A Scalable and Lighweigh QoS Monioring Technique Combining Passive and Acive Approaches On he Mahemaical Formulaion of CoMPACT Monior Masai Aida, Naoo Miyoshi and Keisue Ishibashi NTT Informaion Sharing Plaform Laboraories NTT Corporaion Email: {aida.masai,ishibashi.eisue}@lab.n.co.jp Deparmen of Mahemaical and Compuing Sciences Toyo Insiue of Technology Email: miyoshi@is.iech.ac.jp Absrac To mae a scalable and lighweigh QoS monioring sysem, we have proposed a new QoS monioring echnique, Change-of-Measure based Passive/Acive Monioring (CoMPACT Monior), which is based on change-of-measure framewor and is an acive measuremen ransformed by using passively moniored daa. This echnique enables us o measure deailed QoS informaion for individual users, applicaions, and organizaions, in a scalable and lighweigh manner. In his paper, we presen he mahemaical foundaion of CoMPACT Monior. In addiion, we show is characerisics hrough simulaions in erms of ypical implemenaion issues for inferring he delay disribuions. The resuls show ha CoMPACT Monior gives accurae QoS esimaions wih only a small amoun of exra raffic for acive measuremen. I. INTRODUCTION The Inerne has been growing rapidly wih respec o he number of users and he amoun of raffic and has been recognized as an imporan infrasrucure for informaion in social and business use. So, alhough he iniial and main issue of he Inerne has been is conneciviy and ransmission capaciy, aenion has recenly been paid o is qualiy oo. The raffic conveyed by he Inerne is generaed by a wide variey of applicaions, which have differen characerisics and differen qualiy requiremens. Thus, Qualiy of Service (QoS) and performance measuremens are crucial in conrolling and managing QoS and provisioning newors. However, i is difficul or expensive o measure QoS and performance saisics of each flow direcly. Recenly, many monioring ools have been developed o monior newor performance [], [2], [3], [2] and heir measuremen resuls have also been repored [], [2], [23]. In general, convenional monioring schemes o measure QoS and he performance of newors are classified ino wo ypes: acive and passive monioring. Unforunaely, boh ypes have drawbacs. They are briefly summarized as follows. a) Acive measuremen moniors QoS and he performance of a newor by sending probe paces and monioring hem [6], [7], [22]. There are various acive mehods o measure newor performance such as available bandwidh [6], delay, loss, and o esimae heir lin-by-lin performance [2]. They monior he QoS/performance of he probe-pace sream o deermine he QoS/performance of he user/newor indirecly. This means ha we implicily assume ha he QoS/performance of a user/newors is he same as he values measured from acive probe paces. These acive monioring schemes have he following problems. If we use a probe-pace sream ha simulaes an acual user raffic: The probe-pace sream causes non-negligible amoun of exra raffic on he newors and i affecs QoS/performance of users raffic and The QoS/performance obained from he probe paces is no equal o ha wihou he influence of he probe-pace sream. If we use shor probe paces and send hem in cerain inervals, lie ping: The exra raffic may be negligible, bu he QoS/performance obained from he probe paces is no equal o he QoS/performance experienced by users, in general. Le us add some explanaion abou he las case. Since he ime for sending probe paces is independen of he users behaviors, QoS/performance measured by he acive monioring scheme generally differs from he acual QoS/performance ha users experience. If and only if we can assume ha acive monioring measures he ime average of newor performance and ha he user raffic is Poissonian, hen he performance experienced by he users and he acively-measured performance will be he same. This well-nown propery is called PASTA [25]. I is nown, however, ha curren Inerne raffic exhibis bursy properies and does no generally have Poisson arrivals [9]. In ha case, an average user experiences worse -783-7753-2/3/$7. (C) 23 IEEE IEEE INFOCOM 23
performance han he ime-average performance measured by acive monioring. b) Passive measuremen is mainly used o monior raffic volume bu can measure newor performance as well. Passive monioring is caegorized ino wo ypes: wo-poin monioring and one-poin monioring. Two-poin monioring requires wo monioring devices deployed a ingress and egress poins in a newor. The devices sequenially ae pace daa, and newor performance parameers such as delay and loss can be calculaed by comparing he daa of he corresponding paces aen a each poin. If we apply he wo-poin monioring o measure QoS/performance: All devices should have synchronized iming. The wo-poin monioring requires idenifying each pace a he wo devices by is header and/or conens. Since his idenificaion process is hard when he pace volume is huge, as in a large-scale newor, he wo-poin monioring does no have scalabliliy. To idenify he moniored paces, we should collec all he pace daa. This process requires nonnegligible bandwidh. One-poin monioring uses he TCP acnowledgmen mechanism. When a TCP-sin receives a pace from a TCP-source, i ransmis an acnowledgemen for he pace [24]. Thus, by monioring he pace-ac pair a a poin in he newor, we can measure he round-rip delay beween he poin and he sin. The pace loss can also be deeced in his way. However, if we apply one-poin monioring, measuremen is resriced o TCP flows. Our approach, Change-of-Measure based Passive/Acive Monioring (CoMPACT Monior), is differen from he above mehods. I combines boh acive and passive monioring using easy-o-measure mehods. I is based on change-ofmeasure framewor and is an acive measuremen ransformed by using passively moniored daa. CoMPACT Monior can esimae no only he mixed QoS/performance experienced by users bu also he acual QoS/performance for individual users, organizaions, and applicaions. In addiion, CoMPACT Monior is scalable and lighweigh, where he scalabiliy in his paper means he monioring sysem does no become complex even if he volume and/or number of arge flows (e.g., user flows) ha are sharing he common pah increases. We have proposed he concep of CoMPACT Monior in [5], and have invesigaed he characerisics of is simple implemenaion in [5]. However, our previous wors do no presen is mahemaical foundaion. So, he condiion, in which CoMPACT Monior wors well, has no been clarified. In his paper, we presen he mahemaical foundaion of CoMPACT Monior and show is characerisics wih respec o ypical implemenaion issues for inferring he delay disribuions. The res of he paper is organized as follows. In secion II, we briefly summarize he concep of CoMPACT Monior and relaed wors ha combine passive and acive mehods. In secion III, we presen mahemaical formulaions of he framewor for CoMPACT Monior. In secion IV, we invesigae implemenaions of CoMPACT Monior. To demonsrae he feaures of CoMPACT Monior, secion V shows examples of delay disribuion measuremens for individual users via simulaion. In addiion, we show he characerisics of CoMPACT Monior wih respec o implemenaion issues. Finally, we conclude he paper in secion VI. II. CONCEPT OF COMPACT MONITOR A. Concep CoMPACT Monior is a scalable and lighweigh monioring echnique ha enables us o esimae deailed characerisics of performance for individual users, organizaions, and applicaions. I combines simple measuremens of boh acive and passive ypes by change-of-measure framewor. We can recognize ha he measuremen of QoS saisics fundamenally corresponds o inegrals. This is because i is an accumulaion of some quaniies according o a cerain rule. Our echnique enables us o obain saisics of he measuremen objecive no from he inegral describing a direc measuremen of he objecive, bu from oher inegral ha is easy o measure. These inegrals are in differen forms bu heir values are he same. Le X be he measuremen objecive, e.g., he delay for user s paces, whose disribuion funcion is F. The disribuion of X is obained as follows: Pr(X >a)= {x>a} df (x) =E F [ {X >a}], () where E F denoes he expecaion wih respec o F and { } denoes he indicaor funcion. Suppose we have a siuaion in which i is difficul o measure X direcly, and an esimae of is disribuion canno be obained wih (). Le V () be he newor performance a ime and X be he value of V () measured a a cerain ime. Also, le Y be he value of V () measured independenly of X and le he disribuion funcion of Y be G. Then, Pr(X > a) in () is obained, under a cerain condiion, as df (y) Pr(X >a)= {y>a} dg(y) dg(y) [ ] df (Y ) =E G {Y>a}, (2) dg(y ) where E G denoes he expecaion wih respec o G and df /dg denoes he lielihood raio of F wih respec o G. If Y is easy o measure and we can derive df (Y )/dg(y ), hen he esimaor of he disribuion of X can be derived wih he measuremen values of Y. The fundamenal concep of CoMPACT Monior is as follows: The esimaion of he disribuion Pr(X > a) from direc measuremens of X -783-7753-2/3/$7. (C) 23 IEEE IEEE INFOCOM 23
is difficul. However, if he values Y and df (Y )/dg(y ) are easily obained by respecively using acive and passive monioring, hen we can easily esimae he disribuion Pr(X >a) from (2). The lielihood raio can be obained hrough simple couning of user paces. In addiion, (2) means ha if we have df (Y )/dg(y ) for each class raffic (user, applicaion, organizaion, and heir combinaion specified by ; =, 2,), we can simulaneously obain he individual QoS for each class raffic sharing a common pah from he common acive measuremen of Y. We can expec CoMPACT Monior o have he following advanages: Negligible exra raffic for acive probe paces: Since he exra raffic for acive probe paces can be small, user raffic is lile affeced. Simplificaion of passive monioring devices: To measure he delay disribuion, he convenional passive monioring requires wo-poin monioring. However, passive monioring in CoMPACT Monior only requires pace couning. Since ha is one-poin monioring, passive monioring devices are simplified (Fig. ). Simulaneous esimaion of QoS for individual pace sreams: By deermining he individual lielihood raio for each pace sream sharing a common pah, we can obain QoS parameers for an individual pace sream from he common acive moniored sequence. The lielihood raio is easily deermined by couning he number of paces in he pace sream filered by any class we wan o measure. Proocol independence: CoMPACT Monior is applicable o non-tcp proocols as well. Here, we add some explanaions o he scalabiliy of CoM- PACT Monior. The arge flows measurable by he common acive measuremen of Y are resriced o he flows sharing he same physical and logical pah. When we measure he arge flows in differen pahs, i is necessary o use differen acive probe pace sequences (of course, his is he same feaure as convenional acive measuremens). Therefore, if all he arge flows share he same pah, we can measure all he flows by using a single acive probe pace sequence and he monioring sysem is no complicaed wih respec o increase of he number of arge flows (as well as increase of he volume of arge flows). CoMPACT Monior has his ype of he scalabiliy. In addiion, alhough differen acive probe pace sequences are required for measuring he arge flows in differen pahs, configuraion of passive monioring devices is no always complicaed. If he differen pahs include he common lin, we can reduce he number of passive monioring devices by fixing he passive monioring device a he common lin (Fig. 2). B. Relaed Wor Lindh has proposed a new QoS monioring echnique ha combines passive and acive ways [7], [8]. In his echnique, Fig.. Time synchronizaion Pace idenificaion Two-poin passive measuremen for pace delay. Pace coun Passive monioring device Passive measuremen for CoMPACT Monior. Passive monioring device Simplificaion of passive monioring for CoMPACT Monior. a sends acive probe paces a regular inervals such ha he number of arge user paces passing hrough he becomes a predefined fixed value. The passive monioring device is used o coun he number of paces. Since he densiy of acive probe paces insered ino he newor is proporional o he densiy of he arge user pace sream, his echnique also can measure QoS for a pace sream, e.g., he QoS experienced by a user. However, his echnique has he following drawbacs: This echnique insers many acive probe paces when here are many paces in he arge pace flow (e.g., user flow). This means ha he number of acive probe paces ends o increase when he newor is congesed. Thus, acive probe paces will affec he QoS of users raffic. If we need o measure he individual QoS for each user, his echnique insers differen acive probe pace sequences corresponding o he users. Thus, his echnique does no have scalabiliy wih respec o an increase in he number of arge pace flows. However, in CoMPACT Monior, he exra raffic for acive probe paces is independen of user raffic, and an individual QoS can be derived wih he common acive probe pace sequence even when he number of arge pace flows, in he same pah, increase. III. MATHEMATICAL FORMULATION OF COMPACT MONITOR This secion presens he mahemaical formulaion of CoM- PACT monior in order o clarify he condiions in which i wors well. Since Inerne raffic has a wide variey of characerisics, we presen he mahemaical formulaion for nonsaionary user raffic. This formulaion is also applicable o saionary user raffic. In he framewor of CoMPACT Monior, here are many user paces in he newor compared wih acive probe paces. Thus, we consider a fluid approximaion of user raffic; ha is, user paces are approximaed as a fluid, while he arrivals of acive probe paces are modeled as a poin process. Suppose ha a pah in he newor is shared by K ( ) users.lea (), =,,K, denoe he cumulaive amoun of fluid ransmied by user observed during (,], -783-7753-2/3/$7. (C) 23 IEEE IEEE INFOCOM 23
pah # Passive monioring device for pah # pah # Passive monioring device pah #2 common lin Passive monioring device for pah #2 pah #2 Fig. 2. Simplificaion of he configuraion of passive monioring devices. where each {A ()} is a deerminisic, real-valued and nondecreasing process saisfying A () =. We assume ha lim inf A ()/ > and ha {A ()} is absoluely coninuous wih densiy {a ()} ; ha is, A () = a (s)ds,, where we also assume ha {a ()} is righ-coninuous wih lef-limis and is bounded on. Le V () denoe he virual delay in he pah a ime, where {V ()} is a deerminisic, real-valued, and nonnegaive process. We assume ha {V ()} is righ-coninuous wih leflimis in. The deerminisic process {(V (),a (); =,,K)} is considered as a sample pah exraced from he corresponding sochasic process, where we assume neiher saionariy nor ergodiciy. Noe ha {V ()} is influenced no only by {a (); =,,K} bu also oher flows ha share all/a par of he pah of {a (); =,,K}. Define A (x) =inf{ :A () x}, =,,K, for x. Noe ha A (x) represens he ime a which he cumulaive fluid ransmied by user reaches level x. More inuiively, we can inerpre A (x) as he arrival ime of he fluid molecule (pace) labeled x ransmied by user. The delay W (x) of he fluid molecule x ofuser is hen represened by W (x) =V (A (x)) for x. Therefore, for any y> and any =,,K, he empirical average newor delay disribuion for he fluid of user over he amoun y of fluid is given by π,y (C) = y y {W (x) C} dx = y y {V (A (x)) C} dx = A (y) y A (y) A (y) {V (s) C} a (s)ds, C B(R + ). (3) Thus, since A (y) as y due o he bounded propery of {a ()}, if he limis lim y A lim y (y) {V (s) C} a (s)ds, (4) A () a (s)ds (5) exis, we can see ha here is a long-erm average delay disribuion for he fluid of user and i is given by π (C) y π,y(c), C B(R + ), (6) where lim inf A ()/ > is ensured by he assumpion. Now, consider esimaing he long-erm average delay disribuion π (C), C B(R + ), by monioring he newor a random sampling epochs. Le {N()} denoe a simple couning process represening he monioring epochs of he newor and le {T n } n be he corresponding poin sequence; ha is, T n =inf{ :N() n} for n =, 2,.We assume ha N has saionary and ergodic incremens wih respec o a probabiliy measure P and also has he posiive and finie inensiy λ N = E[N()], where E denoes he expecaion wih respec o P. Then, we have he following: Theorem If, for some {,,K} and some C B(R + ), he following hold wih consans α (C) and α, lim m m m {V (Tn) C} a (T n )=α (C), P-a.s., (7) n= lim m m m a (T n )=α, P-a.s., (8) n= hen limis (4) and (5) also exis for such and C, and we have π (C) = α (C) α m n= {V (T n) C} a (T n ) n= a, P-a.s. (9) (T n ) Proof: We show ha limi (4) exiss and coincides wih α (C) in (7) along similar lines o he proof of Theorem 3. in [4]. Since {(V (),a ())} is a deerminisic process, we have [ E N() [ =E = n= ] {V (Tn) C} a (T n ) ] {V (s) C} a (s)dn(s) {V (s) C} a (s) λ N ds, () -783-7753-2/3/$7. (C) 23 IEEE IEEE INFOCOM 23
where we use he relaion E[N()] = λ N due o he saionariy of N. Since {a ()} is bounded, for he inside of he expecaion in he lef-hand side above, we have N() {V (Tn) C} a (T n ) a sup n= N(), where a sup = sup {a ()} and E[N()/] = λ N <. Thus, applying he dominaed convergence heorem o (), we obain [ N() E lim λ N n= ] {V (Tn) C} a (T n ) {V (s) C} a (s)ds. For he limi on he lef-hand side, we have by he condiion of he heorem and he ergodiciy of N: N() lim {V (Tn) C} a (T n ) n= N() N() N() n= = λ N α (C), P-a.s., {V (Tn) C} a (T n ) so limi (4) exiss and coincides wih α (C). The exisence of limi (5) and is coincidence wih α in (8) are immediae by replacing C wih R +. We hen have resul (9) from (3) and (6). Theorem shows ha he long-erm average delay disribuion for he fluid of user is esimaed hrough m-imes monioring of he newor by n= Z,m (C; N) = {V (T n) C} a (T n ) n= a, () (T n ) which is indeed srongly consisen in he sense ha lim Z,m(C; N) =π (C), m provided ha (7) and (8) hold. P-a.s., Remar In he above discussion, {(V (),a (); =,,K)} is inerpreed as a sample pah exraced from he corresponding sochasic process, where we assume neiher saionariy nor ergodiciy of he sochasic process. Indeed, he value of (α (C),α ) in (7) and (8) may depend on he individual samples of {(V (),a ())}, while i can no depend on he sample of {N()} once a sample of (α (C),α ) is given. Furhermore, we can weaen he assumpion of {N()} such ha i is asympoically ergodic. Therefore, we can use as {N()} a non-delayed renewal process wih a spread-ou inerarrival disribuion (see [8]). Remar 2 Also, once we assume ha {(V (),a ())} is sochasic and joinly ergodic wih he sampling process N, he resul (9) reduces o P A (V () C) = E N [ {V () C} a ()] E N [a, ()] neighborhood before T n δ T n ime of an acive probe pace arrival. Fig. 3. neighborhood afer T n δ Difference in implemenaions. where P A denoes he Palm probabiliy defined by (P,A ) and E N denoes he expecaion wih respec o he Palm probabiliy P N defined by (P,N) (see [9] and [3]). In his case, we can replace he boundedness of {a ()} wih E N [a ()] <. In his formula, we see ha a ()/E N [a ()] plays a role of he lielihood raio dp A /dp N. This is jus he origin of he name Changeof-Measure-based monioring (see Secion 2. and also [5], [5]). Remar 3 In he above remars, hough {(V (),a (); =,,K)} is considered sochasic, i is sill assumed o be independen of he sampling process N. Now, consider he case where (V (),a ()) depends on {N(s)} s< for >. In his case, if N is Poisson and {(V (),a ())} is joinly ergodic wih N, we can verify he following by using he Poisson calculus [] (see also [25]); P A (V () C) = E N [ {V ( ) C} a ( )] E N [a, ( )] where V ( ) V () and a ( ) a (). The corresponding esimaor is given by Z,m (C; N) = n= {V (T n ) C} a (T n ) n= a. (2) (T n ) IV. IMPLEMENTATION Since he raffic is no fluid in pracice, we have o consider he pracical implemenaion of he esimaor Z,m (C; N) in () as well as Z,m (C; N) in (2) for =,,K and C B(R + ). Noe ha he newor is moniored a he arrival epochs of he acive probe paces. When he influence of he acive probe paces on he newor is negligible, we can assume ha he sampling process N and {(V (),a (); =,,K)} are muually independen. In his case, he esimaor Z,m (C; N), C B(R + ), in () can be implemened as eiher of he following: Z +,m (C; N) = n= {V (T n) C} ã + (T n,δ) n= ã+ (T, (3) n,δ) Z,m (C; N) = n= {V (T n ) C} ã (T n,δ) n= ã (T, (4) n,δ) where ã + (, δ) and ã (, δ) denoe he numbers of paces ransmied by user observed during [, + δ) and [ δ, ), respecively, and δ is a small posiive number (Fig. 3). In -783-7753-2/3/$7. (C) 23 IEEE IEEE INFOCOM 23
TABLE I TRAFFIC MODEL. ranspor layer applicaion layer raffic connecion pace mean mean ON/OFF lengh shape rae a ype ID proocol lengh ON period OFF period disribuion parameer ON period ype # #5 TCP.5 KB s 5 s exp Mbps ype 2 #6 # TCP.5 KB 5 s s exp Mbps ype 3 # #5 TCP.5 KB 5 s 5 s pareo.5.5 Mbps ype 4 #6 #2 TCP.5 KB s 9 s pareo.5.5 Mbps he implemenaion of (3) [resp. (4)], {V (T n )} m n= [resp. {V (T n )} m n=] can be obained by acive monioring of he newor and {ã + (T n,δ)} m n= [resp. {ã (T n,δ)} m n=] is by passive monioring. Le us consider he following wo ways o realize he passive monioring device in CoMPACT Monior (see he boom figure in Fig. ). Realime couning: The passive monioring device performs pace filering and couning, on-line. I records a sequence of he number of paces observed during [, + δ) or [ δ, ), for each. Non-realime couning: The passive monioring device moniors all paces and records a par of hem, which includes sufficien informaion for pace filering. Anoher procedure exracs pace daa observed during [, + δ) or [ δ, ) from he recorded pace daa, and couns hem for each. In he firs case, he implemenaion of (3) is easier han ha of (4). This is because, while he arrival of he acive probe pace a T n, n =,,m, riggers he couning of he user pace arrivals during [T n,t n + δ) in he implemenaion of (3), we have o record all he arrival epochs of user paces o eep ready for he arrivals of acive probe paces in ha of (4). In addiion, since realime couning requires high-speed pace filering, i is difficul o realize for a broadband lin. In he second case, boh he implemenaions of (3) and (4) are easy. So, when he influence of he acive probe paces on he newor is no negligible, by leing he acive probe pace sream be a Poisson process (he case of Remar 3), Z,m (C; N) in (4) can be used as he implemenaion of Z,m (C; N) in (2). In addiion, since he passive monioring device is simple, i can be applicable o a broadband lin. V. CHARACTERISTICS OF COMPACT MONITOR: SIMULATION RESULTS A. Newor and Traffic Models We invesigae he characerisic of CoMPACT Monior by simulaion. We use he newor model shown in Fig. 4, which has 2 pairs of he source/desinaion. Alhough he newor model loos simple, i can be considered as par of a whole newor, exraced as a pair of source and desinaion subnewors. Lin capaciy beween and a is.5 Mbps and ha beween s is Mbps. Each hos 2 source 2 desinaion 2.5 Mbps.5 Mbps 2 3 Mbps 3 2 source of acive probe paces Fig. 4. 2 passive monioring device for couning paces desinaion of acive probe paces Newor model. on he lef in Fig. 4 is a source and ransfers daa o he corresponding hos on he righ. Characerisics of applicaion raffic are ON-OFF processes and are caegorized ino four differen ypes described in Table I. Each applicaion raffic ype is assigned o five and raffic is ransferred by TCP/IP. The size of user paces is 5 byes. In addiion, o suppor he use of acive probe paces, here is a pair of for sending and receiving he acive probe paces. They are conneced in he same manner as user. The acive probe paces are 64 byes long and are insered ino he newor according o Poisson process. The passive monioring device shown in Fig. 4 is for couning paces in order o deermine he lielihood raio. We conduced a 36-s simulaion using ns2 [4] and moniored he queueing delay disribuions for boh acive probe paces and user paces. Simulaneously, we calculaed he queueing delay disribuion by using he framewor of CoMPACT Monior. Here, queueing delay means he sum of he waiing ime a buffers in he s on he flow, i.e., endo-end delay is obained from he sum of he queueing delay and fixed delay deermined by lin capaciy and pace size. B. Queueing Delay Disribuions for Individual Users In his subsecion, we show ha CoMPACT Monior can esimae he queueing delay disribuion for each user from one common sequence of delay measuremens using acive probe paces. We have chosen a simpler implemenaion of CoMPACT Monior (3). To obain ã + (T n,δ), n =, 2,, he passive monioring device couns he number of paces. The lengh of he period [T n,t n + δ) for couning paces is 2 ms, i.e., δ =2ms. Hereafer, we call he period [T n,t n + δ) he neighborhood of T n and δ he lengh of he neighborhood. -783-7753-2/3/$7. (C) 23 IEEE IEEE INFOCOM 23
user pace user pace CoMPACT Monior CoMPACT Monior acive probe pace acive probe pace....4.8.2.6.2.24 [s] Fig. 5. Queueing delay disribuions for connecion #. user pace CoMPACT Monior acive probe pace..4.8.2.6.2.24 [s] Fig. 7. Queueing delay disribuions for connecion #. user pace CoMPACT Monior acive probe pace....4.8.2.6.2.24 [s] Fig. 6. Queueing delay disribuions for connecion #6...4.8.2.6.2.24 [s] Fig. 8. Queueing delay disribuions for connecion #6. We inser acive probe paces ino he newor o have Poisson arrivals wih a mean inerval of 5 ms. The exra raffic caused by he acive probe paces is only abou.% of he lin capaciy of Mbps so he influence on user raffic is negligible. Among he 2 connecions shown in Table I, we show he queueing delay disribuions (complemenary disribuions) for connecions #, #6, #, and #6, represening four differen raffic ypes, in Figs. 5 8. These figures show he queueing delay disribuions of user paces, hose of acive probe paces, and hose obained from CoMPACT Monior. The disribuions of acive probe paces are, of course, he same in hese figures. Alhough simple acive probe paces canno esimae he queueing delay ha users experience, an implemenaion of CoMPACT Monior (3) can esimae he queueing delay according o user raffic characerisics. C. Implemenaion and Neighborhood This subsecion shows he difference beween wo implemenaions (3) and (4), and invesigaes he influence of neighborhood size, δ. We show a resul for connecion #6 among he connecions shown in Table I. The raffic ype including connecion #6 has he smalles average rae and he sronges bursiness. The significan difference beween implemenaions (3) and (4) is in he difference beween ã + (T n,δ), and ã (T n,δ), n =, 2,. Tha is, he period for couning paces is afer T n, [T n,t n + δ), or before T n, [T n δ, T n ) (Fig. 3). Figure 9 shows queueing delay disribuions for boh implemenaions (3) and (4) wih δ = 2 ms. Acive probe paces are insered ino he newor o have Poisson arrivals wih a mean inerval of 5 ms. From his figure, boh implemenaions give almos he same disribuions. Since implemenaion (3) is simpler han ha of (4), CoMPACT Monior can be implemened as (3) when he exra raffic for acive probe paces is negligible. Nex, we invesigae he characerisics of CoMPACT Monior wih respec o δ. Figure shows queueing delay disribuions for connecion #6 obained from he implemenaion (3) wih δ = 2, 4, and 8 ms. Oher condiions are he same as in he above simulaion. This figure shows ha he accuracy of implemenaion (3) is independen of he neighborhood size, a leas, in his range of hese simulaions. This means ha i is no necessary o se a very shor size for δ, and we can avoid quic swiching of he pace couner beween sar and sop by seing a medium lengh for δ. -783-7753-2/3/$7. (C) 23 IEEE IEEE INFOCOM 23
before T n afer T n user pace CoMPACT Monior (inerval: msec)....4.8.2.6.2.24 [s] Fig. 9. Queueing delay disribuions for wo implemenaions, (3) and (4). δ = 2 ms δ = 4 ms δ = 8 ms...4.8.2.6.2.24 [s] Fig.. Queueing delay disribuions for differen neighborhood sizes. D. Inerval of Acive Probe Paces This subsecion shows he characerisics of CoMPACT Monior wih respec o he inerval of acive probe paces. Similarly o he above simulaions, we choose connecion #6. Figures and 2 show queueing delay disribuions for connecion #6 obained by he implemenaion (3) wih ms and 25 ms for he mean acive probe pace inerval, respecively. Queueing delay disribuions experienced by connecion #6 are also shown in hese figures. In boh cases, he exra raffic caused by acive probe paces is negligible, abou.5% and.2% of he lin capaciy, respecively. We compare hem wih Fig. 8 for a mean inerval of 5 ms. We can recognize ha a smaller inerval gives a more accurae delay esimaion. Because he inerval of acive probe paces does no influence he accuracy of esimaion from he framewor of CoMPACT Monior, he inerval is no essenial bu he number of samples is. To verify his, we compare relaive errors (x%ile from CoMPACT Monior) (x%ile of user delay) (x%ile of user delay) for he 9%ile, 95%ile, and 99%ile of he disribuions for hree differen mean inervals, and each is shown in Figs. 3 5. They are obained from five independen simulaions. The relaive errors of 9%ile value are almos he same bu ha of 99%ile value is differen. These resuls imply ha we canno..4.8.2.6.2.24 [s] Fig.. Queueing delay disribuion for inerval of acive probe paces: ms. Fig. 2. 25 ms.. user pace CoMPACT Monior (inerval: 25 msec)..4.8.2.6.2.24 [s] Queueing delay disribuion for inerval of acive probe paces: have enough samples o esimae he 99%ile value for a - ms inerval of acive probe paces. From he above discussion, i is necessary o deermine an appropriae inerval for acive probe pace aing ino consideraion he following facor: Required accuracy of esimaion, Time consrain o finish he monioring, and Permissible exra raffic caused by acive probe paces. VI. CONCLUSIONS In his paper, we showed he mahemaical formulaion of CoMPACT Monior wihou assuming saionariy or ergodiciy for user raffic. The characerisics and performance associaed wih he implemenaion issues in CoMPACT Monior were invesigaed by simulaion. Unlie convenional acive measuremens, CoMPACT Monior can esimae he delay disribuion for individual flows ha we wan o measure. In addiion, i enables us o mae a scalable and lighweigh measuremen sysem and can be implemened in a simple way. Since he passive monioring device described in his paper couns he number of pace, we can obain he delay disribuion wih respec o pace. In he framewor of CoMPACT Monior, if he passive monioring device accumulaes he -783-7753-2/3/$7. (C) 23 IEEE IEEE INFOCOM 23
.5.4.3.2. Fig. 3..5.4.3.2. Fig. 4..5.4.3.2. Fig. 5. ms 5 ms 25 ms Relaive error of 9%ile value of queueing delay. ms 5 ms 25 ms Relaive error of 95%ile value of queueing delay. ms 5 ms 25 ms Relaive error of 99%ile value of queueing delay. byes of paces, we can obain he delay disribuion wih respec o bye. We focused on one-way delay in his paper. Alhough his is imporan for video sreaming, VoIP, and he oher realime services, here are oher significan QoS parameers: for example, loss, round-rip delay, hroughpu, and Web server worload experienced by a user pace flow. We should exend CoMPACT Monior for oher QoS parameers. These issues are for furher sudy. REFERENCES [] CAIDA cooporaive associaion for inerne daa analysis. hp://www.caida.org/ools/. [2] NLANR measuremen and operaion analysis eam. hp://moa.nlanr.ne/. [3] IPMA: Inerne performance measuremen and analysis. hp://www.meri.edu/ipma/. [4] UCB/LBNL/VINT Newor Simulaor ns (version 2). hp://www.isi.edu/nsnam/ns/. [5] M. Aida, K. Ishibashi and T. Kanazawa. CoMPACT-Monior: Changeof-measure based passive/acive monioring weighed acive sampling scheme o infer QoS. Proc. of IEEE SAINT 22 Worshop (22) 9 25. [6] G. Almes, S. Kalidindi, and M. Zeausas. A one-way delay meric for IPPM. RFC2679, (999). [7] G. Almes, S. Kalidindi, and M. Zeausas. A one-way pace loss meric for IPPM. RFC268, (999). [8] S. Asmussen. Applied Probabiliy and Queues. Wiley (987). [9] F. Baccelli and P. Brémaud. Elemens of Queueing Theory: Palmmaringale Calculus and Sochasic Recurrences. Springer (994). [] J.C. Bolo. Characerizing end-o-end pace delay and loss in he inerne. Journal of High Speed Newors, 2(3), Sepember (993) 289 298. [] P. Brémaud. Marov Chains: Gibbs Fields, Mone Carlo Simulaion, and Queues. Springer (999). [2] R. Caceres, N.G Duffield, J. Horowiz, D.F. Towsley, and T. Bu. Mulicas-based inference of newor-inernal characerisics: Accuracy of pace loss esimaion. Proc. of IEEE INFOCOM 99, (999) 37 379. [3] D.J. Daley and D. Vere-Jones. An Inroducion o he Theory of Poin Processes. Springer (988). [4] P. Glynn and K. Sigman. Independen sampling of a sochasic process. Sochasic Process. Appl., 74 (998) 5 64. [5] K. Ishibashi, T. Kanazawa, and M. Aida. Acive/passive combinaionype performance measuremen mehod using change-of-measure framewor. Proc. of IEEE GLOBECOM 22, (22). [6] S. Keshave. A conrol heoreic approach o flow conrol. Proc. of ACM SIGCOM 9, (99) 3 5. [7] T. Lindh. A framewor for embedded monioring of QoS parameers in IP-based virual privae newors. Proc. of Passive and Acive Measuremens (PAM 2), 2. [8] T. Lindh. A new approach o performance monioring in IP newors combining acive and passive mehods. Proc. of Passive and Acive Measuremens (PAM 22), 22. [9] V. Paxson and S. Floyd. Wide-area raffic: The failure of Poisson modeling. IEEE/ACM Trans. on Neworing, 3(3), June (995) 226 244. [2] V. Paxson, J. Mahdavi, A. Adams, and M. Mahis. An archiecure for large-scale Inerne. IEEE Communicaions, 36(8) (998) 48 54. [2] V. Paxson. End-end Inerne pace dynamics, IEEE/ACM Trans. on Neworing, 7(3) (999) 277 292. [22] V. Paxson, G. Almes, J. Mahdavi, and M. Mahis. Framewor for IP performance meric. RFC 233, (998). [23] S. Savage, A. Collins, E. Hoffman, J. Snell, and T. Anderson. The endo-end effecs on Inerne pah selecion. Proc. of ACM SIGCOM 99, (999) 289 299 [24] W.R. Sevens. TCP/IP illusraed, Vol.. Addison-Wesley, Reading MA, 994. [25] R.W. Wolff. Poisson arrivals see ime averages. Oper. Res., 3 (982) 223 23. -783-7753-2/3/$7. (C) 23 IEEE IEEE INFOCOM 23