Task-Execution Scheduling Schemes for Network Measurement and Monitoring

Transcription

1 Task-Execuion Scheduling Schemes for Nework Measuremen and Monioring Zhen Qin, Robero Rojas-Cessa, and Nirwan Ansari Deparmen of Elecrical and Compuer Engineering New Jersey Insiue of Technology Universiy Heighs, Newark NJ Absrac Measuremen is a required process in high performance neworks for efficien qualiy-of-service (QoS) provisioning and service verificaion. Acive measuremen is an aracive approach because he measuremen raffic injeced ino he nework can be conrolled and he measuremen asks can be disribued hroughou he nework. However, he execuion of measuremen asks in common pars of a nework may face conenion for resources, such as compuaional power, memory, and link bandwidh. This conenion could jeopardize measuremen accuracy and affec nework services. This conenion for limied resources defines a conflic beween measuremen asks. Furhermore, we consider wo ses of measuremen asks, hose used o monior nework sae periodically, called periodic asks, and hose for casual measuremens issued as needed, called on-demand measuremen asks. In his paper, we propose a novel scheduling scheme o resolve conenion for resources of boh periodic and on-demand measuremen asks from graph coloring perspecive, called ascending-order of he sum of clique number and degree of asks. The scheme selecs asks according o he ascending order of he sum of clique number and conflic ask degree in a conflic graph and allows concurren execuion of muliple measuremen asks for high resource uilizaion. The scheme decreases he average waiing ime of all asks in periodic measuremen asks scheduling. For on-demand measuremen asks, he proposed scheme minimizes he waiing ime of insered on-demand asks while keeping ime space uilizaion high. In oher words, he oal ime spen on finishing all he asks is shorened. We evaluae our proposed schemes under differen measuremen ask assignmen scenarios hrough compuer simulaions, and compare he performance of his scheme wih ohers ha also allow concurren ask execuion. The simulaion resuls show ha he proposed scheme produces effecive conenion resoluion and low execuion delays. Key words: Scheduling, Nework Measuremen, Acive Measuremen, Graph Coloring, Clique, Qualiy of Service, QoS, Lis Coloring 1. Inroducion Some applicaions, such as voice over IP (VoIP), sreaming video and online gaming have sringen requiremens for Qualiy-of-Service (QoS) provisioning, which furher requires accurae and upo-dae informaion of he nework performance, hrough measuring and monioring ools o esimae and collec hose daa. Therefore, nework measuremen becomes an imporan subjec driven address: {zq4, rojas, ansari}@nji.edu (Zhen Qin, Robero Rojas-Cessa, and Nirwan Ansari) by Inerne Service Providers (ISPs) o quanify nework saus, monior exising raffic, and service verificaion on service agreemen compliance for applicaions wih QoS requiremens. Measuremen echniques can be coarsely divided ino passive and acive approaches. Passive measuremen uses raversing raffic, wheher carrying users daa or nework conrol packes, o deermine he nework sae. The accuracy of passive measuremen is a funcion of he amoun of exising raffic. On he oher hand, acive measuremen has conrollable properies ha are independen of Preprin submied o Compuer Communicaions Sepember 19, 2009

2 he absence of user raffic, hus making i an aracive approach [1]-[12]. In acive measuremen, a measuremen poin, which can be a rouer or end hos or some equipmen aached o hem, creaes and sends probing packes o he arge (desinaion) measuremen poin wih conrolled deparure imes. Eiher he desinaion measures he arrival ime in a synchronized nework, or he source esimaes he delay ime by using he response of he desinaion poin [13]-[16]. Figure 1 shows an example of a nework wih acive measuremen for (a) end-o-end (using end hoss) pahs, or (b) local links (beween neighbor rouers). Wihou loss of generaliy, Figure 2 shows a measuremen infrasrucure designed by Inerne2 E2E pipes projecs [18]. The nework informaion obained by acive measuremens can be, for example, available bandwidh, capaciy, one-way delay, round-rip ime (RTT), jier, and opology daa. The adopion of acive measuremen can be found in several largescale neworks [20]-[23] Figure 1: Nework measuremen implemenaion opology. Examples of acive measuremen ools ha can be deployed in any nework in general, range from he simple ones, such as Ping and Traceroue, o he more sophisicaed, such as Pipechar [24], Pahload [25], Cing [26], Clink [27], Neimer [28], Pahrae [29], Pahchar [30], and Yaz [31], among ohers. A nework measuremen oolki includes he various measuremen ools o evaluae he differen QoS parameers. The oolki shown in Table 1, hough rouer 1 rouer 2 per-hop link or muli-hop pah 5 U 5 U measuremen server 1 measuremen resuls measuremen reques periodic scheduling asks on-demand scheduling asks erminal compuer measuremen resuls resuls reques sorage daabase of measuremen resuls measuremen reques measuremen resuls measuremen server 2 Figure 2: An example of nework measuremen infrasrucure. Table 1: Seleced measuremen ools for QoS parameers. QoS Parameer Tool One-way delay Round-rip delay Available bandwidh Topology Bandwidh capaciy OWAMP[32] Ping Pipechar, Pahload Traceroue Pahchar no an exclusive one, is an example. Differen ools require differen nework resources and execuion imes. The measuremen ools are normally run periodically o monior he consecuive nework saus, by which he asks are called periodic measuremen asks. These asks are known in advance and can be scheduled before heir execuion sars. Moreover, he ools can also be invoked once (or for shor periods) a any arbirary ime o measure a nework parameer as needed. These asks are referred o as on-demand asks. On-demand asks emerge a any ime and need o be scheduled in combinaion wih he periodic asks while he nework is in operaion. Independenly of he measuremen approach used, probing overhead is a general concern for acive measuremen mechanisms as i may affec he user raffic. For example, an acive measuremen experimen [19] showed ha a 700-Bye packe size used in 60-packe probing rains can achieve sufficienly accurae resuls of available bandwidh measuremen per pah on he Inerne. In his case, one pah overhead is abou 42KB, and so measuring all end-o-end pahs in a 200-nodes bidirecional mesh sysem requires abou 1.7GB for jus

3 Table 2: Comparison of nework consumpion of sample ools. Tool CPU/ Bandwidh Time Memory Ping very low very low 2s Pipechar Low Low 20s Pahload Low Medium 7s one snapsho if all nework links are simulaneously esed. Therefore, he nework resources need o be efficienly managed under acive probing. In addiion, disribued measuremen asks may be execued simulaneously a one measuremen poin in a nework. Hence, i is possible ha differen measuremen asks conend for nework resources, including ransmission channels and bandwidh. Measuremen processes ha are execued in differen common poins also conend for resources, such as processing ime, bandwidh, and memory. The accuracy of some measuremen processes may be affeced by oher measuremen processes run concurrenly. This conenion for resources is called measuremen conflic problem. To gain insigh of he implicaions of conenion for resources, we execued Pipechar, Pahload, and Ping in a hos, all a he same ime, and used hem o measure several parameers in he ransmission from one hos o anoher hrough a 100-Mbps fas Eherne link [16]. We observed ha he measuremen resources and measuremen processing ime had a large discrepancy among hose measuremen ools, as shown in Table 2, and he obained measuremen resuls are insable because of he disurbance from oher measuremen processing. Sommers and Barford [17] also implemened a esbed hrough which he experimen resuls show ha he measuremens of packe loss and delay from acive probes can be skewed significanly due o he conenion of probing packes. Thus, he acive measuremen asks ha are performed a each measuremen poin need o be scheduled o avoid boh poenial resource conenion and measuremen disurbance from each oher while achieving a saisfacory measuremen in erms of ime and accuracy. To solve he above problem, we provide a soluion o schedule he periodic and on-demand measuremen asks o achieve he following four goals: 3 1. Avoid conflics among concurren execued measuremen asks. 2. Nework resources are no exhaused by measuremen asks. 3. Shoren he waiing ime of each measuremen ask for he execuion. 4. Shoren he oal compleion ime of measuremen asks se, ha is, improve he resource uilizaion. To comply wih he above requiremens, we propose an algorihm o schedule periodic asks and o improve he measuremen efficiency. We also propose an algorihm o schedule on-demand measuremen asks ha minimize he delay of boh periodic asks and he incoming on-demand asks. Boh algorihms are based on graph coloring heory, where each measuremen ask is reaed as a verex in a graph, and he conenion/conflic by wo asks is represened as an edge connecing hose wo verices. The remainder of his paper is organized as follows. Secion 2 analyzes he conenion problem of disribued nework measuremen asks. Secion 3 inroduces relaed scheduling algorihms for nework measuremen. Secion 4 describes he modeling of measuremen asks for scheduling by using a coloring approach. Secion 5 inroduces our proposed scheduling schemes for periodic and ondemand measuremen asks, respecively. Secion 6 shows he performance evaluaion obained by compuer evaluaion, and analysis of he proposed schemes and oher comparable schemes. Secion 7 presens our conclusions. 2. Problem Analysis According o he classificaion approach of scheduling inroduced by Graham e al. [33], he ask scheduling problem is defined in erms of a hree-uple classificaions [α, β, γ], where α defines he machine (processor) environmen, β specifies he job s characerisics, and γ denoes he opimaliy crierion. Following his classificaion mehod, he measuremen scheduling problem can be described as [P, {rec, r i }, C i ]. Here, P is he number of idenical parallel processors o perform he required jobs. However, differen from ha approach [33], P is a variable insead. The value of P depends on he number of measuremen asks run simulaneously. Considering ha n asks need o be processed, he following relaionship exiss: P n (1)

4 rec refers o he consrains on he resources used by he execuion of measuremen asks. In order o minimize or o avoid he impac of probing packes on he performance of regular daa raffic, a nework resource consrain, such as he maximum bandwidh, is se a each measuremen poin. This is called measuremen resource consrain (MRC) in his paper. Scheduling measuremen asks need o ensure ha he oal amoun of resources consumed by he measuremen asks are wihin his consrain rec. Measuremen ask i is denoed as τ i in he remainder of his paper. The parameer r i denoes he release ime of a measuremen ask τ i, upon which one insance of he ask τ i becomes available for processing or execuion. Ci indicaes ha he opimal crierion chosen is o minimize he oal compleion ime on P parallel processors, where C i denoes he compleion ime of he measuremen ask τ i. This opimal crierion reflecs he fourh goal lised in Secion 1. I is easy o see ha he hird goal lised in Secion 1 is he sufficien and necessary condiion of he fourh goal, as described by Lemma 1. Therefore, C i can cover boh he hird and fourh goals. Lemma 1. Minimizing he oal compleion ime of a se of measuremen asks is equivalen o minimizing he average waiing ime of he measuremen asks in his se. Proof. For a measuremen asks se, he compleion ime of ask τ i is: C i = e i + w i (2) where e i is he execuion ime of measuremen ask τ i and w i is he waiing ime of ask τ i. Hence, he oal compleion ime of he measuremen asks se is: Ci = e i + w i = e i + m w avg (3) where m is he number of measuremen asks in he se and w avg is he average waiing ime of he asks. Since he execuion ime of each measuremen ask is a consan, he sum of he execuion ime e i is a consan oo. According o Equaion 3, minimizing C i is equal o minimizing m w avg, and hus is equal o minimizing w avg. A scheduling algorihm can be furher classified as preempive or non-preempive. In preempive 4 scheduling, he execuion of a ask can be inerruped prior o compleion and resumed laer. On he oher hand, in non-preempive scheduling, a ask mus be execued o compleion once execuion has sared. In general, measuremen ask scheduling is regarded as non-preempive scheduling as he measuremen resuls are expeced a compleion and he measuremen resuls may be ime sensiive. Anoher issue wih his problem ha differeniaes i from he ohers is he poenial conflic ha measuremen asks have wih each oher. This characerisic increases he complexiy of he scheduling scheme because he asks canno be jus sored according o one parameer (e.g., deadline or execuion ime of he ask), bu also he conflic wih scheduled asks has o be considered. 3. Relaed Work Round robin is one of he simples scheduling schemes [22, 34, 35] where he asks are execued by a fixed order in uni-processor sysems and only one ask is execued a a ime. This scheme requires he longes processing ime for measuremen asks as i does no admi concurren execuion. Nework Weaher Service (NWS), a well-known nework measuremen infrasrucure, adaps a oken passing scheme [36] o ensure muual exclusion beween measuremen asks. In his scheme, he measuremen poin ha receives a oken is eniled o execue a measuremen ask. Aferwards, he measuremen poin releases he oken o a successor. However, his mehod does no allow concurren execuion of measuremens. Deadline driven scheduling (DSS), also known in he lieraure as he Earlies Deadline Firs (EDF) scheduling scheme [37], selecs asks based on heir deadlines, and was originally defined for uni-processor execuion. I is shown ha he problem of deermining wheher a given periodic ask sysem is nonpreempively feasible on eiher a single processor or muliprocessors is NP-hard in a srong sense [38], [39]. To provide nework measuremen scheduling, a scheduling algorihm based on EDF ha allows muliple concurren execuions, referred o as EDF- CE [40], was recenly proposed. This approach iniializes a queue ha sacks all pending asks o be processed in an EDF order, where he deadline is defined as he ime before he ask mus be execued again. Whenever a ask is ready o be released or a ask finishes execuion, he available asks in

5 he queue are scheduled. This mehod inroduces he possibiliy of overlapping muliple asks in some ime slos, bu i does no consider he uilizaion raio; in oher words, soring he asks in he pending queue wih heir deadlines ignores he fac ha he concurren execuion of muliple asks grealy depends on he exising conflics beween he asks as much as on he asks deadlines. 4. Modeling of Nework Measuremen Scheduling Schemes 4.1. Definiions Le τ = {τ 1,τ 2,...,τ n } represen he measuremen asks se wih up o n measuremen asks o be execued in he nework. Here, τ i is characerized by a hree-uple of parameers: a (τ i ): he ime he measuremen ask is released, which is he ask s arrival ime. e (τ i ): he execuion ime required by a measuremen ask o complee he measuremen. a( 1) a( 3) e( i) a( i) e( 1) a( 2) e( 3) i1 i2 i3 i4 i5 i6 p( i) p( 1) p( 2) p( 3) e( 2) Figure 3: Illusraion of nework measuremen asks. he leas common muliple of he periods of all measuremen asks in τ. p h = lcm (p (τ 1 ),p(τ 2 ),...,p(τ n )) (4) p (τ i ): he period of he measuremen ask, or he ime o execue ask τ i afer he previous insance. This parameer describes how ofen a measuremen ask is execued. A imeable of periodic measuremens is consruced by sequences of asks, each of which is execued again in p (τ i ) unis of ime, and each ask requires execuion of e (τ i ) ime unis. The j h job (or repeiion) of measuremen ask τ i is denoed as τ ij.thus,hefirsjob,τ i1, of measuremen ask τ i occurs a ime a (τ i ); consecuive jobs generaed by τ i occur exacly p (τ i ) ime unis apar. Figure 3 illusraes an example delineaing he erms defined above. In a se of periodic asks where he asks (and he number of hem) do no change and where each ask can have any paricular period, he combinaion of asks release imes is finie. This is, afer a long period of ime, because of he ask periodiciy, he combinaion of release imes repeas again. Therefore, for he measuremen se τ, we define he erm hyperperiod p h o be he period of ime where all asks in he se occur a differen imes and wihou replicaion of he combinaion of release imes. Tha is, all periodic asks in one hyperperiod are able o follow he same schedule as used in he previous hyperperiod. The hyperperiod is defined as 5 Wihou loss of generaliy, we define he execuion ime e (τ i ), iniial available ime a (τ i ), and he period p (τ i ) as ineger muliples of a ime uni which is referred o as a ime slo. The deadline of each job d (τ ij ) coincides wih he period, ha is, he job τ ij should be compleed before he nex job τ i(j+1) is available o be execued. According o his definiion, Lemma 2 can be readily obained: Lemma 2. Given a measuremen asks se τ = {τ 1,τ 2,...,τ n }, a any ime insance, here is a mos one job available o be execued for any measuremen ask τ i τ. Proof. A any ime insance, here mus be a job available for execuion a he beginning of ha period. If here are some jobs generaed from previous periods sill pending for execuion, hose posponed jobs passed heir own deadlines and hey are considered as missed jobs. Hence, here is a mos one job for each measuremen ask a any imeinsance Modeling of Measuremen Scheduling Our scheduling algorihms are based on graph heory. In he lieraure, here are some aricles using graph coloring o solve ime slos assignmen problem [41, 42, 43], bu mos of hem are designed

6 for single processing, which are no fi for muliask processing such as he nework measuremen scenario. Consider a measuremen asks se τ = {τ 1,τ 2,...,τ n } o be execued in a nework. Each measuremen ask can be represened as a node ( V ) in a graph and any wo measuremen asks are conneced by a link ( E) ifheyareobe execued wih muual exclusion on he measuremen poin or channel. These asks are said o be adjacen o each oher. The graph G(V,E) ha describes hese nodes and links is called a conflic graph. Figure 4 illusraes an example of a conflic graph where wo measuremen asks are o be execued beween measuremen poins 1 and 2 in a fullduplex connecion. Assume ha ask τ 1 conends wih τ 2 for he available memory a measuremen poin 1, and a he same ime, i conends for he ransmission channel wih τ 3.Taskτ 3 also conends wih τ 4 for available memory a measuremen poin 2. Therefore, hese four asks comprise a conflic graph wih hree links. In his example, measuremen asks τ 1 and τ 4 (represened by shaded nodes), or τ 2 and τ 3 (represened by unshaded nodes) can be concurrenly execued. measuremen poin measuremen poin 2 Figure 4: Illusraion of he relaionship beween measuremen asks by a conflic graph. In our considered nework, here is a cenral conroller o compue he schedule of all measuremen asks and o send ou he schedule informaion o each measuremen poin. This cenral managemen mode is feasible and adoped in real nework measuremen frameworks. Scheduling is requesed each ime when a new job is available for execuion and when a job execuion has been compleed. We name hese ime insances as scheduling poins. There is 6 a waiing queue o sore he jobs available for execuion. A each scheduling poin, jobs sored in he waiing queue become eligible candidaes for he scheduler. Based on he conflic relaionship beween he measuremen asks, hese jobs ha belong o differen measuremen asks consruc a conflic graph a he job level. The conflic relaionship beween jobs follows he same conflic relaionship beween measuremen asks. For periodic asks, he conflic relaionship among hem is known prior o performing scheduling because he submied asks and he amoun of resources hey consume are boh known in advance. For ondemand asks, he aribues of measuremen ools are aprioriso he asks conflics are known once an on-demand ask emerges. As he measuremen resuls obained by earlier periodic measuremen asks are used o describe he curren nework performance, i is desired ha he measuremen asks can be compleed as soon as possible afer a ask is available for execuion. Therefore, he scheduling problem is convered ino a process o schedule he available jobs a each scheduling poin so as o minimize he job waiing ime for execuion. A he same ime, he scheduling of measuremen jobs a one scheduling poin is enunciaed as he arrangemen of he verices of graph G a he job level such ha none of he nodes conneced wih each oher are scheduled for simulaneous execuion. This process can be described as a verex coloring problem as follows. Scheduling of Measuremen Tasks: Given a conflic graph G(V,E) wih verices V = V (G), assign each verex a color ou of he range [1, 2,...,k] such ha no wo adjacen verices have he same color. Here, each color maps o one ime slo. The color se o be used by a verex v ij in he conflic graph is mapped o he ime range [ c,d(τ ij )] as described by Equaion 5, where c is he curren scheduling poin and d (τ ij ) is he deadline of he job mapped by verex v ij. Tha is, he scheduler only considers he ime slos prior o a job s deadline. [1, 2,...,k] [ c,d(τ ij )] (5) Each measuremen poin is considered o have limied processing and sorage (memory) capabiliies, and each channel o have a limied bandwidh capaciy. Therefore, he load of inrusive probing packes in acive measuremen needs o be resriced wihin a range, so as o minimize he dis-

7 urbance of he measuremen of he exising daa raffic, as described by MRC values. We propose o use a consumpion marix o describe such consrains. Le us denoe he number of schedule slos and he number of he measuremen jobs as he column and row of a marix as shown in Figure 5. The resource uilizaion objecive can be described as follows: 1 A each ime slo, consumpion of resources MRC ime slo Figure 5: Consumpion marix. Resource Uilizaion of Measuremen Tasks: Jobs of measuremen asks se τ = {τ 1,τ 2,...,τ n } wih execuion imes e (τ 1 ), e (τ 2 ),..., e (τ n ), can be represened as a p h n consumpion marix A, where a row indicaes he ask and is duraion in ime slos and he column indicaes he ime slo. The maximum number of rows is bounded by he amoun of processing resources consrained by Equaion 1. Each column as circled in Figure 5 represens he consumpion of nework resources a ha paricular ime slo. The objecive is o place he measuremen asks in he consumpion marix such ha n j=1 A ij MRC, i [1, 2,...,p h ], where p h is he hyperperiod duraion, i.e., he oal consumpion of resources by measuremen asks per ime slo is wihin he measuremen resource consrain. 5. Proposed Scheduling Schemes This secion inroduces our scheduling schemes for periodic and on-demand measuremen asks. The following definiions are used in he descripion of he proposed schemes. Clique: a maximal se of adjacen verices of graph G. Clique number: he number of verices in he larges clique of G, denoed as ω(g). Degree: degree of verex v in graph G is he number of adjacen verices of v in G, denoed as d G (v); he maximum degree of graph G is he larges number of d G (v), and i is denoed as Δ(G) Periodic Measuremen Tasks Scheduling Scheme Following he model of he scheduling problem described in Secion 4.2, our proposed algorihms consider he jobs sored in he waiing queue for scheduling a each scheduling poin. If a job can be scheduled in he ime range [curren scheduling poin, deadline of job] wihou any conflic wih already scheduled jobs a any given ime slo, his job is removed from he waiing queue and he corresponding ime slos for execuion are marked in he consumpion marix; oherwise, he job is kep in he waiing queue and wais for consideraion a he nex scheduling poin. Hence, he goal is o find a feasible scheme o schedule he maximum number of concurren jobs a each scheduling poin, so ha he mos ime space in he consumpion marix can be uilized. Consider available jobs in he waiing queue. Since heir execuion imes are ineger muliples of a ime slo and he ime slo can be mapped o a verex, each ask can be divided ino a se of subverices as follows: In a conflic graph G(V,E) a he job level, each verex v ij ha maps job τ ij has a se of sub-verices (τ 1 ij,τ2 ij,...,τα ij ),whereα is he lengh of e(τ ij) in ime slos. As he sub-verices of v ij represen he differen bu consecuive ime slos of a ask, hey are said o conend wih each oher (or o have a conflic wih each oher). These conflics can be described by a complee sub-graph G ij as in he example shown in Figure 6. Conflic graph G is furher represened by is sub-verices and i is denoed as G s (V s,e s ). The clique number of a sub-graph G ij is equal o he number of verices in G ij. Here, G s is he graph consruced by sub-verices. As each color represens one ime slo, each subverex in graph G s is a candidae for a color assignmen, so ha any wo adjacen sub-verices mus no possess he same color. Each sub-verex is resriced o allowed colors ha saisfy he relaionship denoed by Equaion 5. This is called he lis coloring problem. To solve his problem, we propose o sor he sub-verices in he ascending order

8 waiing queue G 12 & G s (V s,e s G 22 G 33 ) G : sub-verex ij : verex conflic relaionship G(V,E) Figure 6: Example of sub-graph. of heir degree in graph G s : d s G(vij) l =d G (v)+ω(g ij )=d G (v)+e(τ ij ), (6) vij l G ij The raionale o schedule jobs in his fashion is he expecaion ha a sub-verex wih a small degree has a few conflics; herefore, a large number of asks migh be scheduled a he same ime. In a nework wih a measuremen scheduling environmen, his can be described by wo aspecs. For a sub-verex v l ij and is adjacen sub-verex v x: vij l and v x map o he same job: Then, he low degree implies he job has a shor execuion ime. This par is represened as he execuion ime of he verex e(τ ij ), or by he clique number of he sub-graph ω(g ij ). Scheduling a job wih a shor execuion ime will leave more available ime slos for oher jobs in he waiing queue. v l ij and v x map o differen job: Then, he low degree of he sub-verex indicaes he job migh have few conflics wih oher available jobs in he waiing queue. Scheduling a job wih few conflics allows addiional jobs o be execued concurrenly, hus increasing he resource uilizaion. The scheduling procedure is described below: Sep 1. A curren scheduling poin c, check if here is a new job available for execuion. 8 If so, he new job is placed in he waiing queue. Sep 2. Map he candidae jobs in he waiing queue o a conflic graph G and conver G ino sub-graph G s. Sep 3. Sor he sub-verices in he ascending order of heir degree, as described by Equaion 6. Sep 4. Schedule he firs job as indicaed by he sored sequence. Any sub-verex vij l seleced o be scheduled will be colored wih oher sub-verices belonging o he same job τ ij wih consecuive colors. The used colors are he inersecion se as colors in conflic [ c,d(τ ij )] where [ c,d(τ ij )] is he ime inerval from c o d (τ ij ), colors in conflic is he se of available colors possessed by he on-going conflic jobs, and colors in conflic is he complemenary se of colors in conflic, i.e., he available colors ha can be used by vij l. Sep 5. Check if he colored job and oher on-going jobs violae he resource consrain MRC. If here is no violaion, remove he colored job from he waiing queue, remove he corresponding sub-verices from he sored sequence, and add he compleion ime of he job o he scheduling poin lis. Sep 6. Color he nex sub-verex in he sored sequence. Repea Seps 4 o 5. Sep 7. Go o he nex scheduling poin. Repea Seps 1 o 6. The algorihm of periodic measuremen-asks scheduling is described by he pseudo code in Figure On-Demand Measuremen Tasks Scheduling Scheme During he execuion of he periodic measuremen, a nework adminisraor may reques sporadic on-demand measuremen asks o es specific nework performance parameers a a paricular ime. Furhermore, on-demand asks migh conflic wih some periodic or on-demand asks. Each on-demand ask has also defined execuion and deadline imes, and i is considered wih eiher a prioriy higher han or equal o ha of he scheduled periodic asks. The proposed scheduling scheme for on-demand measuremen asks is able o handle boh of hese wo cases adapively. The goal of scheduling on-demand asks wih higher prioriy is o execue he on-demand asks as soon as

9 Periodic Tasks Scheduling Algorihm Inpu: measuremen ask se τ 3-uple parameers of asks a(τ i), e(τ i), p(τ i) asks conflic marix F measuremen resource consrain MRC Oupu: sar ime of jobs T Iniialize hyperperiod p h Iniialize scheduling poin lis S Iniialize waiing queue Q = {} while S is no empy if new available job τ new Q remove he old insance of τ new due o expiraion end Q = Q + τ new se up conflic graph wih sub-verices f :(F, Q) G s (V s,e s ) sor Q by ascending order of degree of sub-verices d G S (v) for each job τ ij in sored Q find he available colors range R if consecuive sequence L = e(τ ij) exissinr & consumpion of τ ij and on-going jobs saisfies MCR assign he firs long enough consecuive colors L o τ ij Q = Q τ ij, record sar ime of τ ij in T updae scheduling poin lis: S = S + compleion ime of τ ij end end Go o nex scheduling poin end Figure 7: Pseudo code of scheduling algorihm for periodic measuremen asks. possible while minimizing he laency of he periodic asks caused by he inserion of on-demand asks. On he oher hand, scheduling on-demand measuremen asks wih he same prioriy as periodic asks aims o shoren he average waiing ime for all measuremen asks including on-demand and periodic asks. The proposed mehod schedules all he asks wih higher prioriy firs, and hen schedules he remaining on-demand and periodic asks according o he ascending order of he degree of sub-verices, as explained below: Sep 1. When a new on-demand ask arrives a c, check he prioriy ype of he on-demand ask. If is prioriy is high, sore his on-demand ask o he waiing queue of high prioriy asks Q high. If he prioriy is equal o ha of he periodic asks, he on-demand ask is sored o Q regular. 9 Sep 2. Schedule all he candidae jobs in he waiing queue of high prioriy asks Q high. In he pre-compued schedule, all he jobs of periodic asks ha finish heir execuion before c and he jobs ha are sill being execued a ime c are discarded/cancelled. The jobs ha sar processing afer c are considered as rescheduled. Follow Seps 2 o 6 of he previous scheduling procedure for periodic asks. Noe ha he scheduling poins are updaed so he compleion ime of he scheduled jobs in Q high are added ino he scheduling poins lis. Afer his sep, all he possible jobs in Q high mus be eiher scheduled or expired because here are no available ime slos o be scheduled before he job s deadline. Sep 3. Add hose jobs ha sar processing afer c in he pre-compued schedule o he waiing queue of regular prioriy asks Q regular. Schedule all candidae jobs in Q regular following he previous scheduling procedure for periodic asks. Figure 8 shows an example o illusrae his scheduling procedure. In his example, he ondemand ask τ od conflics wih periodic asks τ 1 and τ 3, as shown in Figure 8.a. If he prioriy of τ od is higher han ha of oher periodic asks, hen when i arrives a c, all periodic jobs ha sar he execuion afer c are sored in Q regular while τ od is sored in Q high.thus,τ od is he firs o obain a schedule. As shown in Figure 8.b, τ od is firs scheduled and only he schedule of job τ 32 is changed. If τ od has same prioriy as oher periodic ask, hen τ od and all periodic jobs ha sar he execuion afer c are sored in Q regular and sored in he ascending order of sub-verices degree. As shown in Figure 8.c, τ od is scheduled wih longer waiing ime han in Figure 8.b, bu rescheduling for oher periodic jobs is unnecessary. The algorihm of on-demand measuremen asks scheduling is described by he pseudo code shown in Figure Compuaional Complexiy Analysis According o Lemma 2, here are a mos n jobs in he waiing queue if here are n asks in he measuremen asks se. Using a simple soring algorihm such as binary ree sor, he compuaional

10 1 2 3 od On-demand Tasks Scheduling Algorihm Inpu: measuremen ask se τ 3-uple parameers of asks a(τ i), e(τ i), p(τ i) asks conflic marix F on-demand ask τ od measuremen resource consrain MRC c arrive execue c arrive c od rescheduled (a) od (b) execue od (c) Figure 8: Example of scheduling on-demand measuremen ask: (a) pre-compued schedule; (b) on-demand ask has higher prioriy; (c) on-demand ask has same prioriy as periodic asks. complexiy of soring n jobs is n lg(n). In one hyperperiod, assume here are m scheduling poins which indicae he ime jobs arrive, hen he compuaional complexiy of he proposed algorihm is mnlg(n). Le s denoe C as he number of unique compleion imes of all jobs and K as he oal number of jobs o be execued in a hyperperiod. Therefore, we ge: K = n i=1 p h p(τ i ) and so he following relaionship exiss: m n i=1 p n h p(τ i ) + C 2 p h p(τ i ) i=1 Therefore, he compuaional complexiy of he proposed algorihm is n lg(n) n p h i=1 p(τ i), and hus he complexiy can be decreased by limiing he upper-bound of p h. Some previously proposed mehods aimed o achieve his goal [44], bu his is ou of scope of his paper. 10 pre-compued schedule T o Oupu: sar ime of jobs T Iniialize hyperperiod p h Iniialize scheduling poin lis S Iniialize waiing queue Q high = {}, Q regular = {} if prioriy of τ od is high Q high = Q high + τ od elseif prioriy of τ od is regular Q regular = Q regular + τ od end se up conflic graph wih sub-verices: f :(F, Q high ) G s high (V s high,es high ) sor Q by ascending order of degree of sub-verices d G S (v) high schedule each job in Q high and updae scheduling poin lis se up conflic graph wih sub-verices: f :(F, Q regular ) G s regular (V s regular,es regular ) sor Q by ascending order of degree of sub-verices d G S (v) regular schedule each job in Q regular and updae scheduling poin lis Figure 9: Pseudo code of scheduling algorihm for ondemand measuremen asks. 6. Simulaion Resuls To sudy he performance of he proposed algorihms, we compared hem wih oher scheduling algorihms Schemes for Comparison We considered algorihms able o process muliple measuremen asks a he same ime for a fare comparison o he proposed algorihms for heir execuion on an infrasrucure wih sufficien resources. All of hese algorihms have he same compuaional complexiy as he proposed ones. These algorihms are described nex: Round-Robin We improve he original round robin scheme o empower i wih he concurren execuion capabiliy. The improved scheme selecs asks for execuion by following a pre-defined order. The scheme performs scheduling a each scheduling poin. A a scheduling poin, all he available jobs waiing o be scheduled are seleced in a pre-defined round-robin

11 order. If here is no conflic wih curren on-going ask, he job is scheduled; oherwise, he job is kep in he queue o be considered/scheduled a he nex scheduling poin. This algorihm is described in Figure waiing queue & conflic relaionship 12 < 22 < 33 < 41 firs 1 s scheduling poin 12 1 s scheduling poin round-robin order nd scheduling poin rd scheduling poin 22 3 rd scheduling poin las sep 1 sep 2 sep 3 sep 4 sep 5 Figure 10: Illusraion of he improved round robin scheduling algorihm. he ime ha he job sars execuion and he beginning ime he job is available o be execued. In he wors case, some measuremen jobs may be missed due o ime expiraion (i.e., he waiing ime exceeds he ask period). We define he waiing ime of he missed job equal o is period ime. As he nework performance is moniored by periodic measuremen requess, he measuremen jobs are expeced o be scheduled a desired sampling imes ha he inerval ime beween any wo consecuive samplings is a consan. However, because of he conflic of he nework measuremen asks, he measuremen jobs are scheduled a he ime deviaed from he desired sampling imes. The average normalized waiing ime is used o reflec how severe such deviaion impacs he accepance of he measuremen sampling resuls. For example, if a measuremen ask wih period equal o 20 minues wais for 1.5 minue o sar execuion, he measuremen resul is sill accepable o be used as periodic samples. However, if a measuremen ask wih period 2 minues wais for 1.5 minue for execuion, he measuremen sample obained is far from he expeced measuremen sampling ime. Anoher evaluaion parameer is he execuion success raio of jobs o be execued, which is defined as: Execuion success raio = number of execued jobs in one hyperperiod number of oal jobs in one hyperperiod Descending Order of Sub-Verices Degree (DOSD) This scheme, also inroduced here for comparison purposes, follows a similar procedure as described in Secion 5.1 for he ascending order version, excep ha his scheme sors he jobs in he waiing queue in he descending order of he degree of he sub-verices mapped o he jobs, in Sep Evaluaion Mehod The algorihms are compared in erms of he average normalized waiing ime of all jobs in one hyperperiod ha is defined as below: Avg. normalized waiing ime = avg( w(τ ij ) p(τ ij ) ) where w(τ ij ) is he waiing ime of he job τ ij. w(τ ij ) is formally defined as he difference beween Simulaion Resuls of Periodic Tasks Scheduling In his simulaion, he period of he periodic measuremen asks is uniformly disribued in he range of [11,100] ime unis, and he execuion imes of he periodic measuremen asks are uniformly disribued in he range of [2,10] ime unis. The iniial ime of ask a (τ i ) is randomly seleced in he range of [1,5] ime unis. We observed he performance of algorihms for differen conflic probabiliy values from 0 o 1.0 wih incremens of A conflic probabiliy of 0 beween wo asks means ha here is no conflic beween hem, herefore here is no edge connecing hese wo verices in he conflic graph. A conflic probabiliy of 1.0 means ha here is a conflic beween any wo asks, corresponding o a fully conneced conflic graph. There migh be a high conflic probabiliy in a real nework where he ongoing measuremen asks demand

12 nework resources for exclusive use. As an example, he simulaneous measuremen of bandwidh, delay, jier and oher parameers a a gaeway in a small nework could be a nework performance boleneck as all measuremen ools conend for he memory, processing ime, and uplink/downlink bandwidh of ha gaeway. To observe he maximum performance of he scheduling schemes, he measuremen resource is assumed o be large enough so here is no MRC consrain on measuremen asks. We compare he performance of he algorihms wih 10 and 20 periodic asks scenario. The simulaion is run 1000 imes (i.e., for each ime a random asks se and he conflic relaionship are generaed) for each scenario. Figure 11 shows he average normalized waiing imes of 10 periodic asks for hese schemes. The figure shows ha he proposed scheme has he lowes average normalized waiing imes, and EDF-CE has he highes. Normalized waiing ime Round robin DOSD 0 Conflic probabiliy Execuion success raio Round robin 0.6 DOSD 0.55 Conflic probabiliy Figure 12: Execuion success raio for 10 periodic measuremen asks. hese schemes wih 20 asks. The oucome for 20 asks is similar o he case wih 10 asks, where he proposed scheme achieves he lowes waiing ime. The advanage of using he proposed scheme is more pronounced for scenarios wih a larger number of asks. Normalized waiing ime Round robin DOSD Figure 11: Normalized waiing ime for 10 periodic measuremen asks. Figure 12 shows he success raio of 10 periodic asks of he compared schemes. The figure shows ha as he conflic probabiliy increases, he success raio of he schemes decreases. Here, he success raio of he proposed scheme is he highes among oher schemes as his scheme misses scheduling he fewes number of asks as compared o he oher schemes, while DOSD, which sors he ask in he opposie order, has he lowes success raio. The combinaion ha increases he success raio seems o be he selecion of a small ask and wih a small number of conflics. Figure 13 shows he normalized waiing imes of Conflic probabiliy Figure 13: Normalized waiing ime for 20 periodic measuremen asks. Figure 14 shows ha he proposed scheduling scheme and he EDF-CE scheme provide similar execuion success raio, which is he highes success raio as compared o round robin and DOSD schemes. We can see ha when he conflic probabiliy is lower han 0.5, he performance of all algorihms is similar, bu as he conflic probabiliy increases, he performance differences of he schemes become more pronounced. As an ineresing obser-

13 vaion, when he conflic probabiliy is 1, where no more han one job can be execued a a ime by any of he schemes, he waiing ime and success raio of he schemes show differences. The low success probabiliy of DOSD is expeced as i selecs jobs wih long execuion ime firs, and he remaining ime will hen be lef o a large number of asks ha may be delayed close o or beyond he end of heir periods; herefore, a large number of jobs are missed. In he proposed scheduling algorihm, he degree of a sub-verex is decided by he lengh of he execuion ime of he job, so ha scheduling by he ascending order of he degree means ha he job wih he shores execuion ime is scheduled firs. This selecion can poenially save a larger number of ime slos for he subsequen jobs in he waiing queue. Therefore, he performance of his algorihm is also he highes wih he conflic probabiliy of imes under non-uniform disribuion in he execuion ime of he 10 asks. The large number of asks wih long execuion imes is no beneficial o he proposed scheme, bu he proposed scheme sill achieves he lowes normalized waiing ime among all compared schemes. The round-robin scheme achieves similar normalized waiing imes (alhough slighly higher) o hose of he proposed scheme. The oher schemes are favored by his disribuion of execuion imes, bu heir normalized waiing imes are larger han hose of he proposed scheme. This indicaes ha he measuremen samples generaed by scheduling schemes in comparison are more biased from he regular measuremen sampling poins, so ha he jier of he ime inervals beween any wo iner-sampling poins is large Round robin DOSD Execuion success raio Round robin 0.3 DOSD 0.2 Conflic probabiliy Figure 14: Execuion success raio for 20 periodic measuremen asks. We also simulaed a scenario where he execuion imes of periodic measuremen asks are nonuniformly disribued. The periodic measuremen ask se is composed of 10 measuremen asks. The execuion ime of 5 measuremen asks are uniformly disribued in he range of [2,10] ime unis while he execuion ime of he res of 5 asks are randomly seleced in he range of [8,10] ime unis. The period of he asks is uniformly disribued in he range of [11,100] ime unis. The iniial available ime of a ask is randomly seleced in he range of [1,5] ime unis. The simulaion is run 1000 imes. Figure 15 shows he average normalized waiing 13 Normalized waiing ime Conflic probabiliy Figure 15: Normalized waiing ime for 10 periodic measuremen asks wih non-uniformly disribued execuion imes. Figure 16 shows he execuion success raios of hese schemes for asks wih non-uniformly disribued execuion imes. The resuls show ha he execuion success raios of all hese schemes are lower han he values obained under execuion imes wih a uniform disribuion. The consideraion of a larger number of asks wih long execuion imes makes he scheduling schemes less efficien, and more asks miss heir execuions. Neverheless, he resuls show ha he proposed scheme achieves he highes execuion success raio Simulaion Resuls of On-Demand Tasks Scheduling We also simulaed he scheduling of periodic asks combined wih on-demand asks and evaluae he performance of he scheme according o he

14 Execuion success raio Round robin 0.55 DOSD 0.5 Conflic probabiliy Figure 16: Execuion success raio for 10 periodic measuremen asks wih non-uniformly disribued execuion imes. Average waiing ime of on demand asks (ime unis) Round robin DOSD 0 Conflic probabiliy Figure 17: Average waiing ime for on-demand measuremen asks of on-demand asks in a combinaion wih periodic asks. average waiing ime insead of average normalized waiing ime of he jobs since here is no period for he on-demand asks. In his scenario, here are 10 periodic asks, and on-demand asks are creaed a arbirary ime slos. We combine he periodic asks wih on-demand asks creaed a arbirary ime slos, where he arrival of an on-demand measuremen ask is creaed wih a probabiliy of 0.05 for each ime slo. For scheduling (and execuion), he prioriy of on-demand asks is se o be equal o ha of periodic asks. The execuion and period imes are uniformly disribued in he ranges of [2,10] and [11,100] ime slos, respecively. As in he previous secion, we considered he conflic probabiliy among all measuremen asks (including boh periodic and ondemand asks) increasing from 0 o 1.0 wih seps of We ran he simulaion for 500 imes. Figure 17 shows he average waiing imes measured only on he on-demand asks. The resuls indicae ha he proposed algorihm can achieve he lowes waiing ime for on-demand asks among he considered algorihms as all ask are considered wih he same prioriy levels. However, differen from he cases wih periodic asks only, he roundrobin scheme shows he lowes performance (he longes average waiing ime) as some asks canno be re-organized wih he addiion of on-demand asks because periodic asks would sill follow he pre-deermined round-robin order. However, he oher schemes follow similar rends as hose observed for periodic asks only. Figure 18 shows he average waiing imes of he 14 periodic asks only, under his scenario. The resuls show ha he periodic asks undergo similar average waiing imes as in he case of periodic asks only, and he round-robin scheme and he proposed scheme achieve he lowes average waiing imes. The performance of round-robin is high in his scenario as he pre-deermined order followed by his scheme isolaes he periodic ask from he arrivals of on-demand asks. The proposed scheme, however, accommodaes he on-demand asks and sill achieves an efficien oucome, or he lowes average waiing imes. Average waiing ime of periodic asks (ime unis) Round robin DOSD 0 Conflic probabiliy Figure 18: Average waiing ime of periodic asks when hey are combined wih on-demand asks. Figure 19 shows he normalized waiing imes of he periodic measuremen asks. This graph

15 also corroboraes he previous observaions, where he periodic asks have similar resuls o he case of only periodic asks, wih he proposed scheme achieving he highes performance and he EDF- CE scheme achieving he lowes performance. Normalized waiing ime of periodic asks (%) Round robin DOSD 0 Conflic probabiliy Figure 19: Normalized waiing ime of periodic asks when hey are combined wih on-demand asks. 7. Conclusions In his paper, we have analyzed he problem of conenion for resources in nework acive measuremen. The scheduling of acive measuremen asks can be used o resolve his conenion o allow high uilizaion of nework resources and o provide accurae measuremen resuls and leas disurbance o users daa raffic. Criical conenions for any resource are defined as conflics. Based on graph coloring heory, we have proposed o describe he measuremen asks relaion by using a conflic graph, and o conver his scheduling problem ino a graph coloring problem. We have also proposed wo algorihms o schedule asks according o he ascending order of he degree of sub-verices in he conflic graph, one for periodic measuremen asks, and anoher for on-demand measuremen asks. Each sub-verex represens one basic ime uni for he execuion ime of he ask. The resuls showed ha he proposed scheduling schemes provide he shores average waiing ime for cases where periodic asks are considered in he nework as well as when on-demand ask are added in a nework wih exising periodic asks. The proposed schemes also achieve he highes uilizaion of nework resources as shown by achieving he highes execuion success raios in he presened resuls. In addiion, he schemes are able o schedule he on-demand asks wih eiher higher or equal prioriy wih respec o ha of he periodic measuremen asks. Acknowledgemen This work has been parially suppored by Compuaion and Communicaion: Promoing Research Inegraion in Science and Mahemaics (C2PRISM), NSF GK-12 Projec # , a New Jersey Insiue of Technology. References [1] L. Ciavaone, A. Moron, and G. Ramachandran, Sandardized acive measuremens on a ier 1 IP backbone, IEEE Communicaions Magazine, Vol. 41, Iss. 6, pp , Jun [2] T. Tsugawa, T.M. Cao-Leh, G. Hasegawa, and M. Muraa, Inline bandwidh measuremens: Implemenaion difficulies and heir soluions, IEEE Workshop on End-o-End Monioring Techniques and Services (E2EMON), pp. 1-8, May [3] G. Dos Sanos e al., UAMA: a unified archiecure for acive measuremens in IP neworks; End-o-end objeive qualiy indicaors, IEEE/IFIP Inegraed Nework Managemen Symposium, pp , May [4] M. Zhanikeev, S. Xu, and Y. Tanaka, Acive performance measuremen for IP over all-opical neworks, IEEE/IFIP Inernaional Conference in Cenral Asia on Inerne, pp. 1-5, Sep [5] M. Zhanikeev and Y. Tanaka, A esbed for agenbased muli-purpose exensible acive measuremen, Tesbeds and Research Infrasrucures for he Developmen of Neworks and Communiies (TRIDENT- COM), Mar [6] M. Mushaq and T. Ahmed, Adapive packe video sreaming over P2P neworks using acive measuremens, IEEE Symposium on Compuers and Communicaions (ISCC), pp , Jun [7] R. Mishra and V. Sharma, QoS rouing in MPLS neworks using acive measuremens, IEEE Conference on Convergen Technologies for Asia-Pacific Region (TENCON), pp , Oc [8] M. Zangrilli and B. Lowekamp, Comparing passive nework monioring of grid applicaion raffic wih acive probes, Grid Compuing Workshop, pp , Nov [9] M. Aida, K. Ishibashi, and T. Kanazawa, CoMPACT- Monior: change-of-measure based passive/acive monioring weighed acive sampling scheme o infer QoS, Applicaions and he Inerne (SAINT) Workshops, pp , Feb [10] P. Calyam, D. Krymskiy, M. Sridharan and P. Schopis, Acive and passive measuremens on campus, regional and naional nework backbone pahs, IEEE Conference on Compuer Communicaions and Neworks (ICCCN), pp , Oc

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