Routing-Oriented Update SchEme (ROSE) for Link State Updating

Transcription

1 948 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 6, JUNE 28 Routig-Orieted Update SchEme () for Lik State Updatig Nirwa Asari, Gag Cheg, ad Na Wag Abstract Few works have bee reported to address the issue of updatig lik state iformatio i order to effectively facilitate Quality-of-Service (QoS) routig. The idea of modelig the QoS lik state iformatio as radom variables has bee reported, but oe of the existig works have provided a comprehesive probabilistic approach to lik state update that takes the probability desity fuctios of both the user s QoS requiremets ad the etwork s QoS measuremets ito accout. We propose the Routig-Orieted update SchEme () that utilizes the kowledge of the history of etwork operatios ad user s QoS requiremets to improve the efficiecy of lik state update without icreasig the etwork overhead. is a ew class-based lik state update scheme which itelligetly determies class sizes to miimize the impact of iaccurate lik state iformatio. Through theoretical aalysis ad extesive simulatios, we demostrate that outperforms other classbased lik state update policies. Idex Terms Quality of Service (QoS), routig, lik state update. I. INTRODUCTION THE ability to provide Qualify of Service (QoS) is a ecessity for the ext geeratio itegrated etworks. Today, QoS routig has become the fudametal focus of study. The goal of QoS routig is to fid a path that satisfies multiple QoS costraits while maximizig the etwork utilizatio ad miimizig users costs. QoS routig i geeral cosists of two critical issues: lik state dissemiatio ad route selectio [1]. The lik state dissemiatio addresses how the lik state iformatio is exchaged throughout the etwork; while the route selectio elaborates o how to fid the optimal path give the available lik state iformatio. May works have addressed the issue of route selectio [2]- [7]. I this paper, we cocetrate o the issue of lik state dissemiatio. The purpose of lik state dissemiatio is to provide the kowledge of QoS status of all the liks to the routig devices (e.g., routers) i a etwork. Based o this kowledge, the etwork ca the determie the best route for ay give ed-to-ed coectio to meet its QoS requiremets ad utilize the overall etwork resource efficietly. I order to provide the kowledge of all the QoS parameters of each lik, each lik itself must employ some scheme to report its ow QoS parameters, referred to as lik state update. Geerally, it is impractical to assume that routig devices have accurate Paper approved by T.-S. P. Yum, the Editor for Packet Access ad Switchig of the IEEE Commuicatios Society. Mauscript received September 27, 26; revised Jue 11, 27. This work has bee supported i part by the Natioal Sciece Foudatio uder grat The authors are with the Advaced Networkig Laboratory, ECE Dept., NJIT, Newark, NJ 712, U.S.A. ( asari@jit.edu). Digital Object Idetifier 1.119/TCOMM /8$25. c 28 IEEE lik state iformatio of all liks at all time, because this would require rapid lik state updates from all liks, hece cosumig a large amout of etwork resource. Therefore, a effective lik state update algorithm is ecessary to provisio QoS. Lik state update determies the behavior of how each ode updates its status to the etire etwork, icludig whe to update ad how to update. A widely used lik state update protocol, OSPF [8], which has also bee adopted i may types of etworks such as optical etworks [9], recommeds the lik state to be updated oce every 3 miutes. However, because of the highly dyamic ature of the traffic, updatig i such a log time iterval will result i stale/outdated lik state parameters. This will compromise the efficiecy of QoS routig. Several other lik state update policies, such as threshold, equal class ad expoetial class based update policies [1], have bee proposed. I the threshold policy, a update is triggered whe the differece betwee the curret value ad the previously updated value of a certai parameter exceeds a threshold. That is, give a threshold value τ, a update occurs whe b c b >τ,whereb is the previously updated value ad b c is the curret value of a QoS parameter. I the equal-class ad the expoetial-class based update policies, the values of QoS parameters are divided ito classes. A update is triggered whe the curret value of a QoS parameter chages from oe class to aother. For example, i a two-class situatio, if the rage (iterval) of the first class is (,b 1 ), ad the rage of the secod class is (b 1,b 2 ),the a update will happe whe b c chages from <b c <b 1 to b 1 < b c < b 2, or vice versa. What separates the equal class based lik state update policy from the expoetial class based lik state policy is the choice of the boudaries, or i other words, the partitioig of each class. I the equal class based lik state update, the class of a QoS parameter is partitioed ito equal-sized itervals, for example, (,B), (B, 2B), (2B, 3B),..., etc.. I the expoetial class based update, the classes are partitioed ito uequal-sized rages, (,B), (B, (f+1)b), ((f+1)b, (f 2 + f +1)B),..., etc., whose sizes grow geometrically by a factor of f, where B is a predefied costat. No matter which lik state update policy a etwork adopts, it is uavoidable that the QoS parameters of each ode kow to the etire etwork might ot be exactly accurate at ay give time, due to the staleess ad coarse classes. As a result, false routig is ievitable. Some works have bee doe i aalyzig the effect of stale or iaccurate lik state iformatio, ad attemptig to reduce its impact. I [11], extesive simulatios were made to ucover the effects of the stale lik state iformatio ad radom fluctuatios i the traffic load o the routig ad setup overheads. I [12]-[13],

2 ANSARI et al.: ROUTING-ORIENTED UPDATE SCHEME () FOR LINK STATE UPDATING 949 Fig. 1. Illustratio of cocave ad additive costraits: Cocave QoS parameters of lik 1, 2, ad 3 = C1,C2, ad C3. Additive QoS parameters of lik 1, 2, ad 3 = A1,A2, ad A3. The path is acceptable if mi {C1,C2,C3} C ad A1+A2+A3 A, where C ad A are required cocave ad additive costraits. the effects of the stale lik state iformatio o QoS routig algorithms were demostrated through simulatios by varyig the lik state update iterval. A combiatio of the periodic ad triggered lik state update is cosidered i [14]. Istead of usig the lik capacities or istataeous available badwidth values, Li et al. [15] used a stochastic metric, Available Badwidth Idex (ABI), ad exteded BGP to perform the badwidth ertisig. I this paper, for the purpose of savig etwork resources ad reducig the staleess of lik state iformatio, we itroduce a ew lik state iformatio update scheme, Routig- Orieted update SchEme () 1. The uiqueess of is that it takes the QoS requiremets of applicatios ad the etwork QoS behavior ito accout. As reviewed above, most of the existig lik state update schemes do ot cosider both the statistical distributios of the actual user s QoS requiremets ad the etwork s QoS behavior. I fact, we have discovered that the kowledge of the distributio of the user s QoS requiremets ad the history of etwork s QoS behavior ca greatly improve the efficiecy of lik state update ad the accuracy of QoS routig. The statistical distributio of the user s QoS requiremet ad the etwork s QoS behavior ca be obtaied from the etwork operatio history. The key cocept of is to utilize these statistical distributios ad desig a class-based lik state update scheme that is able to provide the most helpful lik state iformatio for the coectio setup processes, hece yieldig better performace tha other existig lik state update schemes. Via theoretical aalysis ad simulatios, we show that greatly outperforms the state of the art. The rest of the paper is orgaized as follows. Sectio II describes the properties of various types of QoS costraits. Sectio III defies the term false routig ad the cost of false routig. The, i Sectio IV, we describe our proposed efficiet lik state iformatio update scheme,. The simulatio results are preseted i Sectio V. Fially, cocludig remarks are give i Sectio VI. II. PROPERTIES OF QOS CONSTRAINTS Most of the QoS costraits (e.g., badwidth, delay) ca be categorized ito the followig three types: cocave, additive, ad multiplicative. Multiplicative costraits ca be coverted ito additive costraits by usig the logarithm operator. Therefore, oly cocave ad additive costraits are cosidered i the study of QoS routig. A cocave costrait works as follows: i the case of a multi-lik ed-to-ed path, 1 Prelimiary results of have bee preseted i [16] ad [17]. as log as the smallest (or largest) QoS parameter amog all the liks is larger (or smaller) tha the correspodig QoS requiremet, the this path is cosidered acceptable. Badwidth is a typical example of the cocave costrait. A additive costrait works as follows: i the case of a multi-lik ed-to-ed path, the sum of all the QoS parameters alog the path has to be less tha the correspodig QoS requiremet i order for this path to be acceptable. Delay is a typical example of the additive costrait. I Fig. 1, the path cosists of 3 liks: lik 1, 2, ad 3. Each of these liks has a cocave QoS parameter C 1,C 2,adC 3, respectively, ad a additive QoS parameter A 1,A 2,adA 3, respectively. If a coectio imposes QoS costraits C ad A, the the path is deemed acceptable if mi{c 1,C 2,C 3 } C,adA 1 +A 2 +A 3 A. Oe of the special characteristics of a additive costrait is that, from a per-lik poit of view, the QoS requiremet of each lik is related to the QoS behavior of all the other liks i the same path. If we cosider lik 2 i Fig. 1 as a example, lik 2 will be accepted if A 2 A (A 1 + A 3 ). Similarly, i a m-lik path, a lik amog these m liks, l j (j m), is acceptable if m A j A A i. i=1,i j Therefore, from the perspective of a sigle lik, it caot make the decisio whether to accept or reject a coectio purely based o its ow additive lik state metrics. As we ca see, the cocave costraits have quite differet properties from those of additive costraits; therefore, they have to be cosidered separately whe desigig a lik state update scheme. Those aforemetioed curret lik state update schemes (threshold, equal class, ad expoetial class updates) do ot take the differece of these properties ito cosideratio. I the ext few sectios, we will show how ca cope with both cocave ad additive costraits better tha the curret lik state update schemes. III. FALSE ROUTING Ideally, whe a coectio request with certai QoS requiremets is made to the etwork, the etwork s routig mechaism will accept this request ad setup the coectio if there are eough resources i the etwork to support the required QoS, ad reject the request otherwise. However, i the real situatio, sice the routig mechaism does ot always have the accurate lik state iformatio, it is uavoidable that some coectios will be falsely accepted whe the etwork actually caot meet the QoS requiremets; while some other coectios will be falsely rejected whe the etwork actually has eough resource to support the QoS requiremets. I this paper, a istace of the first situatio a coectio is falsely accepted is referred to as a false positive, ad a istace of the secod situatio a coectio is falsely rejected is referred to as a false egative. Both false positives ad false egatives costitute the defiitio of false routig. I other words, we cosider false routig has occurred as log as either a false positive or a false egative occurs. False positives ca jeopardize user s satisfactio sice users are experiecig poor QoS i this situatio. Meawhile, false egatives ca cause the uder-utilizatio of etwork resources

3 95 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 6, JUNE 28 by rejectig the coectios that should have bee accepted. Therefore, both false positives ad egatives are cosidered udesired situatios. Oe ca argue that oe situatio is more severe or, i other words, more costly, tha the other. To reflect this cocer, istead of simply gauge the performace of QoS routig by the probability of false routig, oe should compare the cost of false routig for more realistic evaluatio. A cost factor is used i, ad therefore is ot oly capable of miimizig the occurrece of overall false routig, but also miimizig the overall cost of false routig. Throughout the rest of this paper, we will use the cost of false routig as the measure of the efficiecy of various lik state update schemes. IV. ROUTE-ORIENTED UPDATE SCHEME () Here, we describe the ew class-based lik state update scheme,. The fudametal cocept of is to utilize the statistical distributio of the user s QoS request ad the etwork s QoS behavior i order to desig a efficiet class-based lik state update scheme. The distributio of the user s QoS request ca be obtaied from the user profile (for example, x% of the coectios requires y bps of badwidth). The distributio of the etwork s QoS behavior ca be derived from observig the operatio history. Takig delay as a example, may reports have studied the delay measuremets of various traffic types [18][19]. Referece [19] has proposed a method to measure the sigle-hop delay, represeted as the frequecy histogram of delay. Referece [2] directly idicates that the queue legth of a bottleecked lik is likely to be Gaussia distributed as log as there is a large umber of TCP sessios o this lik at ay give time. Sice queuig delay is a major cotributor of the ed to ed delay ad possesses the most dyamic ature, the distributio of queue legth ca also be used to derive the pdf of sigle-hop delay. The subject of Iteret measuremets, which is a readily pursued research, is beyod the scope of this paper. I this paper, we thus assume the pdf s of the user s request ad etwork s QoS behavior are kow for the purpose of illustratig the algorithm. Cosider a etwork composed of m liks, deoted by the graph G(V,E). We assume there is a routig device (either distributed or cetralized) that makes the decisio of whether to accept a coectio request ad fids the ed-toed paths that ca provide the appropriate QoS to all accepted coectios. The routig device makes the decisio based o the lik state iformatio acquired via lik state update. Geerally, i a class-based lik state update scheme, each lik updates its QoS parameter by usig a fiite umber of classes; here, let k be the umber of classes. For a give QoS parameter, we further assume its value ca oly fall withi a fiite rage (for example, the available badwidth of a lik ca oly be raged from up to the full lik capacity). Therefore, with k classes, the rages of the respective classes ca be expressed as: [B mi,b 1 ], [B 1,B 2 ], [B 2,B 3 ],...,[B k 1, B MAX ],whereb mi ad B MAX are the miimum ad maximum of the QoS parameter, ad B 1,,B 2,..., B k 1 are the boudaries of classes. To simplify the otatios, we let B = B mi ad B k = B MAX throughout the rest of the paper. For each class, there is also a represetative value which is ertised by the lik to the routig device as if Fig. 2. Illustratio of class boudaries ad ertised values. I the cocave case, a false positive occurs whe B 1 <b lj <x<b2. it is the exact value, deoted by B1,B2,...,Bk.For istace, if the available badwidth of a lik l j E falls i the rage of [B 1,B 2 ](class 2), the the lik state update message will ertise that the available badwidth of l j is B2.I short, the liks update their QoS status i a quatized maer. Fig. 2 illustrates the cocept of class-based lik state update. The routig device the makes the routig decisio based o the ertised values from all the liks. However, owig to quatizatio, false routig is ievitable. This ca be illustrated by cotiuig the above example: Whe lik l j reports its available badwidth as B2, the true value ca be aywhere from B 1 to B 2. Therefore, if a coectio attemptig to utilize lik j requests x amout of badwidth ad B 1 <x<b2, the routig device will accept this request. However, it is possible that the actual available badwidth of lik l j is less tha x but greater tha B 1, ad therefore icurrig a false positive. O the other had, if B2 <x<b 2 ad the actual available badwidth of lik l j is greater tha x but less tha B 2, a false egative will occur (refer to Fig. 2). The goal of is to desig the class boudaries ad the ertised values itelligetly to miimize the cost of false routig. Owig to the differet properties of cocave costraits ad additive costraits as described i Sectio II, we have to cosider them separately i the desig of. A. Cocave QoS Costraits: We start our aalysis with a sigle cocave QoS metric badwidth. Whe a coectio requests x amout of badwidth from lik l j, the coectio will be accepted if x < B (l j ), where B (l j ) deotes the ertised available badwidth of lik l j, ad will be rejected otherwise. Assume that the actual available badwidth of l j, b lj, is withi the rage of class (1 k, k is the total umber of classes), the B (l j )=B. A false positive occurs whe x<b (l j ) but b lj <x(the actual badwidth is less tha the requested badwidth). For this coditio to hold, the followig has to be true: B 1 <b lj <x<b (l j ). Recall that we assume the statistical iformatio of the user s QoS requiremets ad the etwork s QoS behavior are kow, from which we ca derive their correspodig probability desity fuctios (pdf). Therefore, we ca simply treat x ad b lj as radom variables. Let q (x) be the pdf of the user s request x, adp (b) be the pdf of the actual available badwidth b lj, the we ca write the probability of a false positive as: Pr{False Positive, class=} = B 1 q(τ)dτ p (b) db. (1) b Similarly, the probability of a false egative is: Pr{False Negative, class=}

4 ANSARI et al.: ROUTING-ORIENTED UPDATE SCHEME () FOR LINK STATE UPDATING 951 = b q(τ)dτ p (b) db. (2) B B Equatio (1) represets the situatio of B 1 <b lj <x< B (l j ), ad (2) the situatio of B (l j ) <x<b lj <B. Note that (1) ad (2) are ot coditioal probabilities; they describe the probability of false positive/egative AND the curret class is. Therefore, the overall probability of a false positive is Pr{False Positive}= k Pr{False Positive, class=}, (3) =1 ad the overall probability of a false egative is Pr{False Negative}= k Pr{False Negative, class=}. (4) =1 Sice the severity of a false positive ad a egative might ot be equal, let c p be the cost of a false positive ad c be that of a false egative; the total cost of false routig C ca be writte as: C = c p Pr{False Positive}+c Pr{False Negative} =c p k =1 + c k =1 B B 1 b B b B q(τ)dτ p (b) db q(τ)dτ p (b) db (5) I order to miimize C with respect to B ad B,we eed to fid the solutios to the followig equatios: C B = c C B B = c p B 1 +1 q(τ)dτ c p p(τ)dτ c B q(τ)dτ = (6) B p(τ)dτ = (7) B. Additive Costraits: I the aalysis of additive costraits, we choose delay as our example for the rest of the paper. A uique property of additive costraits is that the decisio of whether a lik l j ca support the QoS requiremet caot be made based solely o this lik s QoS measuremet; it ivolves the QoS measuremets of all other liks alog the path. Therefore, from the routig device s poit of view, the decisio of whether to select lik l j depeds o whether B (l j ) <x B (l i ). (8) i path,i j I other words, the decisio is made based o whether the ertised delay of l j is less tha the user s request x subtracted by the sum of the ertised delays of all other liks i the potetial path. Agai, sice we assume the statistical iformatio of x (request) ad b lj (actual delay i lik l j ) is available, x ad B (l j ) ca be treated as radom variables, where the pdf of B (l j ) ca be derived from the pdf of b lj. The, the right half of (8) ca be viewed as the sum of radom variables. Let S = x B (l i ),ad i path,i j f S (s) be the pdf of S. Essetially, S is the criterio of whether the coectio will be accepted to utilize lik l j. Therefore, S will be referred to as the accept/reject criterio i this paper. Applyig the Cetral Limit Theorem, f S (s) ca be approximated by Gaussia distributio whose mea ad variace ca be derived from the pdf of x ad B (l j ).Note that the mea ad variace are affected by the umber of hops i a coectio. To simplify this problem, adopts the average hop cout i a etwork to estimate f S (s). Aswe will show i our simulatios, this simplified estimatio still produces better performace for tha equal-class ad expoetial-class lik state updates. Assume that the actual delay of lik l j falls i class, i.e., its ertised delay B (l j )=B. O the per-lik basis, a false positive occurs whe B (l j ) <S<b lj <B,ad a false egative occurs whe B 1 <b lj <S<B (l j ). Therefore, we ca write the probability of a false positive ad a false egative as: Pr{False Positive, class=} = b f B B S (s)ds p (b) db, (9) Pr{False Negative, class=} = B B 1 b f S (s)ds p (b) db, (1) where p (b) is the pdf of the actual delay distributio of l j. From (9) ad (1), we ca follow the same procedure as i the aalysis for cocave costraits to obtai the overall cost of false routig: C = c p Pr{False Positive}+c Pr{False Negative} k b =c p f B B S (s)ds p (b) db =1 k B + c B 1 f b S (s)ds p (b) db (11) =1 Agai, to fid B ad B (=1,...,k), we eed to solve the followig equatios: C B = c p C B B = c B 1 +1 f S (s)ds c p(τ)dτ c p f S (s)ds = B (12) B p(τ)dτ = (13) Solvig (6)-(7) ad (12)-(13) requires a certai degree of computatioal complexity. However, the atage of is that oce the boudaries of the classes (B s) ad their respective ertised values (B s) are solved, they ca be simply plugged ito each correspodig router so that the routers will perform lik state update accordigly. I a etwork where the traffic patter varies at differet time of the day, the traffic patter ca be first categorized ito differet types for differet time periods (such as peak-hour/off-peak-hour traffic, etc.), the each of them will have a separate set of B s ad s which will be i effect durig its correspodig time period. As log as the traffic of the same type does ot chage drastically from day to day, (that is, say, every workday s traffic patter betwee 9am to 11am is similar) we do ot B eed to re-calculate the B s ad B s. Therefore, whe the etwork is i operatio, aside from applyig differet B s ad B s at differet time periods of the day, will ot icur additioal computatioal overhead tha equal-class or expoetial-class lik state updates. V. SIMULATIONS We evaluate the performace of by comparig it with the existig class-based update policies i [1]. For

5 952 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 6, JUNE 28 completeess, we briefly review the equal class based ad expoetial class based update policies. Defiitio 1: Equal class based update policy [1] is characterized by a costat B which is used to partitio the available badwidth or delay operatig regio of a lik ito multiple equal size classes: (,B), (B, 2B), (2B, 3B),..., etc. A update is triggered whe the available badwidth o a iterface chages to a class that is differet from the oe at the time of the previous update. Defiitio 2: Expoetial class based update policy [15] is characterized by two costats B ad f(f>1) which are used to defie uequal size classes: (,B), (B, (f+1)b), ((f+1)b, (f 2 +f+1)b),..., etc. A update is triggered whe a class boudary is crossed. Cocave Costrait: Badwidth The etwork topology used i the simulatio is a 32-ode etwork [15]. We adopt two performace idices for the purpose of compariso: the update rate (average umber of updates i a uit time) ad the false routig probability of coectios, which are respectively defied below: Total umber of updates Update rate= (Total simulatio time) (Number of liks), ad False routig probability umber of falsely-routed coectios = umber of coectio requests. The arrivals of coectio requests are geerated by a Poisso process with arrival rate λ =1ad the duratio of each coectio is derived from the stadard Pareto distributio with α=2.5 (the cumulative distributio of the stadard Pareto distributio is F (x) = 1 (β/x) α,whereα is the shape parameter ad β is the scale parameter). Hece, the average duratio of a coectio is d = αβ/(α 1) (the mea of the stadard Pareto distributio). Upo the acceptace ad the ed of a coectio, the available badwidth is re-computed. The badwidth requested by each coectio is uiformly distributed i [b mi,b max ], that is q (x) u (b mi,b max ) i Eqs. (1) ad (2) (do ot cofuse this with the actual available badwidth which is distributed i [,C], where C is the lik capacity.) Without loss of geerality, we assume the costs of a false positive ad a egative are equal. Note that for a sigle class based lik state update policy, the larger umber of the classes the badwidth is partitioed ito, the more accurate the lik state iformatio is, implyig the lower false blockig probability of coectios, while the more sesitive it is to the fluctuatio of the available badwidth, thus resultig i a larger update rate. Hece, we ca claim that policy 1 outperforms policy 2 if ad oly if, for ay give umber of classes used for policy 2, a appropriate umber of classes ca always be foud for policy 1 such that it achieves better performace i terms of both the update rate ad false routig probability of coectios. By extesive simulatios, we foud that our proposed lik state update policy outperforms the equal ad expoetial class based lik state update policies for ay give umber of classes. I this paper, owig to the page limit, we oly selectively preset the simulatio results of the cases that Update rate Fig. 3. False routigs probability =2 Equal class update (B=.1) Expoetial class update B=.5C f= Beta Fig. 4. Update rate whe [b mi,b max] =[,.5C]. = 2 Equal class update (B=.1) Expoetial class update B=.5C f= Beta False routig probability whe [b mi,b max] =[,.5C]. the umbers of classes of the equal class based update policy is 1 (B =.1C), ad for the expoetial class based update policy, B =.5C ad f =2(the umber of classes is 5). I the two simulatios, we set [b mi,b max ] as [,.5C] ad [.5C,.1C], ad the umber of classes of are 3 ad 4, respectively. As the first step of our proposed lik state update policy, we compute the classes to partitio the badwidth. Sice we assume the requested badwidth is uiformly distributed i our simulatios ad the costs of false positive ad egative are equal, (6) ad (7) ca be solved as: B = b mi + (b max b mi ) k ad B = (b max b mi ), 2 where k is the umber of classes i. Hece, the class based update policy adopted i our simulatios is obtaied. Figs. 3-6 illustrate our simulatio results, i which Beta deotes the scale parameter β. I both simulatios,

6 ANSARI et al.: ROUTING-ORIENTED UPDATE SCHEME () FOR LINK STATE UPDATING Estimatio error i mea user requested badwidth.48 Update rate 1.5 =2 Equal class update (B=.1) Expoetial class update B=.5C f=2 Probability of false routig Beta.34 Equal class Error Fig Update rate WHEN [b mi,b max] =[.5C,.1C]. Fig. 7. False routig probability whe there is error ( i measurig user s mea badwidth request. Actual request pdf q (x) N.3C,.2C 2)..1 =2 Equal class update (B=.1) Expoetial class update B=.5C f= Equal class False routig probability probability of false routig Fig Beta False routig probability WHEN [b mi,b max] =[.5C,.1C]. our proposed lik state update policy achieves much better performace tha others, i.e., our proposed lik state update policy achieves lower false routig probabilities with lower update rates tha others, implyig that our proposed lik state update is more practical tha the equal ad expoetial class based lik state update policies i terms of the update rate ad false blockig probability of coectios. Cocave Costrait with Error i pdf Estimatio: Sice relies o the estimatio of the pdf s of the user s request ad the etwork s QoS behavior, it is importat to examie the impact of erroeous estimatio (i other words, fault tolerace). Here, we use badwidth for illustrative purposes. I Fig. 7, error is itroduced i measurig the mea of the user s badwidth request: the actual distributio is assumed to be q (x) N (.3C,.2C 2) while the estimated pdf is q (x) N (.3C (1 + error),.2c 2).IFig.8,the error resides i measurig the variace of user s badwidth request distributio. The icorrectly estimated pdf is q (x) N (.3C,.2C 2 (1 + error) ). For both experimets, the etworks actual available badwidth distributio is assumed to be expoetially distributed. The resultig probability of error Fig. 8. False routig probability whe there is error i ( measurig user s badwidth request variace. Actual request pdf q (x) N.3C,.2C 2). false routig is compared with that of the equal-class update. From these experimets, the algorithm exhibits a good degree of fault tolerace. Additive Costrait: Delay Let D MAX be the maximum amout of delay a lik ca experiece i the etwork (e.g., queue full). The accept/reject criterio S (recall that S = x B (l i )) is i path,i j simulated as ormally distributed with mea =.3 D MAX, ad variace =3 D MAX. The actual delay distributio of D actual is approximated as expoetially distributed i the simulatio. Oe hudred thousad coectio setup attempts were made, each time with a differet value of accept/reject criterio S ad a differet D actual. The class boudaries ad their correspodig ertised delay B were calculated accordig to (12) ad (13). D MAX is fixed at 1 uits. Fig. 9 shows the results of the simulatio whe the umber of classes varies from 3 to 12. As we ca see, whe the umber of classes icreases, the probability of false routig from either

7 954 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 6, JUNE Equal class.7.6 II expoetial Probability of false routig Probability of false routig Number of classes f Fig. 9. Probability of false routig with varyig umber of classes. ( vs. equal class.) Fig. 11. class. Probability of false routig with varyig f ( vs. expoetial Probability of false routig Equal Class Expoetial Class Variace of S Fig. 1. Probability of false routig with varyig variace of S. ( versus expoetial class ad equal class. or equal-class updates decreases. This is due to the fact that the more classes, the more accurate lik state iformatio the etwork ca obtai. However, regardless of the umber of classes, always performs better tha equal-class update, especially whe the umber of classes is small because equalclass update does ot take the accept/reject criterio C ito cosideratio. Fig. 1 shows the results where the umber of classes is fixed to 5 but the variace of S is varyig from 1 to 1. From this figure, we ca see that whe the variace of accept/reject criterio S icreases, the probability of false routig icreases. However, still performs better tha equal-class ad expoetial class updates, especially whe the variace is low. Sice takes the probability distributio of the accept/reject criterio ito cosideratio, the lower variace meas the accept/reject criterio is more predictable, hece yieldig better performace for. Fig. 11 compares the performace betwee ad expoetial-class update. Here, the umber of classes is 5 ad the variace of the accept/reject criterio is 3 D MAX.The factor f i expoetial update varies from 1.1 to 2.. We ca see that the probability of false routig with remais almost costat because the chage of f does ot affect. However, the performace of expoetial-class update decays slightly as the value of f icreases. Expoetial-class update ca be viewed as a special case of i which all QoS parameters are expoetially distributed; i such case the algorithm would also yield class sizes (optimized) resemblig those of expoetial-class update. Nevertheless, the simulatio result idicates that still performs better tha expoetial-class update eve uder expoetially distributed additive QoS parameters. This is because, for additive costraits, eve if the QoS parameter of a idividual lik is expoetially distributed, the accept/reject criterio S is ot. Therefore, the merit of is clearly revealed here. Additive Costraits with various hop couts: As we have previously poited out, the pdf estimatio of the accept/reject criterio S is based o the average hop cout i the etwork. Obviously, serves well for the coectios with the hop cout equal to the average hop cout. However, it is importat to observe the impact to the other coectios with differet umbers of hops. For this purpose, we simulate a etwork i which the delay distributio is expoetially distributed with mea 8x1 3 uits ad variace 6.4x1 7 uit 2. The user s request is Gaussia distributed with mea 1 5 uits ad variace 1 8 uit 2. We assume the average hop cout is 5, ad therefore by applyig the Cetral Limit Theorem, f S, the pdf of S, ca be approximated by Gaussia distributio with mea 6x1 3 uits ad variace of 4.2x1 8 uit 2. To observe the effect of o the coectios with various hop couts away from the average, we ru simulatios over the coectios with hop couts from as low as 2 up to 8. The performace is compared with equal-class update ad expoetial class update, as preseted i Fig. 12. From the result, we ca see that still performs better tha both expoetial-class ad equal-class updates for differet hop couts. It is iterestig to otice that the larger umber of hops a coectio traverses, the higher chace of false routig

8 ANSARI et al.: ROUTING-ORIENTED UPDATE SCHEME () FOR LINK STATE UPDATING 955 prbability of false routig Equal Class Expoetial Class umber of liks Fig. 12. Probability of false routig with various hop cout. Average hop cout =5. ( versus expoetial class ad equal class. it suffers. This is due to the fact that the iaccuracy of the lik state iformatio will accumulate from lik to lik i the case of additive costraits. Summary These simulatio results demostrate that yields lower probability of false routig tha equal class update ad expoetial update i most of the scearios. More importatly, also shows reasoable fault-tolerace eve whe the estimatio of pdf is ot accurate. I most of our simulatios, the etwork QoS parameters are expoetially distributed while the user s request is ormally distributed, but ote that is applicable to differet types of pdf s. The key here is to estimate the pdf s ad solve Eqs. (12) (13); the more accurate the estimatio, the better the performace of. VI. CONCLUSION I this paper, we have demostrated that the statistical distributio of the user s QoS requiremets ad etworks QoS measuremets ca be exploited to efficietly ad effectively update lik state iformatio. We have proposed a efficiet lik state update policy, referred to as. Through theoretical aalysis ad extesive simulatios, we have show that greatly outperforms its coteders which do ot icorporate the statistical iformatio, i.e., achieves a much lower false routig probability ad reduces the cost of false routig without sigificatly icreasig the etwork overhead. Furthermore, ca ot oly be applied to etworks with various types of traffic ad user requests, but is also capable of hadlig the dyamic ature of moder etwork traffic. ca be the fudametal buildig block for QoS lik state update i the ext geeratio etwork. REFERENCES [1] S. Che ad K. Nahrstedt, A overview of quality of service routig for ext-geeratio high-speed etwork: problems ad solutios, IEEE Network, vol. 12, o. 6, pp , Nov./Dec [2] G. Cheg ad N. Asari, O multiple additively costrait path selectio, IEE Proc. Commu., vol. 149, o. 5, pp , Oct. 22. [3] R. Gueri ad A. Orda, QoS based routig i etworks with iaccurate iformatio: theory ad algorithms, i Proc. IEEE INFOCOM 97, Kobe, Japa, Apr. 1997, vol. 1, pp [4] T. Korkmaz, M. Kruz, ad S. Tragoudas, A efficiet algorithm for fidig a path subject to two additive costraits, i Proc. ACM SIGMETRICS 2, Sata Clara, CA, Jue 2, pp [5] L. Gag ad K. G. Ramakrisha, A*prue: a algorithm for fidig k shortest paths subject to multiple costraits, i Proc. IEEE INFO- COM 21, Achorage, AK, Apr. 21, vol. 2, pp [6] S. Che ad K. Nahrstedt, Distributed QoS routig with imprecise state iformatio, i Proc. 7th Itl. Cof. Computer Commuicatios ad Networks, Lafayette, LA, Oct. 1998, pp [7] Z. Wag ad J. Crowcroft, Quality of service routig for supportig multimedia applicatios, IEEE J. Select. Areas Commu., vol. 14, o. 7, pp , Sept [8] J. Moy, OSPF versio 2, RFC2328, IETF, [9] S. Segupta, D. Saha, ad S. Chaudhuri, Aalysis of ehaced OSPF for routig lightpath i optical mesh etworks, i Proc. IEEE ICC 2, vol. 5, pp , 22. [1] G. Apostolopoulos, R. Gueri, S Kamat, ad S. Tripathi, Qualityof-service based routig: a performace perspective, i Proc. ACM SIGCOMM 1998, Vacouver, BC, Caada, Aug. 1998, vol. 28, pp [11] A. Shaikh, J. Rexford, ad K. G. Shi, Evaluatig the impact of stale lik state o quality-of-service routig, IEEE/ACM Tras. Networkig, vol. 9, o. 2, pp , Apr. 21. [12] Q. Ma ad P. Steekiste, Quality-of-service routig for traffic with performace guaratees, i Proc. IFIP It. Workshop Quality of Service, New York, May 1997, pp [13] L. Breslau, D. Estri, ad L. Zhag, A simulatio study of adaptive source routig i itegrated service etworks, Computer Sciece Departmet, Uiversity of Souther Califoria, Tech. Rep , [14] M. Peyravia ad R. Ovural. Algorithm for efficiet geeratio of lik-state updates i ATM etworks, Computer Networks ad ISDN Systems, vol. 29, pp , [15] X. Li, L. K. Sha, W. Ju, ad N. Klara, QoS extesio to BGP, i Proc. IEEE Itl. Cof. Network Protocols (ICNP 2), Paris, Frace, Nov. 22, pp [16] G. Cheg ad N. Asari, : a ovel lik state iformatio update scheme for QoS routig, i Proc. 25 IEEE Workshop o High Performace Switchig ad Routig, Hog Kog, May, 25. pp [17] N. Wag, G. Cheg, ad N. Asari. II: the case of additive metrics for updatig additive lik state iformatio, i Proc. ICC 26, Istabul, Turkey, May 26. [18] J. Dig, M. Kirkpatrick, ad E. H.-M. Sha. QoS measures ad implemetatios based o various models for real-time commuicatios, i Proc. 3rd IEEE Symposium o Applicatio-Specific Systems ad Software Egieerig Techology 2, March 2, pp [19] L. Agrisai, G. Vetre, L. Peluso, ad A. Tedesco. Measuremet of processig ad queuig delays itroduced by a ope-source router i a sigle-hop etwork, IEEE Tras. Istrumetatio ad Measuremet, vol. 55, o. 4, pp , Aug. 26. [2] G. Appezeller, I. Keslassy, ad N. McKeow. Sizig router buffers, Computer Commu. Rev., vol. 34, o. 4, pp , 24. Nirwa Asari (S 78-M83-SM 94) received the B.S.E.E. (summa cum laude) from the New Jersey Istitute of Techology (NJIT), Newark, i 1982, the M.S.E.E. degree from Uiversity of Michiga, A Arbor, i 1983, ad the Ph.D. degree from Purdue Uiversity, West Lafayette, IN, i He joied NJIT s Departmet of Electrical ad Computer Egieerig as a Assistat Professor i 1988, ad has bee a Full Professor sice He has also assumed various admiistrative positios. He authored Computatioal Itelligece for Optimizatio (Spriger, 1997, traslated ito Chiese i 2) with E.S.H. Hou, ad edited Neural Networks i Telecommuicatios (Spriger, 1994) with B. Yuhas. His curret research focuses o various aspects of broadbad etworks ad multimedia commuicatios. He has also cotributed over 3 techical papers icludig over 1 refereed joural/magazie articles. He is a Seior Techical Editor of the IEEE Commuicatios Magazie, ad also serves o the editorial board of Computer Commuicatios, the ETRI Joural, adthejoural of Computig ad Iformatio Techology.

9 956 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 6, JUNE 28 He was the foudig geeral chair of the First IEEE Iteratioal Coferece o Iformatio Techology: Research ad Educatio (ITRE23), was istrumetal, while servig as its Chapter Chair, i rejuveatig the North Jersey Chapter of the IEEE Commuicatios Society which received the 1996 Chapter of the Year Award ad a 23 Chapter Achievemet Award, served as Chair of the IEEE North Jersey Sectio ad i the IEEE Regio 1 Board of Goverors durig 21-22, ad has bee servig i various IEEE committees such as Chair of IEEE COMSOC Techical Committee o Ad Hoc ad Sesor Networks, ad (TPC) Chair/Vice-chair of several cofereces/symposia. His awards ad recogitios iclude the NJIT Excellece Teachig Award i Graduate Istructio (1998), IEEE Regio 1 Award (1999), a IEEE Leadership Award (27, from IEEE Priceto/Cetral Jersey Sectio), ad desigatio as a IEEE Commuicatios Society Distiguished Lecturer. Na Wag received the B.S.E.E. degree from Natioal Cheg Kug Uiversity, Taia, Taiwa i 1995, ad the M.S.E.E. degree from the New Jersey Istitute of Techology, Newark, New Jersey i He has worked for Lucet Techologies as a etwork egieer i the area of ATM etworks, ad Comcast i the VoIP. He is curretly workig towards the Ph.D. degree i electrical egieerig at NJIT, ad his mai research iterests iclude QoS routig, lik state updatig, ad performace evaluatio. Gag Cheg received B.S. i Iformatio Egieerig from Beijig Uiversity of Posts ad Telecommuicatios (BUPT) i He joied Lucet Techologies after he obtaied his M.E. i Iformatio ad Sigal Processig from BUPT i 2. Betwee Jauary 21 ad May 25, he was with the New Jersey Istitute of Techology. His research iterests iclude Iteret routig protocols ad service architectures, iformatio theory based etwork optimizatio ad protocol desig, ad modelig ad performace evaluatio of computer ad commuicatio systems. He received the Ph.D. degree from NJIT i May 25, ad was the recipiet of the Hashimoto Prize, which is awarded aually to the best NJIT doctoral graduate i Electrical ad Computer Egieerig. He joied VPIsystems Corp. i Ja 25, focusig o the etwork plaig optimizatio algorithm desig ad developmet. Sice May 26, he has bee with EMC, workig o the root-cause aalysis etwork maagemet desig ad developmet.