model-based end-to-end available bandwidth inference using queueing analysis

Computer Networks 50 (2006) 1916–1937

www.elsevier.com/locate/comnet

Model-based end-to-end available bandwidth inferenceusing queueing analysis

Xiaojun Hei a,*, Brahim Bensaou b, Danny H.K. Tsang a

a Department of Electrical & Electronic Engineering, Hong Kong University of Science and Technology, Clear Water Bay,

Kowloon, Hong Kongb Department of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Available online 8 November 2005

Abstract

End-to-end available bandwidth estimation between Internet hosts is important to understand network congestion andenhance the performance of Quality-of-Service (QoS) demanding applications. In this paper, we investigate model-basedavailable bandwidth measurement via the use of an active probing stream. A general end-to-end measurement framework,which unifies the current research approaches and highlights insights for measurement practice, is proposed. Within thisframework, the end-to-end available bandwidth is inferred based on the measurement of the performance metrics of anactive probing stream. We study two probing streams: Poisson and periodic probing. Of particular interest to our inves-tigations is the Squared Coefficient of Variation (SCV) of the inter-probing packet arrival time at the receiver. The perfor-mance comparison of the available bandwidth measurements based on loss models and delay models indicates that thedelay-based measurement exhibits many advantages over the loss-based measurements, such as accuracy, overhead androbustness. We conducted a comparison study between the proposed SCV-based probing scheme, namely, SCVProbe,and Pathload using ns-2 simulation in terms of probing accuracy, convergence time and overhead. Our evaluation resultsindicate that SCVProbe achieves similar or even better measurement accuracy than Pathload with much less probing timeand smaller overhead.� 2005 Elsevier B.V. All rights reserved.

Keywords: Available bandwidth measurement; Active measurement; Packet train; Queueing analysis; Delay process

1. Introduction

Available bandwidth estimation has become anactive research topic in the past several years due

1389-1286/$ - see front matter � 2005 Elsevier B.V. All rights reserved

doi:10.1016/j.comnet.2005.09.029

* Corresponding author.E-mail addresses: [email protected] (X. Hei), [email protected]

(B. Bensaou), [email protected] (D.H.K. Tsang).

to a wide range of applications. End-to-end avail-able bandwidth is related to but different fromend-to-end capacity. The end-to-end capacity isthe maximum throughput that a path can providewhen there is no cross traffic, and the end-to-endavailable bandwidth is the maximum throughputthat a path can provide at a certain time periodfor a given cross traffic. The available bandwidthis largely influenced by cross traffic along the pathand the congestion control protocols used by cross

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X. Hei et al. / Computer Networks 50 (2006) 1916–1937 1917

traffic connections; therefore, it can be highlydynamic because the cross traffic has widely differ-ing characteristics.

Various end-to-end available bandwidth estima-tion techniques have been proposed in the pastfew years. They are classified into two categories:self-congestion [1–4], and model-based [5–8].Despite the good characteristics, such as accuracy,simplicity, speed, robustness, etc., claimed by pro-ponents of the self-congestion approach, the conges-tion introduced by the probing stream inevitablychanges the load along the path in such a way thatthe TCP flows along the path are sometimes inter-fered with. Therefore, non-intrusive measurementcan hardly be guaranteed. Conversely, in themodel-based approach, the bandwidth measure-ment tool is operated when the path is not con-gested. This brings forth the possibility of a trulynon-intrusive available bandwidth estimationtechnique.

In the end-to-end context, the available band-width along a path cannot be measured directlybecause the measurement entity is normally notable to access the network internals. One possiblemeasurement approach is actively sending outpackets into the network, and the performancemetrics of the probing stream are measured; there-after, the available bandwidth is inferred accord-ingly. The essence of active measurement is toidentify an ‘‘effect’’ in order to establish the rela-tionship between the target measurement metric,i.e., available bandwidth, and the measurable per-

formance metrics of the active probing stream. Witha well established relationship, available bandwidthis inferred from the performance measurement ofthis active probing stream. Both self-congestionand model-based measurement approaches fall intothis big picture. We present an end-to-end measure-ment framework to unify the current researchapproaches and highlight some insights for mea-surement practice. This framework helps to designmore efficient probing methodologies and toenhance the understanding of the networkperformance.

In the model-based available bandwidth mea-surement, the performance metrics of the activeprobing stream fall into two categories: loss-relatedmetrics [6,7] and delay-related metrics [8]. Wecompare the measurement performance of theloss-based models and the delay-based models foravailable bandwidth measurement using queueinganalysis and extensive simulations. The comparison

indicates that the delay-based measurement exhibitsmore advantages over the loss-based measurement,such as accuracy, overhead and robustness. Theimpact of various parameters in both loss-basedand delay-based models are investigated. The buffersize along the path shows a significant impact on theloss-based measurement. When the buffer size issmall, the loss measurements appear to fluctuate sig-nificantly; when the buffer size is large, the loss ishardly observable and, hence, no valid availablebandwidth estimation can be obtained. In contrast,the delay-based measurement (in particular, theSCV of the inter-probing packet arrival time atthe receiver) is sensitive to the load of the cross traf-fic. Therefore, it provides a more advantageousapproach in available bandwidth estimation. Wealso conducted a comparison study between SCVP-robe and Pathload using ns-2 simulation. Our eval-uation results indicate that SCVProbe achievessimilar or even better measurement accuracy thanPathload with much less probing time and smalleroverhead.

The rest of the paper is organized as follows.First, in Section 2 some related work is outlined.Next, in Section 3 a general end-to-end measurementframework is presented. The available bandwidthmeasurement is considered as one application of thisframework. In Section 4, we evaluate and comparethe available bandwidth measurement using theanalysis of the loss and delay processes of an activeprobing stream. In particular, the impact of the buf-fer size on the loss and delay processes of the probingstream are investigated using queueing models andextensive simulations. In Section 5, the avail-able bandwidth inference using delay models areevaluated along multi-hop paths and SCVProbe isevaluated against Pathload using ns-2. Finally, con-cluding remarks are made in Section 6.

2. Related work

Pathload [1] and Initial Increasing Gap (IGI)/Packet Transmission Rate (PTR) [2] are two avail-able bandwidth measurement methodologies in aself-congestion approach. By trying different prob-ing rates using a binary search, a reasonable esti-mate of the available bandwidth can be found inPathload. In [2] Hu and Steenkiste reported the con-struction of a delay-gap model to understand howcross traffic changes the probing packet gap for asingle-hop path. A turning point exists at whichthe average input gap equals the average output

Network Model Y=F(X, Θ)

Probing Actions Θ

Observed Metrics Y

input output

Fig. 1. A general end-to-end model-based measurement frame-work.

1918 X. Hei et al. / Computer Networks 50 (2006) 1916–1937

gap. At this turning point, IGI utilizes a fluid-flowbased formula to estimate the available bandwidthand PTR estimates the available bandwidth on thebottleneck link as the average rate of the packettrain. Essentially, Hu and Steenkiste studied thefirst-order statistics of the delay process of the prob-ing stream, and their methodology works when thepath is self-congested by the additional probingload. In [4], TOPP shared the same self-congestionnature as Pathload and IGI/PTR. The difference isthat TOPP utilized the throughput measurementto identify a throughput transition point when thepath load q is 1.

In [9], Strauss et al. improved the probe gapmodel of [2] by setting the inter-gap time betweentwo probe pairs to be exponentially distributed.Their measurement tool, Spruce, shows better accu-racy than IGI; however, Spruce essentially retainsthe self-congestion principle. In [3], Ribeiro et al.proposed to create a self-induced congestion usingan active probing stream with an exponential flightpattern, called ‘‘pathChirp’’. The available band-width estimation uses the information on whetherthe delay of pathChirp packets is increasing ordecreasing, and a turning point is also identifiedwhen the probe sending rates and receiving ratesstart to match.

In [5] Sharma and Mazumdar proposed theestimation of the traffic parameters of the Poisson-type cross traffic by measuring the delay experiencedby an active probing stream. However, their infer-ence schemes require that the network nodes arecooperative and provide the local queueing infor-mation, such as the mean queue length and the wait-ing time of a probing stream. In the end-to-endscenario, the network cooperation cannot beguaranteed.

The model-based measurement method most clo-sely related to our work is that of [6], in which Aloufet al. proposed that the network characteristics areinferred via moment-based estimators. The infer-ence (queueing) models were developed for a singlenode case based on the single bottleneck assump-tion. Two models were studied, M1+M2/M/1/Kand M1+M2/D/1/K, to simultaneously estimatethe cross traffic intensity and the buffer size of thebottleneck link given the knowledge of the bottle-neck capacity. Multiple inference schemes were pro-posed based on the moment estimators of variousperformance metrics of the probing stream. Follow-ing an approach similar to that in [6], cross trafficcharacteristics were inferred based on the loss pro-

cess analysis of an MMPP/M/1/N queueing modelin [7].

We believe that the proposed loss-based metricsused in [6,7] do not necessarily perform well in themeasurement practice. For example, consideringthe end-to-end measurement situation, packet lossmight not be easily observable during the measure-ment period. In addition, packets may be droppeddue to Active Buffer Management (AQM) insteadof buffer overflow. A more observable metric, theinter-arrival time between consecutive packets atthe receiver, has not yet been investigated in thequeueing framework to study the available band-width measurement to the best of our knowledge.More importantly the variation of such inter-arrivaltime is of particular interest. This fact motivated usto conduct research on network inference via ananalysis of the inter-arrival time of two consecutiveprobing packets at the receiver.

3. A general end-to-end measurement framework

3.1. Overview

In the end-to-end measurement context, we pres-ent a general measurement framework depicted inFig. 1. This framework consists of two sub-prob-lems, the problem of modelling an end-to-end pathand the problem of inferring the unknown parame-ters of this path model. In the modelling problem,the end-to-end path is abstractly modelled as a ser-ies of tandem queues with a superposition of twoarrival processes, the probing stream and the crosstraffic stream. This network model is determinedby a set of determinable or controllable parameters,H, of the probing actions and a set of unknownparameters, X, which include the target measure-ment metrics, i.e., the available bandwidth.

The output of the measurement process is theobserved metrics Y. With an appropriate hypothet-ical model, the relationship between Y and (X, H)can be established, namely, Y = F(X, H). Therefore,the performance of an active probing stream fromthe sender to the receiver can be predicted given


all the parameters of this hypothetical model. As aninverse process, in the inference problem, theparameters of this hypothetical model, that are ofparticular interests, including path capacity andavailable bandwidth, can be estimated by measuringthe performance of this probing stream. In a math-ematical form, X = F�1(Y, H). With a differentprobing strategy, controlling the parameter set Hof the input probing process, a different F can beidentified. Relatively accurate tools for capacitymeasurement have been proposed in [10,11]. Ourfocus in this paper is on the estimation of the crosstraffic intensity under the assumption that the pathcapacity is known, which is provided for instanceby the packet-pair technique. Given knowledge ofthe capacity information, the available bandwidthis determined by the difference between the capacityand the cross traffic intensity.

3.2. The modelling problem

The accuracy of the model-based measurementlargely depends on whether the hypothetical modelis able to capture the relationship F correctly. Theconstruction of the measurement model involvesthree components: the design of the probingsequence (determining an appropriate parameterset H), the characteristics of the cross traffic stream,and how packets are transmitted in the network.

A commonly used assumption in the active mea-surement literature is the existence of a single bottle-neck along an end-to-end path, in that, theperformance of the probing stream is dominatedby the most congested link along the path [2,6–8].Despite the simplicity, the analysis of this single bot-tleneck leads to valuable insights into understandingthe behavior of the complex network. As a simplestarting point, an end-to-end Internet path is mod-elled as a single server queue with two concurrentstreams, the probing stream and the cross traffic,as shown in Fig. 2.

probing stream delay process

loss process

... ... ......

sender receiver

λ1

λ2

μ

Internet

cross traffic

bottleneck link

Fig. 2. The available bandwidth inference model.

3.2.1. Probe sequence design

A common measurement consists of multipleprobe sequences. Probe sequence design sets thecharacteristics of both the distribution of packetssequences and the distribution of packets within asequence [12]. A probe sequence consists of a num-ber of sequential probing packets. The goal of thisprobe sequence design is to control the parameterset H for establishing a most inferrable X =F�1(Y, H). Depicted in Fig. 3, these parametersinclude the number of sequences (N), the numberof probing packets within a sequence (M), the prob-ing packet size (L), the inter-arrival time betweenprobing packets (1/k1, k1 is the packet arrival rate),the inter-arrival time between probing sequences(1/c, c is the sequence arrival rate).

Probing sequences with three types of inter-arrivaltime distributions are commonly used: a Poissonprobe sequence [13], a periodic probe sequence [14],and an exponential probe sequence [3]. Each probehas applications in the measurement practice. A Pois-son probe sequence can provide unbiased near-con-tinuous detection while a periodic probe sequence iseasier to implement without having to concern aboutthe stochastic robustness of a Poisson sequence. Nev-ertheless, mathematically it is more difficult to ana-lyze the departure process of a periodic stream in aseries of tandem queues. An exponential probesequence was recently proposed to capture the long-term dependence of the Internet traffic; yet, it lacksan accurate analysis for understanding its stochasticbehaviors [15]. In our work, we focus on the Poissonand periodic probing sequences.

3.2.2. Characteristics of the cross traffic

The Internet traffic is a superposition of manyflows, based on many protocols. Tremendousresearch effort has been made both in regard to the-ory and measurement so as to present an under-standing of Internet traffic. Traffic on the Internethas been reported, in numerous studies, to be

1212

1/γ

...M

...M

...

Sequence 1

12...

M

1/λ1L

...

Sequence 2Sequence N

Fig. 3. Probe sequences in one measurement session.


self-similar [16,17]; in large networks, however, ithas been found [18] that the overall arrival rate atnodes within the core of the network is Poisson.

Knowledge of the packet distributions on theInternet provides a guideline in understanding theservice time distribution. Several works on the mea-surement of packet size distributions of the Internethave been published [17,19,20], and all show verycommon features. It is not possible, in practice, toobtain the complete packet size distribution; how-ever, with tremendous effort in Internet measure-ment [17,19,20], it is fair to assume that the firstand second moments of the packet size distributionof the Internet traffic can be determined. Then, thefirst moment matching or two moment matchingschemes can be applied [8].

In what follows, we illustrate a simple first ordermapping scheme for the packet size distributionusing a negative exponential distribution. Basedon the Internet measurement, it is assumed thatthe Internet traffic consists of three types of packetsizes, {40, 550, 1500} bytes, with a distribution of{40%, 50%, 10%}. Because there is only one param-eter in an exponential distribution, we map the firstmoment so that the average packet size (441 bytes)in the mapped negative exponential distribution isthe same as that in the above typical Internet packetdistribution. We used the negative exponential dis-tribution assumption of packet sizes in our simula-tion study. However, our probing method is notlimited to exponentially distributed packet sizes. In[8], we proposed mapping the first and secondmoments of the packet size distribution into a gen-eralized distribution. This two-moment mappingscheme achieved a better accuracy than the firstmoment mapping scheme.

3.2.3. Knowledge about the network services

It is also a prerequisite to understand how pack-ets are transmitted in the network, such as thequeueing discipline at the routers. One commonassumption used in current measurement work isthe First-In-First-Out (FIFO) queueing schemedeployed in Internet routers. It is still largely truefor most current Internet routers; however, variousActive Queue Management (AQM) and differentpacket scheduling algorithms, i.e., Weighted FairQueueing (WFQ), have started to be deployed inrouters. In the loss-based model [6,7], the reasonfor the packet dropping is assumed to be due to buf-fer overflow only. With the application of AQM,more packet dropping is possibly observed. This

indicates the potential inaccuracy of the loss-basedavailable bandwidth estimation by overestimatingthe packet loss probability and, hence, underesti-mates the available bandwidth.

3.2.4. Model construction

The system illustrated in Fig. 2 is modelled as asingle server, a finite capacity queue operating incontinuous time, which accepts two classes of cus-tomer arrivals, the probing packet arrivals and thecross traffic packet arrivals. The probing packetarrival process is assumed to be independent andprobing packets are referred to as customers of class1. The arrival rate of the probing stream is denotedas k1 and the service rate is l1. The cross trafficpackets are referred to as customers of class 2,and the arrival rate of cross traffic is denoted k2

and the service rate is as l2. Assume that the queue-ing system is in a steady state; therefore, the trafficintensity q ¼ q1 þ q2 ¼ k1

l1þ k2

l2< 1. The load of the

cross traffic is also denoted as qCT = q2. Denotethe buffer size of K packets (K P 1) including thepacket in service.

3.3. The inference problem

3.3.1. Metric selection

The inference problem involves an appropriateselection of an observable metric set Y and the res-olution of the inverse of F. A ‘‘good’’ metric (y 2 Y)ought to be observable in the sense that it is sensi-tive to X, and, yet, the inference procedureF �1ðbY ;HÞ leads to a stable estimated bX , beingrobust to measurement noises.

The IPPM working group of the IETF definedsome end-to-end performance metrics [13], includ-ing delay (RFC2679 and RFC2681), delay variation(RFC3393), throughput (RFC3148) and loss(RFC2680 and RFC3357). These candidate metricsare delay-related or loss-related. The throughput-based measurement has turned out to be too intru-sive because it injects too much traffic into thenetwork, and it can also be considered as a loss-related metric because the transmitted traffic is thetotal input traffic minus the traffic dropped in thenetwork.

The available bandwidth measurement, based onthe analysis of the loss process of the probing stream,was discussed in [6,7]. The work in [1,2,8] relies onthe measurement of the delay performance of theprobing stream. To the best of our knowledge, themodel-based available bandwidth measurement

Probing Stream

10 Cross Traffic Sources

SND C

...

RCV

10 Cross Traffic Sinks ...

Fig. 4. A single hop path.


using delay-variation has not been investigated. Ofparticular interest in our investigations, is the SCVof the inter-departure time between two consecutiveprobing packets. In a real measurement system,given the measured SCV of the probing stream,inverting the function F helps to infer the load ofthe cross traffic on the end-to-end path betweentwo end nodes.

3.3.2. Inference procedures

With the assumption that cross traffic is a simplePoisson arrival process and only a single bottleneckexists, the active Poisson-type probing problem canbe formulated into a queueing analysis problem inregard to the performance metrics of the probingstream. These assumptions lead to a tractable math-ematical treatment; however, it is also important toexamine the robustness of the proposed model whenthese assumptions do not hold.

In the loss-based model, the loss process ofthe probing stream was analyzed using M1+M2/M/1/K and M1+M2/D/1/K in [6]. In the delay-basedmodel, the departure process (delay process) of theprobing stream can be analyzed using an M1+M2/GIi/1 queueing system [21] to capture the impactof cross traffic on a Poisson probing stream. Aheavy traffic approximation approach [22] canalso be employed to analyze the delay processof the probing stream in the above queueing system.

4. Model-based available bandwidth inference: loss

models vs. delay models

In Section 4.2, the end-to-end available band-width is inferred based on the measurement of theloss process and we highlight the ineffectiveness ofthe loss-based models. In Section 4.3, we present adelay-gap model using queueing analysis and evalu-ate the impact of the buffer size on the delay-gapmodel using simulations. in Section 4.4, the queue-ing analysis and simulation results show that theSCV-based model provides a promising light-weightprobing methodology in the end-to-end availablebandwidth inference.

4.1. Simulation configurations

The network model used in this section is shownin Fig. 4. It is a single-hop path. (In spite of the sim-plicity, the analysis and simulation can still illustratethe insights. We will present the experiment resultsin a more general multi-hop topology in later sec-

tions.) The link is modelled using a single-serverdrop-tail queue with a processing rate equal to thelink bandwidth. This queue is assumed to deploythe FIFO scheduling scheme. The maximum queuesize is equal to the buffer size of the router. This linkhas a bandwidth capacity of 2 Mbps and the buffersize is 500 Kbytes. There are 10 homogeneous crosstraffic sources, and the packet size of the cross trafficfollows a negative exponential distribution with amean value of 441 bytes. For each set of simulationpoints for the evaluation of the loss models, thereare 11 batches in one simulation run and the lengthof each batch is 105 probing packets. The first batchof probing packets are not used to collect statisticsin order to avoid the effect of the transient states.The latter 10 batches simulation results are usedto calculate the 95% confidence intervals, indicatedby the error bars in the figures. The delay informa-tion is much easier to measure compared to the lossmeasurement and, hence, the length of each batch isset to 104 probing packets for the evaluation of thedelay model while the accuracy and robustness ofthe measurement are still good. The whole simula-tion model was constructed using SimLib 2.2[23].

4.2. Loss model using M1+M2/M/1/K

In [6], the network characteristics were inferredvia moment-based estimators. The inference (queue-ing) models were developed for a single node casebased on the single bottleneck assumption. Twomodels were used, M+M/M/1/K and M+M/D/1/K, to simultaneously estimate the cross traffic inten-sity and the buffer size of the bottleneck link giventhe bottleneck capacity. Multiple inference schemeswere proposed based on the moment estimators ofthe packet loss probability (PL), server utilization


(U), the expected response time (R), the conditionalloss probability (qL) (the probability that two con-secutive losses occur), and the conditional non-lossprobability (qN) (the probability that a probingpacket arrives to find room in the buffer given thatthe previous probing packet was also admitted intothe queue). The best scheme was shown to be theinference via the estimators of the packet loss andthe expected response time using the simulationstudy. (A brief summary of the equations used inthe related inference schemes can be found inAppendix A.)

Considering the end-to-end measurement situa-tion, the packet loss is not easily measured duringthe measurement period (there is, possibly, no lossat all) and the slow convergence is within expecta-tion; the server utilization cannot be measured with-out the cooperation of the network; due to thepossible clock drifting between the sender and thereceiver, the estimation of the expected responsetime of the probing packets is, possibly, inaccuratebased on the arriving time instant to the queueingsystem at the sender side and the departure timeinstant out of the queueing system at the receiverside. Since the packet loss probability, the condi-tional loss probability, and the conditional non-lossprobability are the only three ‘‘good’’ candidatemetrics in the end-to-end measurement scenario,the schemes of PL � qL, PL � qN, qL � qN areevaluated in the later part of this section.

In M1+M2/M/1/K, the probing stream is gener-ated with the arrival rate of k1 and the cross trafficis generated with the arrival rate of k2. The averageservice rates of two streams are l1 = l2 = l. Thisindicates that the configuration of the probingstream ought to ensure that the probing packet sizeis the average packet size of the cross traffic packets.The aggregate traffic intensity is q ¼ k1þk2

l . In theremaining of this section, we discuss the impact ofthe buffer size using the M1+M2/M/1/K model aswell as simulations.

Fig. 5 shows the relationship between the lossprobability PL and the normalized probing load1

q1 for different buffer sizes. Only when the probingstream congests the path (q! 1), do loss eventsstart to be observable in practice (e.g., PL 6 0.01).

1 This normalized probing load is q1 = probe_arrival_rate *probing_packet_size/bottleneck_link_capacity.

For measurement purposes, it is important to reallydetect the loss events in order to provide informa-tion for the available bandwidth inference. Toobtain a loss measurement of PL = 0.01, at least100 probing packets have to be sent out to detect1 packet loss. For a practical statistically-reliablemeasurement of PL = 0.01, 10 times (or even higher)the required number of the packets should be sentout (i.e., at least 1000 probing packets). This impliesa heavy measurement overhead and long measure-ment intervals.

In Fig. 6, we can observe that the measurementoperating point ensures an aggregate loadapproaching to 1 when the buffer size increases inorder to have a practical measurable PL = 0.01.When K = 10 packets, the aggregate load (q) islarger than 0.71 for the measurement pointPL = 0.01. When K = 80 packets, the requiredaggregate load (q) increases very quickly to 0.99for detecting PL = 0.01. This indicates that even ifthe cross traffic load is small, i.e., qCT = 0.1, theprobing load has to be as high as q1 = 0.89 so thata loss probability PL = 0.01 is practically measur-able when K = 80 packets.

Fig. 7 shows the relationship between the condi-tional loss probability qL and the normalized prob-ing load q1 for different buffer sizes. The qL curvesappear to be insensitive to the buffer size. Since apacket drop is a rare event when q < 1, the condi-tional loss probability is even harder to obtain inthe actual measurement. This was verified by theM1+M2/M/1/K simulation results, which are pre-sented in Fig. 8. In Fig. 8(a) (K = 20), the measuredconditional loss probability has a large variationindicated by a large confidence interval whenqCT = 0.26 and the probing load q1 is small. Asshown in Fig. 8(b), the situation is even worse.Besides the large measurement variation, there arepractically no conditional loss events recorded dur-ing the simulation when the probing load is small infour different cross traffic load scenarios. Thisimplies that measuring the conditional loss proba-bility for the available bandwidth inference doesnot provide a reliable result.

From the above discussions, all of the PL � qL,PL � qN, qL � qN inference schemes have practicaldifficulties when the probing load is small. To ensurea more observable loss measurement, Salamatianet al. [7] proposed to further increase the probingload so that the aggregate load q P 1. However, thisnegates the advantage of the model-based measure-ment without congesting the network.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

102

101

100

Normalized probing load (ρ1)

Pack

et lo

ss p

roba

bilit

y (P

L)

ρCT

=0.26: M1+M

2/M/1/K

ρCT

=0.44: M1+M

2/M/1/K

ρCT

=0.62: M1+M

2/M/1/K

ρCT

=0.80: M1+M

2/M/1/K

(a) (b)0 0.2 0.4 0.6 0.8 1

102

101

100


Pack

et lo

ss p

roba

bilit

y (P

L)

ρCT

=0.26: M1+M

2/M/1/K

ρCT

=0.44: M1+M

2/M/1/K

ρCT

=0.62: M1+M

2/M/1/K

ρCT

=0.80: M1+M

2/M/1/K

Fig. 5. The relationship between the loss probability PL and the Poisson probing load q1 ¼ k1

l with different buffer sizes (K) using (5):(a) K = 20 packets, (b) K = 200 packets.

10 20 30 40 50 60 70 800.7

0.75

0.8

0.85

0.9

0.95

1

Buffer size (K)

Agg

rega

te lo

ad (

ρ)

Fig. 6. The sensitivity of the loss probability when PL = 0.01 onthe Poisson probing load q1 with Poisson-type cross traffic anddifferent buffer sizes (K) using (5).


4.3. Delay-gap model using GI1+GI2/GIi/1/1

The analysis of the delay process of the probingstream in GI1+GI2/GIi/1/K, depicted in Fig. 2, isdifficult because packet dropping may destroy thedelay pattern. Under the assumption that the buffersize is infinite, the original queue becomes GI1+GI2/GIi/1/1. In this section, we will also discuss theimpact of packet dropping on the delay pattern ofthe probing stream when the buffer size is finiteand the cross traffic is modelled as an aggregatePoisson process.

Fig. 9 depicts the time diagram of the delay pro-cess in GI1+GI2/GIi/1/1. Denote the nth probing

packet arrival as Cn of the class-1 customer arrival(the probing stream). Its service time is Xn. Let In

denote the inter-arrival time (i.a.t.) between thenth and (n + 1)th probing packets and Dn the corre-sponding inter-departure time (i.d.t.). Ny denotesthe number of arrivals from the cross traffic streamwhich occur during the inter-arrival time Cn andCn+1. Zn is the waiting time of Cn. Yj is the servicetime for the jth packet from the cross traffic streambetween the arrival of Cn and Cn+1. When probingpackets traverse the network along a path in themulti-class queue as depicted in Fig. 4, the depar-ture process of the probing stream is determinedby its arrival process and the disturbance from thecross traffic and the network service process.

The delay gap ratio is defined as the ratiobetween the average inter-departure time Dn andthe average inter-arrival time In of the probing pack-ets. This ratio essentially provides first-order delayinformation of the delay process.

With the FIFO scheduling algorithm in a queuewith an infinite size, E[Ny] = k2/k1, E[In] = 1/k1.When q < 1, for a queue with an infinite buffer,the waiting time of probing packets is finite. Thesepackets eventually leave the queue after their ser-vice. Due to the flow conservation law, the depar-ture rate of the probing stream equals its arrivalrate. Note that the inverse of the packet arrival rateis E[In] and the inverse of the packet departure rateis E[Dn]; therefore, E[Dn] = E[In]. Thus,

GapRatio ¼ E½Dn�E½In�

¼ 1.

0 0.2 0.4 0.6 0.8 1

0.1

0.2

0.3

0.4

0.5

0.6


Con

ditio

nal l

oss

prob

abili

ty (

qL)

ρCT

=0.26: M1+M

2/M/1/K

ρCT

=0.44: M1+M

2/M/1/K

ρCT

=0.62: M1+M

2/M/1/K

ρCT

=0.80: M1+M

2/M/1/K

(a) (b)0 0.2 0.4 0.6 0.8 1

0.1

0.2

0.3

0.4

0.5

0.6


Con

ditio

nal l

oss

prob

abili

ty (

qL)

ρCT

=0.26: M1+M

2/M/1/K

ρCT

=0.44: M1+M

2/M/1/K

ρCT

=0.62: M1+M

2/M/1/K

ρCT

=0.80: M1+M

2/M/1/K

Fig. 7. The relationship between the conditional loss probability qL and the Poisson probing load q1 with Poisson-type cross traffic anddifferent buffer sizes (K) using (7): (a) K = 20 packets, (b) K = 200 packets.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Con

ditio

nal l

oss

prob

abili

ty (

qL)


ρCT=0.26 SimulationρCT=0.44 SimulationρCT=0.62 SimulationρCT=0.80 Simulation

(a) (b)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Con

ditio

nal l

oss

prob

abili

ty (

qL)



Fig. 8. The relationship between the conditional loss probability qL and the Poisson probing load q1 with Poisson-type cross traffic anddifferent buffer sizes (K) in simulation: (a) K = 20 packets, (b) K = 200 packets.

Cn arrives Cn+1 arrives

Cn departs Cn+1 departs

In

Zn Xn

Fn Dn

Y1 Xn+1

Time

Y2 YNyY3 ...Queue

Fig. 9. The time diagram of the delay process in GI1+GI2/GIi/1/1.


If q P 1, the server is always busy; therefore,

Dn ¼XNy

j¼1

Y j þ X nþ1.

Ny is the number of packet arrivals from the crosstraffic stream during the inter-arrival time In. SinceqCT < 1; therefore, E[Ny] < +1. All these random

variables are assumed to be independent, andE[Yj] < +1 and E[Xn+1] < +1; thus

E½Dn� ¼ E½Ny �E½Y j� þ E½X nþ1� < þ1.

By considering the GI1+GI2/GIi/1/1 queueingsystem, the above equations can be simplified asfollows: E½X nþ1� ¼ 1

l1, E½Y j� ¼ 1

l2, E½Dn� ¼ E½N y �

E½Y j� þ E½X nþ1� ¼ k2

k1l2þ 1

l1; hence,

GapRatio ¼ E½Dn�E½In�

¼ k1

l1

þ k2

l2

¼ qprobe þ qCT.

Therefore,

GapRatio ¼1; q < 1;

qprobe þ qCT; q P 1.

(ð1Þ

Note that the above independence assumptionsare fair. Ny and Yj are the parameters of the crosstraffic. Xn+1 is the service time of probing packet


n + 1. The cross traffic stream and the probingstream are assumed to be two independent streams.Hence, Ny, Yj and Xn+1 are independent.

Intuitively, Eq. (1) deals with the first order delayinformation of the arrival process and the departureprocess of the probing sequence. The cross trafficburstiness does not impact the measurement of theaverage input gap and the average output gap foran infinitely-long probing sequence. However, inpractice, we cannot send infinitely-long probingsequences. The impact of the traffic burstiness onthe accuracy of a finite-length probing sequenceshould be investigated carefully. Nevertheless,according to our simulation study, when the prob-ing sequence consists of more than 4000 probingpackets, the measured SCV of the probing sequenceconverges to the theoretical value. With a few hun-dred probing packets, the average gap of the prob-ing sequence also converges to the theoretical value.

From (1), there exists a transition point when theaggregate load q = 1. When q < 1, the averageinter-departure time (E[Dn]) equals the averageinter-arrival time (E[In]) of the probing packets. In[2], the IGI/PTR algorithms essentially utilize thisproperty of the delay process of the probing streamto identify this transition point. Note that the identi-fication of this transition point requires that the prob-ing rate has to be large enough to congest the network(q P 1) for a period of time. The existence of this gaptransition point also explains the basic principle usedin Pathload [1]. When the delay gap is larger than 1, itequivalently indicates that the one way delay of theprobing packets is exhibiting a strong increasingtrend. When the delay gap equals 1, this one waydelay increasing trend is practically not observable.

1

1.05

1.1

1.15

1.2

1.25

1.3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Con

ditio

nal g

ap r

atio



(a) (b

Fig. 10. The relationship between the conditional gap ratio and the Pobuffer sizes (K) in simulation: (a) K = 20 packets, (b) K = 200 packets.

The delay gap in (1) is obtained under theassumption of infinite buffer size. In practice, prob-ing packets are prone to being dropped because ofbuffer overflow or active buffer management. Thispacket dropping can destroy the structure of thedelay gap pattern. In case of packet dropping, onlya delay gap of two consecutive probing packets arecollected for statistical computation, namely, a con-ditional gap ratio. To this end, each probing packetis assigned a unique sequence number when it is sentout. This sequence number increases by one when-ever a new probing packet is sent out. By checkingthe sequence number of received packets, the recei-ver extracts those consecutive probing packets fordata collection. This conditional gap ratio is plottedin Fig. 10 for two different buffer size (K) withincreasing probing load. In Fig. 10, when the buffersize is finite, the gap ratio is not increasing linearlywith the increasing probing load as predicted using(1). When the buffer size is small (K = 20 packets),the packet dropping is more severe and the locationof the transition point is shifted. When the buffersize becomes larger (K = 200 packets), this delaygap transition point is preserved to some extent.In both cases, in order to ensure the identificationof this transition point, the overall load should beq > 1, at least temporarily. This partially explainswhy Pathload and IGI tend to overestimate theavailable bandwidth [9]. Another reason might bethat this transition point exists at q = 1, the link isalready congested and packet dropping occurs;hence, those elastic TCP flows might detect packetdropping and slow down their transmission rate.As a result, the probing stream grabs more availablebandwidth.

)

1

1.05

1.1

1.15

1.2

1.25

1.3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Con

ditio

nal g

ap r

atio


ρCT=0.26: SimulationρCT=0.44: SimulationρCT=0.62: SimulationρCT=0.80: Simulation

isson probing load q1 with Poisson-type cross traffic and different


4.4. SCV-based model using GI1+GI2/GIi/1/1

4.4.1. Overview

The delay variation is defined as Jn = Dn � In.Note that there are possible negative jitters as wellas positive jitters. Negative variation correspondsto a clustering of packets. This may result in bufferoverflow; a positive variation corresponds to a dis-persion of the packets and this may result in exces-sive delay. Because In is known in advance (thecustomers of class 1 are probing packets under thecontrol), the task of characterizing Jn is reduced tofind the property of Dn. For different probingstreams, the queueing models can be constructedcorrespondingly. When the path load is less than1, the average output gap equals the average inputgap regardless of the types of arrival processes ofthe cross traffic and traffic intensity. Therefore, thisfirst order characteristics of the delay process can-not provide information about the exact load ofthe cross traffic when q < 1. Therefore, we turnedour investigation to the second order characteristicsof the delay process of the probing stream. The SCVof the inter-probing packet arrival time at the recei-ver is defined in (2). The SCV is a dimensionlessmetric used to describe the delay variation of theprobing stream. Intuitively, SCVDn is a normalizedversion of the variance of Dn with respect to In

because E[Dn] = E[In] when q < 1. It shows howthe departure process of the probing stream is dis-turbed with respect to its arrival process due tothe impact of the cross traffic. The absolute varianceof Dn cannot offer an accurate information aboutthe load of the cross traffic; only the relative vari-ance of Dn with respect to In can serve our purposeof estimating this load.

SCVDn ¼Var Dn½ �E2 Dn½ �

. ð2Þ

4.4.2. Poisson probing

For a Poisson probing stream and a Poissoncross traffic stream, the GI1+GI2/GIi/1/1 queuebecomes M1+M2/GIi/1/1. SCVDn in M1+M2/GIi/1/1 is analytically solvable using the procedurereported in [21] (see Appendix B). SCVDn is influ-enced by various factors, including the variance ofthe probing stream, the variance of the packet sizeof the cross traffic, and the load of the cross traffic.The first two are determinable parameters and thelast one is the targeted measurement metric. Therelationship between SCVDn and the normalized

probing load q1 with Poisson-type cross traffic anddifferent probing packet sizes using M1+M2/GIi/1,is shown in Fig. 11. It is different from the delaygap ratio in that, when q < 1, SCVDn

is significantlyinfluenced by the load of the cross traffic, and thiseffect can serve as the basis for the inference ofavailable bandwidth.

Fig. 11 depicts the relation between the load ofthe cross traffic and the conditional SCVDn . Wesolved the M1+M2/GIi/1 queueing model using anumerical method, because there is no closed-formsolution for M1+M2/GIi/1. The plots in Fig. 11are obtained using an iterative algorithm. Basedon these plots, we can observe that the SCV is muchmore differentiable with respect to the load of crosstraffic when the probing packet size is small (e.g., 40bytes) than when the probing packet size is large(441 bytes, 1500 bytes). Of particular interest is thatSCVDn exhibits an almost linear relationship to theprobing load when the probing packet size isL = 40 bytes. This promising result indicates thata simple relationship can be established betweenthe available bandwidth and SCVDn . When theprobing packet size (L = 441 bytes) equals theaverage packet size of the cross traffic, SCVDn isnot sensitive to the load of the cross traffic. Thisimplies that the probing packet size should be muchsmaller than the average packet size of the crosstraffic. In our probing method, we recommend touse the probing packet size of 40 bytes to ensurean invertible function so as to infer the load ofcross traffic. Sending small probing packets alsominimizes the probing load and 40 bytes is thesmallest IP packet size when TCP/UDP protocolsare used.

As presented in the previous sections, packetdropping may destroy the pattern of SCVDn . Weare also interested in the conditional SCVDn in thatonly Dn of consecutive probing packets are collectedfor the computation of SCVDn . Fig. 12 depicts thesecond-order property of the delay process of theprobing stream obtained by simulation with the dif-ferent types of arrival processes of the cross trafficand traffic intensities. The SCV increases when thenormalized probing load increases. For differenttypes of the arrival processes of the cross traffic(including Pareto, Hyper-Exponential, Poisson,Erlang), the probing stream has a similar SCV, espe-cially when the cross traffic is lightly loaded. Whenthe load of the cross traffic increases, the impactof the higher order statistics of the arrival processstarts to occur; however, the effect is still small.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.081

1.2

1.4

1.6

1.8

2

2.2

Normalized probing load (ρ1) Normalized probing load (ρ

1)

Normalized probing load (ρ1) Normalized probing load (ρ

1)

Con

ditio

nal S

CV

Dn

Con

ditio

nal S

CV

Dn

Con

ditio

nal S

CV

Dn

Con

ditio

nal S

CV

Dn

ρCT

=0.26: M1+M

2/GI

i/1

ρCT

=0.44: M1+M

2/GI

i/1

ρCT

=0.62: M1+M

2/GI

i/1

ρCT

=0.80: M1+M

2/GI

i/1

(a) (b)

(c) (d)

0 0.2 0.4 0.6 0.8 10.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

ρCT

=0.26: M1+M

2/GI

i/1

ρCT

=0.44: M1+M

2/GI

i/1

ρCT

=0.62: M1+M

2/GI

i/1

ρCT

=0.80: M1+M

2/GI

i/1

0 0.1 0.2 0.3 0.4 0.50.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1ρ

CT=0.26: M

1+M

2/GI

i/1

ρCT

=0.44: M1+M

2/GI

i/1

ρCT

=0.62: M1+M

2/GI

i/1

ρCT

=0.80: M1+M

2/GI

i/1

0 0.1 0.2 0.3 0.4 0.50.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1ρ

CT=0.26: M

1+M

2/GI

i/1

ρCT

=0.44: M1+M

2/GI

i/1

ρCT

=0.62: M1+M

2/GI

i/1

ρCT

=0.80: M1+M

2/GI

i/1

Fig. 11. The relationship between SCVDn and the Poisson probing load q1 with Poisson-type cross traffic and different probing packet sizes(L) using M1+M2/GIi/1/1 (GI1 = D and GI2 = M): (a) L = 40 bytes, (b) L = 200 bytes, (c) L = 441 bytes, (d) L = 1500 bytes.

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Con

ditio

nal S

CV

Dn

Normalized probing load ρ1 Normalized probing load ρ1

Pareto CT (α = 2.2, SCVIn = 1.51)

Pareto CT (α = 1.9)Pareto CT (α = 1.5)

HyperExp CT (SCVIn = 1.36)Poisson CT (SCVIn

= 1)

Erlang CT (SCV In = 0.58)

Pareto CT (α = 2.2, SCVIn = 1.51)

Pareto CT (α = 1.9)Pareto CT (α = 1.5)

HyperExp CT (SCVIn = 1.36)Poisson CT (SCVIn

= 1)

Erlang CT (SCV In = 0.58)

(a) (b)

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Con

ditio

nal S

CV

Dn

Fig. 12. Relationship between the conditional SCVDn and the normalized probing load with various type cross traffic arrival processes andthe probing packet size is 40 bytes: (a) qCT = 0.26, (b) qCT = 0.62.


Therefore, the analysis of the per-class departureprocess for the Poisson-type cross traffic can be usedto infer the non-Poisson type cross traffic without

much loss on accuracy. In the simulation experi-ments of a multi-hop path in Section 5, the arrivalprocess of the cross traffic is Pareto-type with a

1

1.2

1.4

1.6

1.8

2

2.2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Con

ditio

nal S

CV

Dn

Normalized probing load Normalized probing load


ρCT=0.26: M1+M2/GIi/1ρCT=0.44: M1+M2/GIi/1ρCT=0.62: M1+M2/GIi/1ρCT=0.80: M1+M2/GIi/1

(a) (b)

1

1.2

1.4

1.6

1.8

2

2.2

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Con

ditio

nal S

CV

Dn


ρCT=0.26: M1+M2/GIi/1ρCT=0.44: M1+M2/GIi/1ρCT=0.62: M1+M2/GIi/1ρCT=0.80: M1+M2/GIi/1

Fig. 13. The relationship between the conditional SCVDn and the Poisson probing load q1 with Poisson-type cross traffic and differentbuffer sizes (K) in simulation: (a) K = 20 packets, (b) K = 200 packets.


shape value of a = 1.9, the inference accuracy is stillquite good even though the model assumes Poisson-type cross traffic. What we conjecture is that theSCV of the probing stream is dominated by thelow frequency components of the cross traffic. Thismay be explained by the queueing analysis in[24,25].

Fig. 13 shows the relationship between the condi-tional SCVDn and the normalized probing load q1

for different buffer sizes (K). We can observe thatthe impact of the buffer size on SCVDn is very smallin both cases. This is due to the deployment of asmall probing packet size (L = 40 bytes), and theperturbation of the probing stream on the networkis quite small; yet, SCVDn is quite differentiable invarious load situations. In addition, the model andsimulation results match very well. This providesa firm basis for accurate available bandwidthinference.

4.4.3. Periodic probing

For a periodic probing stream and a Poissoncross traffic stream, the GI1+GI2/GIi/1/1 queuebecomes D+M/GIi/1/1. An exact calculation ofSCVDn is difficult; hence, we proposed a hybridapproximation for calculating SCVDn for periodicprobing.

As in [26] and also shown in (3), for a two-classqueueing model of GI1+GI2/GIi/1/1,

CD1 ¼ q2

1CS1 þ q2

2

p1

p2

� �ðCS

2 þ CA2 Þ

þ ð1� q1qþ q21ÞCA

1 ; ð3Þ

where CDi is the SCV of the departure process for

class i, CSi is the SCV of the service process for class

i, CAi is the SCV of the arrival process for class i, qi is

the traffic intensity for class i and pi is the probabil-ity that an arrival is from class i. Eq. (3) is anapproximation which can be solved by simple itera-tive algorithms. Nevertheless, for our measurementpractice, numerical solution still serves our purpose.

Replace the periodic probing stream with a Pois-son probing stream and maintain the other para-meters unchanged. The D+M/GIi/1/1 queuebecomes an M1+M2/GIi/1/1 queue, which can beexactly analyzed in [21]. Our idea of analyzing thedeparture process of the periodic stream in D+M/GIi/1/1 is to identify the relationship between thesetwo queueing systems using (3). We propose anapproximate formula for calculating the SCVDn fora periodic stream as in (4), namely, ‘‘hybridapproximation’’.

For a periodic stream with a constant probingpacket size, CS

1 ¼ 0 and CA1 ¼ 0:

SCVPeriodicDn

¼ q21CS

1 þ q22

p1

p2

� �ðCS

2 þ CA2 Þ


1

¼ q22

p1

p2

� �ðCS

2 þ CA2 Þ.

For a Poisson stream with a constant probingpacket size, CS

1 ¼ 0 and CA1 ¼ 1:

SCVPoissonDn

¼ q21CS

1 þ q22

p1

p2

� �ðCS

2 þ CA2 Þ


1

¼ q22

p1

p2

� �ðCS

2 þ CA2 Þ þ ð1� q1qþ q2

1Þ.

Therefore,

SCVPeriodicDn

¼ SCVPoissonDn

� ð1� q1qþ q21Þ. ð4Þ

20 40 60 80 100 120Probing rate (Kbps)

ρCT

=0.26: Simulationρ

CT=0.44: Simulation

ρCT

=0.62: Simulationρ

CT=0.80: Simulation

ρCT

=0.26: Hybridρ

CT=0.44: Hybrid

ρCT

=0.62: Hybridρ

CT=0.80: Hybrid

0 0.01 0.02 0.03 0.04 0.05 0.060

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Con

ditio

nal S

CV

Dn

(a) (b)


ρCT

=0.26: Simulationρ

CT=0.44: Simulation

ρCT

=0.62: Simulationρ

CT=0.80: Simulation

ρCT

=0.26: Hybridρ

CT=0.44: Hybrid

ρCT

=0.62: Hybridρ

CT=0.80: Hybrid

0 0.01 0.02 0.03 0.04 0.05 0.060

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Con

ditio

nal S

CV

Dn

Fig. 14. The relationship between SCVDn and the Periodic probing load q1 with two types of cross traffic and probing packet sizes L = 40bytes using the hybrid approximation: (a) Poisson cross traffic, (b) Pareto cross traffic (a = 1.9).


As shown in Fig. 14, the SCVDn of the periodicprobing stream is sensitive to the load of the crosstraffic; however, for the Poisson-type and Pareto-type cross traffic, the periodic probing stream hasa similar SCVDn . In addition, the proposed hybridapproximation predicts the SCVDn of the probingstream quite accurately. In an inverse process, giventhe measured SCVDn , the intensity of the cross trafficcan be inferred accordingly.

4.4.4. Model inference

The exact inference can be accomplished numer-ically using a standard non-linear equation solver,since F�1 is already known. In our experiments,we used ‘‘fsolve’’ available in Matlab to achievethe inversion of F�1. The inversion process ingeneral only requires dozens of iterations in our

20 40 60 80 100 120 140 160Probing rate (Kbps)

M1+M

2/GI

i/1: ρ

CT=0.26

M1+M

2/GI

i/1: ρ

CT=0.44

M1+M

2/GI

i/1: ρ

CT=0.62

M1+M

2/GI

i/1: ρ

CT=0.80

0 0.02 0.04 0.06 0.08 0.1 0.120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Est

imat

ed c

ross

traf

fic

load

(ρ C

T)

(a) (

Fig. 15. Accuracy of the Poisson probing using M1+M2/GIi/1 with Posingle-hop path depicted in Fig. 4: (a) cross traffic estimation, (b) relat

practice and this numerical inversion finishes inless than 1 s using a Pentium III PC.

In order to demonstrate the estimation accuracy,we introduce the notion of ‘‘Relative EstimationError’’, which is defined as the ratio between theabsolute estimation error and the true value of thecross traffic intensity. Fig. 15 shows the accuracyof the intensity inference of the cross traffic usingthe M1+M2/GIi/1 queue for Poisson-type crosstraffic. The estimation accuracy improves withthe normalized probing load increasing. When thenormalized probing load is larger than 0.05, therelative estimation error is less than 5%.

In Fig. 16, the accuracy of the intensity inferenceof the cross traffic using the hybrid approximationfor D+M/GIi/1 is depicted for Pareto cross traffic(a = 1.9) in the single-hop path depicted in Fig. 4.

b)

20 40 60 80 100 120

Probing rate (Kbps)

ρCT

=0.26ρ

CT=0.44

ρCT

=0.62ρ

CT=0.80

0 0.01 0.02 0.03 0.04 0.05 0.060

10

20

30

40

50

60


Rel

ativ

e es

timat

ion

erro

r (%

)

isson-type cross traffic and the probing size L = 40 bytes in theive estimation error.

20 40 60 80 100 120 140 160

Probing rate (Kbps)

Hybrid: ρCT

=0.26Hybrid: ρ

CT=0.44

Hybrid: ρCT

=0.62Hybrid: ρ

CT=0.80

0 0.02 0.04 0.06 0.08 0.1 0.120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Normalized Probing Load (ρ1)

Est

imat

ed C

ross

traf

fic

Loa

d (ρ

CT)

(a) (b)


ρCT

=0.26ρ

CT=0.44

ρCT

=0.62ρ

CT=0.80

0 0.01 0.02 0.03 0.04 0.05 0.060

10

20

30

40

50

60

Normalized Probing Load (ρ1)

Rel

ativ

e E

stim

atio

n E

rror

(%

)

Fig. 16. Accuracy of the periodic probing using the hybrid approximation for D+M/GIi/1 with Pareto-type cross traffic (a = 1.9) and theprobing size L = 40 bytes in the single-hop path depicted in Fig. 4: (a) cross traffic estimation, (b) relative estimation error.


The estimation accuracy improves with the normal-ized probing load increasing. However, furtherincreasing the probing load does not improve theinference accuracy significantly. The reasons canbe two fold. One is that the Pareto-type cross trafficalready breaks the assumption of Poisson cross traf-fic in D+M/GIi/1. The other may be due to the nat-ure of the approximate calculation for SCVDn of theperiodic probing stream. Nevertheless, when thenormalized probing load is larger than 0.02, the rel-ative estimation error is less than 10%.

4.5. Summary

The network topology used in the simulationexperiments of this section has only a single-hop.Despite the simplicity of the simulation model, theloss-based model exhibits the difficulty with lossevent detection when the probing load is smalland, hence, it is not suitable for providing a light-weight available bandwidth measurement. We con-tinue the performance evaluation of the SCV-basedinference scheme along more general multi-hoppaths in Section 5.

5. Multi-hop effects

The loss process and the delay process of theprobing stream in Fig. 2 were analyzed usingM1+M2/M/1/K, M1+M2/GIi/1/1 and D+M/GIi/1/1 presented in Sections 4.2, 4.3 and 4.4, respec-tively. These models assume a single congested linkalong an end-to-end path in the sense that this link

produces most of the losses and significant queueingdelays on this end-to-end path. Because this single-congested link assumption is still widely believed tobe true [27], we focus on the evaluation of our SCV-based inference scheme on multi-hop paths withonly one congested link in this section. However,with multiple tight links, underestimation of theavailable bandwidth may occur because SCV ofthe probing stream tends to be cumulative. Thisissue will be investigated further in our futurework.

The network path used in this section is a 3-hoppath (R1 � R2 � R3 � R4), as in Fig. 17. The prob-ing packets enter the network at router R1 and exitat router R4. The links along the path are classifiedas the tight link and non-tight links. The tight linkhas the smallest link capacity along the path andthe rest of the links along the path are referred asnon-tight links [1]. The tight link has capacity Ct

and available bandwidth At. The non-tight linkshave the same capacity Cnt and available bandwidthAnt. Cross traffic is generated at each link from 10random sources. These cross traffic connectionsonly traverse one hop on this path. The arrival pro-cess of the cross traffic follows a Pareto distributionwith a shape value of a = 1.9. The cross trafficpacket sizes follow an exponential distribution witha mean value of 441 bytes. By controlling the arrivalrate of the cross traffic, the load of the links can bevaried. The probing packet size is 40 bytes. The pathtightness factor b is defined as the ratio between theavailable bandwidth in the non-tight links Ant andthat in the tight link At (i.e., b ¼ Ant

AtP 1).

S R1

...

R4 D10 Mbps 10 ms

probesender probe

receiver

10 cross traffic sources

R2 R3

50 Mbps 10ms

50 Mbps 10ms

100 Mbps 2ms

...


......

10 crosstraffic sinks

...



...


100 Mbps 2ms

100 Mbps 2ms

100 Mbps 2ms

link 1 link 2 link 3

(non-tight link) (tight link) (non-tight link)

Fig. 17. A 3-hop path used in ns-2 simulation.


Shown in Fig. 17, link 2 is the tight link (Ct = 10Mbps) and link 1 and 3 are non-tight links (Cnt = 50Mbps). Those access links have a bandwidth capac-ity of 100 Mbps. Four cross traffic load scenarios atthe tight link (link 2) are simulated: qCT = 0.80,qCT = 0.62, qCT = 0.44, qCT = 0.26. For qCT =0.80 at link 2, the available bandwidth of the linksalong this path from R1 to R4 are {42.0, 2.0, 42.0}Mbps, respectively. The cross traffic rates at otherlinks are configured the same as the one at link 2.Therefore, only link 2 is mostly congested and link1 and 3 have a light load 1/5 of the load of link 2.The path tightness factor b = 21. The buffer sizesof link 1 and 3 are set to 500 packets and the buffersize of link 2 is set to 200 packets. The access linkshave buffers of 500 packets each. In this section,simulation experiments are conducted using ns-2[28] to include the effects of various network compo-nents on the performance of the proposedSCV-based inference scheme, including protocols,propagation delay, and so on.


ρCT

=0.26ρ

CT=0.44

ρCT

=0.62ρ

CT=0.80

0 0.01 0.02 0.03 0.04 0.05 0.061

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

Normalized probing load (ρ1)(a) (b)

100 200 300Probing r

ρCT

=0.26ρ

CT=0.44

ρCT

=0.62ρ

CT=0.80

0 0.01 0.02 0.031

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

Normalized probin

Con

ditio

nal S

CV

Dn

Con

ditio

nal S

CV

Dn

Fig. 18. The relationship between the conditional SCVDn and the Poiss3-hop path depicted in Fig. 17: (a) link 1, (b) link 2, (c) link 3.

In Fig. 18, the conditional SCVDn of a Poissonprobing stream at the outport of each link is plot-ted. At link 1, the overall load is light; therefore,the SCVDn of the probing stream is around 1.SCVDn at the outport of link 1 is almost the sameas the SCV of the arrival process of this Poissonprobing stream (SCVIn ¼ 1). This can be explainedusing the light approximation in [29]. After the con-gested link at link 2, a significant SCVDn is observedand this SCVDn traverses links 3, and is finally mea-sured at the probe receiver with little distortion.

Fig. 19 shows the accuracy of the load inferenceof the cross traffic using the M1+M2/GIi/1 modelfor the cross traffic of Pareto-type with a shapevalue of a = 1.9. The estimation accuracy improveswith an increasing probing rate for four cross trafficload scenarios. When the probing rate q1 is largerthan 400 Kbps, the relative estimation error is below10%. However, further increasing the probing ratedoes not improve the inference accuracy signifi-cantly. Note that the normalized probing load on

(c)

400 500 600ate (Kbps)

0.04 0.05 0.06g load (ρ

1)


ρCT

=0.26ρ

CT=0.44

ρCT

=0.62ρ

CT=0.80

0 0.01 0.02 0.03 0.04 0.05 0.061

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9


Con

ditio

nal S

CV

Dn

on probing rate with Pareto-type (a = 1.9) cross traffic along the

200 400 600 800 1000Probing rate (Kbps)

M1+M

2/GI

i/1: ρ

CT=0.26

M1+M

2/GI

i/1: ρ

CT=0.44

M1+M

2/GI

i/1: ρ

CT=0.62

M1+M

2/GI

i/1: ρ

CT=0.80

0 0.02 0.04 0.06 0.08 0.1 0.120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Est

imat

ed c

ross

traf

fic

load

(ρ

CT)

(a) (b)


ρCT

=0.26ρ

CT=0.44

ρCT

=0.62ρ

CT=0.80

0 0.01 0.02 0.03 0.04 0.05 0.060

10

20

30

40

50

60

70

80

90

100


Rel

ativ

e es

timat

ion

erro

r (%

)

Fig. 19. Accuracy of the Poisson probing using M1+M2/GIi/1 with Pareto-type cross traffic (a = 1.9) and the probing size L = 40 bytesalong the 3-hop path depicted in Fig. 17: (a) cross traffic estimation, (b) relative estimation error.


the congested link capacity (10 Mbps) is only 0.04.In contrast, using self-congestion based availablebandwidth measurement [1,2], the probing load dur-ing the measurement period is a few Mbps in orderto fill in the residual capacity of link 2 for the pur-pose of measurement.

The convergence speed of the inference schemeusing Poisson probing is illustrated in Fig. 20 forfour cross traffic load scenarios when the probingrate is k1 = 2025 packets/s. After approximately4000 probes, the estimation process converges andthe relative estimation error is below 10%. Note thatthe probing rate is k1 = 2025 packets/s; therefore,within a few seconds, the probing process con-verges. In addition, the packet size is 40 bytes and

101

102

103

104

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Number of probes

Est

imat

ed c

ross

traf

fic

load

(ρ C

T)

M1+M

2/GI

i/1: ρ

CT= 0.26

M1+M

2/GI

i/1: ρ

CT= 0.44

M1+M

2/GI

i/1: ρ

CT= 0.62

M1+M

2/GI

i/1: ρ

CT= 0.80

(a) (b

Fig. 20. Evolution of the estimated cross traffic load vs. the numberthe probing size L = 40 bytes and Pareto-type cross traffic (a = 1.9) alo(b) relative estimation error.

the bottleneck link capacity is 10 Mbps; hence, thenormalized probing load is quite light, approxi-mately 6.5% of the bottleneck capacity.

We implemented the proposed SCV-based prob-ing scheme, namely, SCVProbe, in ns-2. SCVProbehas two variants: Poisson and periodic. SCVProbeis evaluated against Pathload in terms of probingaccuracy, convergence time and overhead. Theprobing accuracy is evaluated by comparing theavailable bandwidth estimates against the realvalue; the convergence time is calculated consider-ing the total time for the tool to provide an estimate;the probing overhead is the total data bytes used bythe measurement tool during one measurementsession.

)10

210

310

40

10

20

30

40

50

60

70

80

90

100

Number of probes

Rel

ativ

e es

timat

ion

erro

r (%

)

ρCT

=0.26ρ

CT=0.44

ρCT

=0.62ρ

CT=0.80

of probes with a Poisson probing rate k1 = 2025 packets/s andng the 3-hop path depicted in Fig. 17: (a) cross traffic estimation,

Table 1Simulation parameters of Pathload for ns-2 experiments

Fleet length 12 streamsStream length 100 packetsBandwidth resolution x = 400 KbpsGrey region resolution v = 400 KbpsPCT threshold 0.55PDT threshold 0.4Aggregate threshold 0.7


The simulation configuration is the same as inFig. 17. The simulation duration lasts for 300 s.The cross traffic connections start randomlybetween t = 0 and t = 10. The measurement toolsstart at t = 20. When the tools terminate and returnwith an available bandwidth estimate, we restart thetool immediately. We run the periodic SCVProbewith the probing sequence of 4000 packets andprobing packet size of 40 bytes and the probing ratek1 = 1599 packets/s. We configure Pathload using

0 50 100 150 200 250 3000

1

2

3

4

5

6

7

8

9

10

Time (sec)

Ava

ilabl

e ba

ndw

idth

(M

bps)

ρCT

=0.26ρ

CT=0.44

ρCT

=0.62ρ

CT=0.80

(a) (b)

10

12

Ava

ilabl

e ba

ndw

idth

(M

bps)

Fig. 21. SCVProbe Pathload Comparison of measuremen

6

8

10

12

14

16

18

20

22

0 50 100 150 200 250 300

Con

verg

e tim

e (s

ec)

Time (sec)

ρCT=0.26ρCT=0.44ρCT=0.62ρCT=0.80

(a) (b

Fig. 22. Probing convergency time and overhead of Pathload along the

the recommended parameters in [1], as shown inTable 1.

In Fig. 21 the measurement results are shown forSCVProbe and Pathload. Pathload returns with arange of available bandwidth, and the middle pointof this range tends to be larger than the real avail-able bandwidth. The available bandwidth estimatesmeasured by SCVProbe are quite close to the realvalue and they have relative error rates smaller than20% for the four scenarios with different cross trafficloads. More importantly, these estimates by theperiodic SCVProbe tend to be smaller than the realavailable bandwidth. This conservative estimationhelps not to over-use the network available band-width for actual applications.

Our current implementation of SCVProbe uses afixed number of probing packets for one measure-ment session. Therefore, the overhead and conver-gence time are constant. For periodic SCVProbewith the probing rate k1 = 1599 packets/s and the

0

2

4

6

8

0 50 100 150 200 250 300Time (sec)

ρCT=0.26ρCT=0.44ρCT=0.62ρCT=0.80

t accuracy along the 3-hop path depicted in Fig. 17.

)

1000

1200

1400

1600

1800

2000

2200

2400

2600

0 50 100 150 200 250 300

Pro

bing

ove

rhea

d (K

byte

s)

Time (sec)

ρCT=0.26ρCT=0.44ρCT=0.62ρCT=0.80

3-hop path shown in Fig. 17: (a) convergence time, (b) overhead.


probing sequence of 4000 packets and the packetsize of 40 bytes, the convergence time is around2.5 s and the overhead of each SCVProbe measure-ment session is 160 Kbytes. Fig. 22 shows the prob-ing overhead and the convergence time of Pathload.Because Pathload is an iterative algorithm, theactual convergence time depends on the dynamicbehavior of the network. In Fig. 22(a), the conver-gence time of most measurement sessions are shownto be larger than 10 s. In particular, when the crosstraffic is heavily loaded (qCT = 0.8), Pathload takeslonger time to converge. Correspondingly, the prob-ing overhead is mostly over 1 Mbps in Fig. 22(b).

The above comparison study indicates thatSCVProbe achieves similar or even better measure-ment accuracy than Pathload with much less prob-ing time and smaller overhead.

6. Conclusion

In this paper we investigated model-based avail-able bandwidth measurement via the use of anactive probing stream. A general end-to-end mea-surement framework, capable of unifying the cur-rent research approaches and highlighting insightsin the measurement practice, is proposed. Thisframework helps to design more efficient probingmethodologies and to enhance the understandingof the network performance.

A comparison study was conducted between theperformance of the available bandwidth measure-ments based on loss models and on delay models.The queueing analysis and the extensive simulationsindicate that the delay-based measurement exhibitsmore advantages over the loss-based measurements,such as accuracy, overhead, robustness.

The queueing analysis on the delay process of theprobing stream shows that a transition point existsfor the delay gap ratio when the path load q = 1.From a queueing analysis point of view, our studyconfirms the basic self-congestion principle of thedelay gap model [1–3,9]. The extensive simulationsrevealed that the buffer size appears to be part ofthe reason that Pathload and IGI tend to overesti-mate the available bandwidth. The SCV-basedinference scheme converges within a few secondsand the relative estimation error can become lessthan 10% when the normalized probing load is lar-ger than 0.04. However, the current SCV inferencescheme assumes that there exists only a single con-gested link along the end-to-end path. Nevertheless,the basic methodology can be extended for paths

with multiple congested links by modelling thepath as a series of tandem queues. The delay pro-cess of the probing stream along these tandemqueues is difficult to analyze in an exact queue anal-ysis approach; therefore, we are investigating anapproximate analysis of the departure process ofthese tandem queues in a decomposition approach[26].

Acknowledgement

The authors would like to thank Manish Jain forsharing his ns-2 simulation codes of Pathload. Theywould also like to thank the anonymous reviewers�for their constructive comments, and the editorJennifer Hou for her efforts in handling thepaper.

Appendix A. The M1+M2/M/1/K queue

Following the derivations in [6], the intensity ofthe cross traffic and the buffer size were estimatedusing the scheme of PL � qL (using (5) and (7)), thescheme of PL � qN (using (5) and (8)), the schemeof qL � qN (using (7) and (8)) and the scheme ofPL � R (using (5) and (6)):

P L ¼ð1� qÞqK

1� qKþ1; ð5Þ

R ¼ 1

lð1� qÞ �KqK

lð1� qKÞ ; ð6Þ

qL ¼k1

k2

� �ð1� aÞ�1 � ðb=aÞKþ1ð1� bÞ�1

ðb=aÞKþ1 � 1; ð7Þ

qN ¼ 1� k1

k2

� �1� q

1� qK

� �1

bKþ1 � aKþ1

� �� a2ð1� ðqaÞKÞð1� aÞð1� qaÞ �

b2ð1� ðqbÞKÞð1� bÞð1� qbÞ

!; ð8Þ

where

a ¼k1 þ k2 þ lþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðk1 þ k2 þ lÞ2 � 4k2l

q2k2

;

b ¼k1 þ k2 þ l�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðk1 þ k2 þ lÞ2 � 4k2l

q2k2

.

Appendix B. The M1+M2/GIi/1/‘ queue

In this section, the derivation of the M1+M2/GIi/1 queue is repeated following [21]. Let Ui(s)


(i = 1, 2) be the Laplace–Stieltjes transform (LST)of the service time distribution of class i and gi(s)be the LST of the distribution of a busy cycleconsisting solely of class i customers:

giðsÞ ¼ Uiðsþ kið1� giðsÞÞÞ. ð9ÞThe inter-arrival times (i.a.t.) between successivecustomers of class 1 are assumed to be i.i.d., de-noted as r.v. I. Customers from class 2 arrive atthe queue in the form of i.i.d. in the continuoustime.

Let Wn be Cn�s waiting time (excluding service),and Fn = Wn + Xn its flow time. The LST of class1 flow time, UF nðsÞ, is the product of the waitingtime LST UW nðsÞ and UX nðsÞ ¼ U1ðsÞ. The LST ofthe composite service time is denoted as UZ(s). LetBn represent the busy cycle (possibly null) of thecross traffic packets served after Cn until eitherCn+1 enters service or the server becomes idle. Inthe busy cycle Bn, the cross traffic packet arrivalsare counted as B1

n;B2n; . . . Let Vn be the interval (pos-

sibly null) from Cn�s departure from the system untilCn+1 enters service:

Dn ¼ V n þ X nþ1.

The exact Laplace–Stieltjes transform of the inter-departure time distribution for each class in theM1+M2/GIi/1 queue on a first-come-first-servedbasis was derived and is summarized as follows:

UDnðsÞ ¼ UV nðsÞUX nþ1ðsÞ ¼ UV nðsÞU1ðsÞ;

UV nðsÞ ¼ H1ðsÞ þH2ðsÞUbðsÞ;

H1ðsÞ ¼ E e�sBn ; In 6 F n þ Bn

� �;

H2ðsÞ ¼ E e�sBn ; In > F n þ Bn

� �;

UbðsÞ ¼k1

kþsþk2

kþs AðsÞ½U2ðsÞ � g2ðsþ k1Þ�1� k2

kþs g2ðsþ k1Þ;

AðsÞ ¼ k1

k� k2U2ðsÞ;

H2ðsÞ ¼ UF nðk� k2g2ðsþ k1ÞÞ;

H1ðsÞ ¼ AðsÞ½1� UF nðk� k2g2ðsþ k1ÞÞ�;

g2ðsÞ ¼ U2ðsþ k2ð1� g2ðsÞÞÞ;

UF nðsÞ ¼ UW nðsÞUX nðsÞ ¼ UW nðsÞU1ðsÞ;

UW nðsÞ ¼ð1� qÞs

s� kð1� UZðsÞÞ;

UZðsÞ ¼k1

kU1ðsÞ þ

k2

kU2ðsÞ.

References

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[3] V.J. Ribeiro, R.H. Riedi, R.G. Baraniuk, J. Navratil, L.Cottrell, pathChirp: Efficient available bandwidth estimationfor network path, in: Proceedings of PAM2003, 2003.

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[7] K. Salamatian, B. Bruno, T. Bugnazet, Interpretation oflosses observed on the Internet by inferring traffic charac-teristics, in: Proceedings of the DIMACS Workshop onInternet and WWW Measurement, Mapping and Modeling,Rutgers University, Picscataway, NJ, USA, 2002.

[8] X. Hei, D.H.K. Tsang, B. Bensaou, Available bandwidthmeasurement using Poisson probing on the Internet, in:Proceedings of the 23rd IEEE International PerformanceComputing and Communications Conference, IPCCC 2004,Phoenix, AZ, 2004, pp. 207–214. Available from: <http://hdl.handle.net/1783.1/1933>.

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[16] W. Leland, M. Taqqu, W. Willinger, D. Wilson, On the self-similar nature of Ethernet traffic (extended version), IEEE/ACM Transactions on Networking 2 (1) (1994) 1–15.

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Xiaojun Hei received the B.Eng. degreesin Information Engineering from Huaz-hong University of Science and Tech-nology, Wuhan, P.R. China, in June1998. He also obtained his M.Phil.degree in Electrical and ElectronicEngineering from the Hong Kong Uni-versity of Science and Technology inAugust 2000. He is currently workingtowards his Ph.D. degree in the Depart-ment of Electrical and Electronic Engi-

neering at the Hong Kong University of Science and Technology.His research interests include Network Modelling and Measure-
ment, Congestion Control and Overlay Networking.
Brahim Bensaou received the B.Sc.degree in computer science from theUniversity of Science and Technology ofAlgiers, Algiers, Algeria, in 1987, theD.E.A. degree from the University ParisXI, Orsay, France, in 1988, and theDoctorate degree in computer sciencefrom the University Paris VI, Paris,France, in 1993. He spent four years as aResearch Assistant with France Tele-com�s Centre National d�Etudes des

Telcommunications, known now as France Telcom R&D,working towards the Ph.D. degree on queueing models and

rks 50 (2006) 1916–1937

performance evaluation of ATM networks. He then spent twoyears as a Research Associate with the Department of Electricaland Electronic Engineering, Hong Kong University of Scienceand Technology (HKUST), Kowloon, from 1995 to 1997,working on various problems in traffic and congestion control inhigh-speed broadband networks. In 1997, he joined the Centerfor Wireless Communications, Singapore (known now as theInstitute of Infocomm Research, I2R), where he was a SeniorMember of Technical Staff and Leader of the NetworkingResearch Group. Since fall 2000, he is on the faculty of HKUSTas an Assistant Professor of Computer Science. His researchinterest is primarily in quality-of-service in computer communi-cation networks, with current focus on wireless and mobile net-working. In particular he is focussed, medium access control,scheduling, traffic control, congestion control and QoS routing inwireless, and mobile ad hoc networks. Dr. Bensaou is a memberof the IEEE Communications Society, the Association forComputing Machinery (ACM), and the ACM SIGCOMM. Hehas been on many IEEE sponsored conference program com-mittees and has reviewed extensively for various IEEETRANSACTIONS.

Danny H.K. Tsang was born in HongKong. He received the B.Sc. degree inMathematics and Physics from the Uni-versity of Winnipeg, Winnipeg, Canada,in 1979, and the B.Eng. and M.A.Sc.degrees both in Electrical Engineeringfrom the Technical University of NovaScotia, Halifax, Canada, in 1982 and1984, respectively. He also received thePh.D. degree in Electrical Engineeringfrom the University of Pennsylvania,

Philadelphia, PA, in 1989.He joined the Department of Mathematics, Statistics & Com-

puting Science, Dalhousie University, Halifax, Canada, in 1989,where he was an Assistant Professor in the computing sciencedivision. He joined the Department of Electrical & ElectronicEngineering at the Hong Kong University of Science and Tech-nology in the summer of 1992. He is currently an AssociateProfessor in the department. His current research interestsinclude congestion controls in broadband networks, wirelessLANs, Internet QoS and applications, application-level multicastand overlay networks, and optical networks. He was the GeneralChair of the IFIP Broadband Communications�99 held in HongKong. He also received the Outstanding Paper from AcademeAward at the IEEE ATM Workshop�99. He is currently anAssociate Editor for OSA Journal of Optical Networking, an

http://www.caida.org/outreach/papers/1998/Inet98/

http://www.caida.org/outreach/papers/1998/Inet98/

http://www.caida.org/outreach/papers/2000/AIX0005/AIX0005.pdf



http://www.ind.uni-stuttgart.de/INDSimLib/

http://www.ind.uni-stuttgart.de/INDSimLib/

http://www.isi.edu/nsnam/ns/

http://www.isi.edu/nsnam/ns/


Associate Technical Editor for the IEEE CommunicationsMagazine, and a TPC member for IEEE BroadNets�05,HPSR�05, GI�05, ICC�05, VTC�06, HPSR�06 and INFOCOM�06.He has been an IEEE Senior Member since May 2000.

During his leave from HKUST in 2000–2001, Dr. Tsangassumed the role of Principal Architect at Sycamore Networks in

the United States. He was responsible for the network architec-ture design of Ethernet MAN/WAN over SONET/DWDMnetworks. He invented 64B/65B encoding and also contributed tothe 64B/65B encoding proposal for Transparent GFP in the ITUT1X1.5 standard.

model-based end-to-end available bandwidth inference using queueing analysis

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