE 1 or CASE ) 4. CASE 1: if ( succ H(S i, i, j): succ unslctd && succ r{}) 5. if ( tnt_dly(src,succ) > ) 6. loop: go to lin /*gt anothr succssor*/ 7. ls if ( tnt_dly(src,succ) ) 8. if ( H(S i,had,succ) 1 ) 9. snd final PATHRQST to dst 10. EN ROUTING /*dlay-constraind path is found to dst*/ 11. ls if ( H(S i,had,succ) > 1) 1. if ( prdictor rsidual-qos ) 13. snd PATHRQST to succ /*succssor bcoms had*/ 14. ls if ( prdictor > rsidual-qos ) 15. loop: go to lin /*gt anothr succssor*/ 16. CASE : if ( succ H(S i, i, j): succ slctd succ r{}) 17. if (had src) 18. snd CRANKBACK to prdcssor 19. go to lin /*prdcssor bcoms had*/ 0. ls if (had src) 1. EN ROUTING /*connction stablishmnt faild*/ loop rmoval mchanisms [14]. This loop limination phas adds xtra complxity and incurs mor mssags, in addition to bing tim consuming. On advantag is small siz of rqust mssags can b usd. To avoid forwarding loops from occurring with CMH, routing path nodal addrsss ar rcordd in th PATHRQST and CRANKBACK mssag. In th CMH huristic, an idntity xamination is prformd by th had to nsur that th slctd succssor succ is not nlistd in r{ }. This prvntativ tchniqu avoids routing loops from vr occurring during routing computation. This schm is fundamntally simpl and fficint to implmnt. On potntial drawback is PATHRQST mssag payload may incras linarly with hop distanc. Suddn trmination in routing computation is invitabl if th mssag payload is out-of-bounds of th mssag siz. Nvrthlss, two constructiv and logical xplanations ar givn to trivializ th prcivd problm. 1. Th lngth of a loop may only span a fw nods away. Only small siz loops xist in most instancs of forwarding loop occurrncs. In addition, studis [15], [16] indicat that th Intrnt possss a small-world proprty whr th avrag hops-pr-path ratio for many combinations of routing paths is small. For th

9 54 JOURNAL OF NETWORKS, VOL., NO. 3, JUNE 007 rasons abov, w say that small siz of r{ } is ndd in th PATHRQST and CRANKBACK mssag.. If th IPv4 [10] addrss siz (i.. 3 bits) is considrd, a 10 hop routing path only occupis a small 40 byts mssag spac to carry th full addrsss of th routing path nods r{ }. Routr addrss siz for IPv6 [11] is incrasd to 18 bits. Th spcifications of IPv6 dmand th minimum link Maximum Transfr Unit (MTU) to b at 180 byts. Again, a 10 hop routing path consums 160 byts payload spac of th allocatd 140 byts data siz (+ 40 byts of hadr). Suffic to say, PATHRQST and CRANKBACK mssags will not b lost or droppd bcaus th control mssags would not undrgo packt fragmntation. Th siz of routing information containd in PATHRQST and CRANKBACK mssags is guarantd to not consum link bandwidth and buffr spac. B. Tim and Computational Complxity Th tim complxity of a distributd routing algorithm concrns th total tim ndd to stablish a connction from a sourc to a dstination. This corrsponds to a singl round trip tim of th call connction phas. For squntial distributd computation of th CMH, xactly on singl mssag is spnt on ach link, quivalnt to on unit tim of mssag xcution. If th lngth of th path from th sourc to th dstination is givn as L, thn th bound for th tim complxity of CMH is of O(L) units of tim. Optimally, CMH rachs th dstination in th shortst hop distanc H opt whr ach nod on th optimal routing path slcts only th first succssor listd in th routing tabl. Routing crankbacks ar non-xistnt. Thr is at most on PATHRQST and PATHACK mssag on ach link, round trip on th optimal hop path. Th bstcas computational complxity is linar and is of O(H opt ). In th worst-cas complxity, CMH will hav travrsd all possibl paths btwn th sourc and th dstination. Each link on th numratd paths will xprinc a crankback. Th worst cas computational ffort rquird in numrating all paths in a compltly connctd ntwork is prsntd in [9] using a mthod calld sliding-window. For a ntwork with N nods and dgr, (17) rprsnts th uppr-bound on th computational complxity in finding all possibl combinations of routing paths btwn any sourcdstination pair. F ( N, ) ( N 5N + 8)( 1) + 1 (17) For a compltly connctd ntwork, N-1; by nglcting th constants and rmoving th smallr ordr of th function, th worst cas computational complxity is polynomial and boundd by O(N 3 ). Rmarkably, simulation shows that th avrag numbr of mssags xchangd for CMH is much lowr than th worst cas and CMH s rsults ar closly matchd to th bst-cas complxity. Succss CMH MFA CUR LP lay Constraint (ms) Figur 3. Connction succss, ntwork siz of 100 nods, dlayconstraint from 10ms to 45ms VII. SIMULATION AN RESULTS W dvlopd a routing application to simulat th routing prformanc of CMH in random ntworks and compar against MFA [7], lay-constraind Unicast Routing (CUR) [14] and LP (i.. ijkstra s) [17]. CUR kps a cost vctor and a dlay vctor tabl, and altrnats btwn th two to sarch for a suitabl dlayconstraind last-cost path. A random modl [8] is usd to gnrat a ralistic random topology with an avrag nod dgr of four. Th graphs wr gnratd until a fully connctd random ntwork with a minimum individual nod dgr of on is found. Nods wr placd in a rctangular coordinat of km. Ntwork links wr bidirctional with homognous capacitis of 155Mb/s. Link dlays wr asymmtric and wr a function of propagation and quuing dlay, (i,j) p(i,j) + q(i,j) whr p(i,j) p(j,i) and q(i,j) q(j,i), thrfor (i,j) (j,i). A random amount of traffic was gnratd on ach link dnotd as arrvrat, and a sourc and dstination wr randomly slctd and rfrrd to as a connction rqust sssion. Th link utilization factor, ρ was randomly gnratd btwn 0 and 0.8 with a uniform distribution. Quuing dlay on ach link was takn as, ρ/(1-ρ) (1/arrvRat). In ach sssion, th numbr of mssags xchangd to construct a path was rcordd. Th sssion procdur was rpatd until confidnc intrvals blow than 5% of th avrag valu was achivd, using 95% confidnc lvls. Simulation was rpatd for varying ntwork sizs from 0 to 00 nods across 8-point dlay constraints from 10ms to 45ms. A. Prformanc Comparison with MFA, CUR and LP algorithm Th connction succss prformanc for 100-nod ntwork siz is shown in Fig. 3. CUR and LP achivd optimum succss prformanc sinc both algorithms ar abl to dtrmin a fasibl dlayconstraind path from its global-stat. W calculatd th ovrall blocking prcntag rlativ to LP. Connction sssion blocking for CMH is only 1.5% compard to

10 JOURNAL OF NETWORKS, VOL., NO. 3, JUNE MFA, which is 3.33%. Blocking for MFA is highr for tight dlay-constraints i.. 10ms 10.%. MFA s poor connction succss is du to two factors. First, th variabl ) min in (9) that is a natural variabl of link dlays in th ntwork can b high if th routs which MFA follows lis on th ntwork or sub-ntwork that is loadd with high traffic. For loadd ntworks with high hops-pr-path ratio, th multiplicativ product of H jk(d) ) min in (9) will b hug. As a rsult, routing computation in MFA is unabl to travrs som potntial paths. Scond, whn ithr tntativ_dlay > or T (9) is violatd, MFA initiats a crankback. This rdundancy limits th chancs of finding a fasibl routing path simply bcaus of th incras in th prdictor product, contributd by a highr hop count to dstination quantity H jk(d), for vry crankback suffrd. spit bing slightly bttr than MFA, succss rats for CMH ar lowr compard to CUR and LP. W infr that th fixd man, Fix (10) in (15) contributd to th drop in connction succss. For rlativly strict (small) and incrasing hop siz (a routing path with high hop lngth), th numrator in (10) causs Fix to b small. If th tntativ man, T,v (11) of th computd path is clos or abov Fix, this condition will consquntly caus th mismatch ratio, φ (1) to hav ngativ valus. As a rsult, th factor k 1, causing th prdictor to b pnalizd mor oftn. Th total product H jk(d) I (1-φ) bcoms tight and is rstrictiv of forward movmnt. CMH was forcd to mak frqunt crankbacks and was thrfor not abl to xplor many paths. Unlik MFA, optimum connction succss is achivabl by softning of th initial man, I (10) which would compnsat th prdictor if th path followd is rstrictiv. Th I has an uppr-bound valu whn its dnominator is th SP hop count btwn th sourc and th dstination, (i.. whn H jk(d) H sk(d) for v j v s ). Avrag Computational Mssag NOFx layx laylp laylp (18) 4 CMH, 10ms CUR, 10ms CMH, 45ms CUR, 45ms Numbr of ntwork nods Figur 4. Avrag mssag ovrhad, ntwork siz from 0 nods to 00 nods, dlay-constraint of 10ms and 45ms Avrag Hop CMH, 10ms CUR, 10ms LP, 10ms CMH, 45ms CUR, 45ms LP, 45ms Numbr of Ntwork Nods Figur 5. Avrag hop distanc travrsd, ntwork siz from 0 nods to 00 nods, dlay-constraint of 10ms and 45ms NOF CMH (10ms) CMH (45ms) CUR (45ms) Numbr of Ntwork Nods CUR (10ms) Figur 6. Th NOF of CMH and CUR rlativ to LP at dlay constraint of 10ms and 45ms In most computation sssion, th succssfully computd routing path would not b optimal bcaus it would dviat by on or mor hops away from th optimal lngth i.. H jk(d) H sk(d). This dviatd hop valu is actually th h variabl found in (10). Knowing this h valu a priori and utilizing it in stting an appropriat valu for I i.. I H jk(d) + h, can guarant highr connction succss prformanc and vn bttr path prdictability. Figur 4 shows th avrag mssag ovrhad vrsus varying ntwork sizs for CMH and CUR. Avrag mssag growth is slow and logarithmic in th incrasing ntwork siz. Th computational ovrhad of CMH is lowr than CUR. This is bcaus CUR spnt thr diffrnt control mssags as th distributd huristics altrnats btwn th last-cost and last-dlay paths at ach routing nod. CMH on avrag xchangd about thr fwr mssag compard to CUR to construct dlay-constraind paths at 45ms,.g. N 100, CMH 4.6 and CUR 8.0 mssags, N 00, CMH 5.0 and CUR 8.6 mssags. Th avrag numbr of hops travrsd for succssful connctions is shown in Fig. 5. W first say that for LP that uss ijkstra s algorithm to comput shortst-dlay path to th dstination, this dlay-optimization is achivd at th xpns of high hop cost. For rlativly strict, only a limitd st of routs ar availabl. Th

11 56 JOURNAL OF NETWORKS, VOL., NO. 3, JUNE 007 probability of availabl routs with short hop lngths that satisfis th is low. In addition, th strict causs Fix to b small rsulting in th slction of links with low dlays on th path. For 10ms, th hop cost of CMH is modratly bttr compard to CUR. As th is incrasd to 45ms, a rout with smallr hop distanc that satisfis th is mor prfrrd than a rout that optimizs th dlay. This suggsts that links with highr dlays ar mor likly to b part of th computd path. Th quantity, H jk(d) in (15) mans that CMH prioritizs and so chooss minimum hop routs instad of shortst dlay routs. pnding on th lvl and ntwork siz (or th hop count btwn a sourc-dstination pair) that ultimatly dtrmins Fix, CMH inhrntly can bhav from an algorithm that prioritizs dlay to mor lik on that optimizs hop cost. From Fig. 5, th avrag masurd cost at 45ms for CMH is comparabl to of CUR. CMH is abl to achiv good connction succss rat using modst mssag ovrhad with minimal hop-cost, and at th sam tim satisfying th dlay-constraint without vr nd to stor additional global-stat information. On limitation of CMH as discussd is th rstrictiv computation of a fasibl dlay-constraind path whn th prdictor product of th PFP bcoms tight. Nvrthlss, w hav providd a logical xplanation on ngating connction sssion blocking of CMH. B. Analysis of istribution of lays ovr Routd Paths On of th important QoS rquirmnts of dlaysnsitiv multimdia applications is maintaining low jittr. Convntional mthods of controlling jittr ar to control th rat of packt strams by sourcs and provid adquat buffr spacs along th computd path to avoid packt loss. Bcaus jittr is partly du to variations in quuing dlays and propagations, w bliv QoS-routing algorithms can aid jittr control [4] by computing a routing path that has a low varianc of dlays (i.. low link to link path dlay variations). In this simulation, w masurd path dlay variancs of CMH and CUR in random topology for th ntwork siz of 100-nods. From th rcordd rsults, w analyzd th 100-sampl (i.. α 0.0) long trm profil of path dlay variancs using an Exponntial Wightd Moving Avrag (EWMA). A similar simulation procdur was usd to gnrat random topology and ntwork link dlays for this simulation. W masurd path dlay variancs of CMH and CUR whn both qually rtrivd a dlayconstraind solution with a hop cost of 6 hops. Figur 7 shows th masurd path dlay variancs and th moving avrag (i.. EWMA) of CMH and CUR for 0ms. W infr two opinions. First, paths computd by CMH ar mor likly on avrag to hav smallr computd path dlays. W dmonstrat this opinion by rfrring to th Non-Optimality Factor (NOF) plot in Fig. 6 whr rsults indicat bttr optimality of CMH than CUR. Th NOF (18) rprsnts a masur of infficincy of a distributd routing algorithm x (i.. CMH and CUR) compard to th optimal path computd by LP. Scond, paths computd by CMH would prsnt lowr dlay varianc compard to CUR. lay (s) CUR CMH CUR (100-point EWMA) CMH (100-point EWMA) 5.0E E E E E-03.5E-03.0E E E E E Rqust Figur 7. Th EWMA of computd paths dlay varianc at 0ms In Fig. 7, CMH xhibits smallr long trm avrag fluctuations of variancs compard to CUR. Rsults in Fig. 7 most importantly indicat that I and Fix hnc th path fasibility prdictor k (1-φ) (13) prvnts (or limits) a computd path from having a wid path dlay varianc. This is an inhrnt fatur of th PFP inquality of CMH. VIII. CONCLUSION In this papr, w prsntd a nw distributd dlayconstraind routing algorithm. Our CMH is uniqu from othr RAs as it mploys a novl adaptiv path fasibility prdictor that is abl to mak an a priori prdiction of th fasibility of a tntativ routing path, don intlligntly by utilizing both global topological and local link-stat information. W valuatd through simulation and compard CMH against th wll-known CUR and LP. Avrag mssag prformanc of CMH is modst and bttr than CUR for th sam masurd cost prformanc. CMH toggls from bing a dlay-optimization to a dlay-constraind hopminimization algorithm. Th proposd CMH is vry simpl to implmnt, highly scalabl, fficint and provids gratr insnsitivity to th stalnss of th linkstat than algorithms that rly on global link-stat information such as CUR and LP. Also, nodal storag rquirmnts ar minimal in comparison with many contmporary routing algorithms. Most importantly, w hav dmonstratd with CMH and th PFP modl that for a RA that mploys th local-stat whr no global information is prsnt, suitabl computation modls can b dvisd that ar adaptiv and intllignt to improv routing prformanc. This stratgy can bst achiv ovrall scalability of QoS-routing algorithms. W bliv that RAs ar qually usful and important as SRAs for som routing problms whr th xistnc of th globalstat is trivial.

12 JOURNAL OF NETWORKS, VOL., NO. 3, JUNE IX. REFERENCES [1] S. Chn and K. Nahrstdt, An Ovrviw of Quality of Srvic Routing for Nxt Gnration High-Spd Ntworks, IEEE Ntworks Mag., Novmbr/ismbr, 1998, pp [] A. R. M. Shariff and M. E. Woodward, A istributd Algorithm for Unicast QoS-Routing using Path Fasibility Prdiction, IEEE Workshop on High Prf. Switching and Routing, Poznan, Jun 006. [3] G. Apostolopoulos, R. Gurin, S. Kamat and S. K. Tripathi, Quality of Srvic Routing: A Prformanc Prspctiv, ACG SIGCOMM Comp. Comm. Rv., vol. 8, issu 4, Octobr, 1998, pp [4] H. Zhang and S. Kshav, Comparison of Rat-Basd Srvic isciplins, ACM SIGCOMM Comp.Comm. Rviw, vol. 1, pp , Sptmbr [5] S. Lin and. J. Costllo, Error Control Coding: Fundamntals and Applications, Prntic Hall, Englwood Cliffs, Nw Jrsy, [6].. Kandlur, K. G. Shin and. Frrari, Ral-Tim Communication in Multi-Hop Ntworks, 11 th Intl. Conf. on istributd Computing Sys., pp , [7] S. S. b and M. E. 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Rxford and K. G. Shin, Evaluating th Impact of Stal Link Stat Quality-of-Srvic Routing, IEEE/ACM Trans. on Ntworking, vol. 9, no., April 001. [3] C. M. Aras, J. F. Kuros,. S. Rvs and H. Schulzrinn, Ral-Tim Communication in Packt Switchd Ntworks, Proc. of th IEEE, vol. 8, pp , January [4]. C. Vrma, H. Zhang and. Frrari, lay Jittr Control for Ral-Tim Communication in a Packt Switching Ntwork, IEEE Proc. of TRICOMM 91, pp , April A.R. Mohd Shariff was born in Pnang, Malaysia in H rcivd a B.Eng(Hons) in Elctrical and Elctronics dgr in 1998 from th Univrsity of Plymouth (UK). In 00, h obtaind his MSc. in Prsonal, Mobil and Satllit Communications from th Univrsity of Bradford (UK). H is currntly with th partmnt of Computing at th sam institution pursuing a Ph. dgr in Communication Ntworks. H workd as a sign and vlopmnt Enginr at Motorola CGISS R& (Pnang) from 1999 until 001 whr h was rsponsibl for th dvlopmnts of UHF VCO and PLL circuits, rcivr systms and antnnas of two-way analog and TETRA digital portabls. His currnt rsarch intrsts includ fixd and wirlss ad-hoc routing, QoS and ubiquitous ntworking. Mr. Mohd Shariff is a mmbr of th IEEE socity and a rcipint of th Malaysian govrnmnt scholarship. M. E. Wooward was born in rby, England in H graduatd with a 1st class honours dgr in Elctronic and Elctrical Enginring from th Univrsity of Nottingham (UK) in 1967 and rcivd a Ph. dgr from th sam institution in 1971 for rsarch into dcomposition of squntial logic systms. In 1970, h joind th staff of th partmnt of Elctronic and Elctrical at Loughborough Univrsity (UK) as a lcturr, bing promotd to Snior Lcturr in 1980 and Radr in Stochastic Modlling in H rmaind at Loughborough until 1998 whn h was appointd to th Chair in Tlcommunications at Univrsity of Bradford (UK) whr h also bcam th irctor of Tlcommunications Rsarch Cntr. His currnt rsarch intrsts includ quuing ntworks, tlcommunications traffic modling, quality of srvic routing and mobil communications systms. Profssor M. E. Woodward is th author of two books and ovr on hundrd rsarch paprs. H holds two ESPRC grants and is suprvisor to fiftn full tim rsarch studnts. H is a Fllow of th Institut of Mathmatics and its Applications (FIMA) and is both a Chartrd Mathmatician (CMath) and Chartrd Enginr (CEng).