Impact of transient CSMA/CA access delays on ActiveBandwidth Measurements

Marc Portoles-Comeras†, Albert Cabellos-Aparicio‡, Josep Mangues-Bafalluy†, Jordi Domingo-Pascual‡†Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)

Castelldefels (Barcelona), Spain{mportoles,jmangues}@cttc.cat

‡Universitat Politècnica de CatalunyaBarcelona,Spain

{acabello,jordid}@ac.upc.edu

ABSTRACTWLAN devices based on CSMA/CA access schemes havebecome a fundamental component of network deployments.In such wireless scenarios, traditional networking applica-tions, tools, and protocols, with their built-in measurementtechniques, are usually run unchanged. However, their ac-tual interaction with the dynamics of underlying wirelesssystems is not yet fully understood. A relevant example ofsuch built-in techniques is bandwidth measurement. Whenconsidering WLAN environments, various preliminary stud-ies have shown that the application of results obtained inwired setups is not straightforward. In this case, the con-tention for medium sharing among multiple users inherent toCSMA/CA access schemes has remarkable consequences onthe behavior of and results obtained by bandwidth measure-ment techniques. In this paper, we focus on evaluating theeffect of CSMA/CA-based contention on active bandwidthmeasurement techniques. As a result, it presents the rateresponse curve in steady state of a system with both FIFOand CSMA/CA-based contending cross-traffic. It also re-veals that the distribution of access delay shows a transientregime before reaching a stationary state. The duration ofsuch transient regime is characterized and bounded. Andit also shows how dispersion-based measurements that use ashort number of probing packets are biased measurements ofthe achievable throughput, the origin of this bias lying onthe transient detected in the access delay of probing packets.Overall, the results presented in this paper have several con-sequences that are expected to influence the design of band-width measurement tools as well as to better understand theresults obtained with them in CSMA/CA links.

Categories and Subject DescriptorsC.4 [Performance of Systems]: Measurement Tech-niques

General TermsWireless, Measurement, Performance

KeywordsBandwidth measurements, Wireless, Achievable Through-put

1. INTRODUCTIONWLAN devices have become a fundamental compo-

nent of network deployments. They can be found in sce-narios that range from simple single-hop home networksto complex mesh-like multi-radio multi-hop infrastruc-tures. In such wireless scenarios, traditional network-ing applications, tools, and protocols, with their built-in measurement techniques, are usually run unchangedover wireless links. However, their actual interactionwith the dynamics of underlying wireless systems is notyet fully understood.

A relevant example of such built-in techniques is band-width measurement. Its interest is exemplified by themany applications found in the literature, including con-gestion control algorithms [29, 30, 31, 34], overlay rout-ing [32], dynamic server selection [33], and inter-domainpath monitoring [25], among others. As a result, band-width measurements have become a mature researchtopic with well-developed results both at a practicallevel (e.g. [1, 19, 20, 21, 22, 25, 26]) and, lately, at amore fundamental level [15, 16]. However, most resultshave been obtained in wired environments.

When considering WLAN environments, various pre-liminary studies have shown that the application of theseresults is not straightforward ([2, 3, 28]). The main rea-sons for this reside in the assumptions taken to developbandwidth measurement models and tools. In fact, tra-ditional active bandwidth measurement techniques as-sume a single bit-carrier multiplexing several users inFIFO order (e.g. [1]). But, when applied to WLAN en-vironments, this fundamental assumption does not holdany longer. In this case, the contention, among multipleusers, for medium access inherent to CSMA/CA accessschemes has relevant consequences on the behavior ofbandwidth measurement techniques[3].

1

In this paper, we focus on evaluating the effect ofCSMA/CA-based contention on active bandwidth mea-surement techniques. As a consequence, the results andconclusions derived not only apply to wireless environ-ments, but also to any CSMA/CA-based system (e.g.PLC). Other effects appearing as a consequence of wire-less channel impairments are not dealt with in this pa-per.

Furthermore, this paper uses an analytical frameworkthat better accounts for the particularities of CSMA/CAlinks. The results of applying this framework are val-idated through extensive experimentation and simula-tion.

In short, the contributions of the paper follow:

• It presents the rate response curve in steady stateof a system with two types of cross-traffic, onesharing the queue with probing traffic and the othercontending for access with it.

• It reveals how the distribution process describingthe access delay (i.e. the time it takes to transmitprobing packets in a CSMA/CA system) is not thesame for the whole probing sequence. Instead, thedistribution shows a transient regime before reach-ing steady-state. The duration of such transientregime is characterized and bounded.

• It shows how using dispersion-based measurementsto infer steady-state bandwidth metrics may sufferof deviations, specially when the number of prob-ing packets is short. The origin of the deviationslies in the transient regime detected.

The results presented in this paper have several con-sequences that transcend its scope. First, we extendprevious studies [?], showing that tools designed to mea-sure available bandwidth in wired environments in factmeasure achievable throughput in CSMA/CA links. Sec-ond, we show how the packet pair technique [26], widelyused in the wireless mesh routing literature [24], con-stitutes a biased measure of the achievable throughput.Third, we introduce a simple yet effective method to im-prove the accuracy and convergence properties of band-width measurement tools based on a previous charac-terization of the transient regime. Interestingly, thismethod not only improves measurements in wireless sce-narios but also in wired ones.

Furthermore, we follow a packet-based (i.e. network-layer) approach in which no knowledge of lower layerdetails are assumed. This approach is taken to notlimit the applicability of our findings to restricted paths.Overall, these contributions are expected to help buildtools that better take into account the characteristicsof CSMA/CA links.

Even though they can be expected to happen, the ex-istence and impact of transient-states when probing a

system with trains of packets has not been extensivelyconsidered. An exception to this is [16] where the au-thors characterize, analytically, the transients presentin a FIFO queue with constant service rate and burstycross-traffic. Following the framework developed in [16],we extend it to consider also transients present in CSMA/CAsystems. Additionally, our findings are validated bymeans of simulation and experiments over a WLANtestbed.

The rest of the paper is organized as follows. Sec-tion 2 presents the current state-of-the-art in bandwidthmeasurement in CSMA/CA links. Section 3 introducesthe approach to CSMA/CA links used along the pa-per and provides a complete steady-state rate responsecurve describing CSMA/CA links. Section 4 studiesthe transient regime of the access delay of active prob-ing packets traversing a CSMA/CA link. Sections 5and 6 introduce the analytical framework used to studythe impact of the transitory regime and use it to de-rive its consequences on bandwidth measurements overCSMA/CA links. Section 7 discusses the consequencesof the findings of the paper while section 8 concludesthe paper. Finally, the appendix A describes the toolsthat have been used to validate the results.

2. BACKGROUNDThe rate response curve [14, 15] is one of the basic

models used in bandwidth measurement literature tocharacterize network paths. It essentially describes therelation between the input rate (ri) and output rate (ro)that a flow observes when traversing a network path.Multiple bandwidth measurement tools, specially thoserelated to measuring the available bandwidth, are basedon the rate response model of a FIFO queue. Suchmodel places fluid assumptions on the cross-traffic thattraverses the same FIFO queue as the probing flow andstates the following relation,

ro = min(ri, Cri

ri + C −A) =

{ri ri ≤ AC ri

ri+C−A ri ≥ A(1)

where C is the capacity or rate at which data is sentand A is the available bandwidth i.e. the part of C thatis not being used. Further, in [15], the authors showhow the rate-response curve of a FIFO queue is an accu-rate description of the expected interaction between theprobing traffic and the cross-traffic when the system isin steady-state. However, they show how the first pack-ets of a probing sequence are not in such steady-stateconditions which may lead to measurement errors.

Recent literature related to bandwidth measurementin wireless networks [3, 5, 28] has reported that existingtools that aim at measuring the available bandwidth arenot accurate. Many of these measuring tools have been

2

designed following the rate response model of the FIFOqueue. However, as shown in [28], the rate responsecurve for an IEEE 802.11 system differs from that of aFIFO queue. The main reason behind this is the pro-tocol used to access the medium, the DCF, that usesa CSMA/CA mechanism to regulate medium accessbetween contending stations. Under the DCF mech-anism packets from different stations are not scheduledin FIFO order, thus breaking the assumption taken in(1).

In order to formulate a rate response curve describ-ing WLAN links, researchers have identified the needto use different bandwidth metrics to describe their be-havior. In particular, the authors of [4] propose usingthe achievable throughput metric, however they providean empirical definition to be used in IEEE 802.11 basedlinks. Further, the authors of [28] propose the use ofthe concept of fair-share related to the functionality ofthe system in backlog.

Here we inherit the same term from [4] but propose,alternatively, the following definition of the achievablethroughput B,

B = sup{ri :rori

= 1} (2)

The reason behind using this definition will be madeclear later but notice, in advance, that in (1) the achiev-able throughput B corresponds to the available band-width A.

Now, with the achievable throughput metric, the au-thors of [28] propose the following rate response curveto describe the behavior of a probing flow that contendsfor channel access in an IEEE 802.11 system.

ro = min(ri, B) (3)

In this case the achievable throughput corresponds tothe fair-share portion of the capacity that the probingflow can get when contending for channel access withother wireless stations. Note that, according to (3),the available bandwidth can only be detected when itcoincides with B, and this does only happens undercertain conditions in a CSMA/CA system.

In order to illustrate all this consider the experimen-tation result depicted in figure 1. The figure plots therate response curve describing the interaction of a prob-ing flow contending for channel access with anotherflow1. The figure also shows the evolution of the cross-traffic throughput for each probing rate. As it can beseen, when the cross-traffic starts experiencing a de-crease in its throughput, that is, when the probing traf-fic arrives at the available bandwidth (∼2Mbps), therate response curve shows no sign of deviation. Instead,1In order to obtain the rate response curve we use long prob-ing trains (>10000 packets) and evaluate it in steady-state

0 2 4 6 8 100

1

2

3

4

5

6

7

Probe Traffic Input Rate (in Mbps)

Thro

ughp

ut (i

n M

bps)

Probe TrafficCross Traffic

Available Bandwidth (A)

Capacity (C)

Achievable Throughput (B)

Figure 1: Experimental steady-state rate re-sponse curve of probe traffic in a WLAN set-ting versus throughput of cross-traffic flow.C=6.5Mbps, A=2Mbps, B=3.4Mbps (tesbed)

the rate response curve flattens when the probing ratereaches the fair-share (∼3.5Mbps) that it can get fromthe wireless medium. This fair-share corresponds, infact, to the achievable throughput defined above.

The present paper completes this analysis taking twobasic observations of the system. First, we notice thatcross-traffic may not only appear in the access but canalso share transmission queue with probing traffic. Sec-ond, we show that in a CSMA/CA access the interactionbetween probing traffic and the system presents a tran-sient in the delay to access the medium. This transientis not present in (wired) FIFO systems and producesdifferent deviations than those described in [15].

2.1 Validation SetupThe study presented in this paper is based on theoret-

ical analysis, simulation and experimentation. In orderto validate our model we have reproduced the model(figure 2) in a testbed, simulator (NS2) and a Matlabqueing simulator (see figure 14). The interested readercan find all the details at appendix A. It is worth notinghere that unless noted otherwise, the results presentedin this work have been obtained from repeating exper-iments over 80 times while the simulations have beenrepeated 25.000 (NS2) to 70.000 (Matlab) times. Fur-ther, the cross-traffic generated follows a Poisson distri-bution.

3. RATE RESPONSE CURVE IN STEADYSTATE: COMPLETE PICTURE

3.1 Model of a WLAN linkA considerable part of bandwidth measurement stud-

ies over wireless networks consider only the inter-relationbetween the probing flow and the access to the wirelessmedium. However, one should also consider the pos-

3

Figure 2: Experimental/simulation scenario

sibility that the station that is being used to measureis also transmitting data at the same time. In sucha case probing packets would be sharing the transmis-sion queue with such traffic before entering contentionfor channel access. Then, the probing flow can interactwith cross-traffic in two differentiated manners when ittraverses a WLAN link. Figure 3 illustrates this.

Figure 3: Model of the interaction betweenprobing traffic and cross-traffic in a WLAN sys-tem

On one side the probing flow shares the transmissionqueue with cross-traffic that the wireless station sendsat the same time. We refer to this type of cross-trafficas FIFO cross-traffic throughout the rest of the paper.On the other side, once a probing packet is at the headof the transmission queue it has to contend for chan-nel access with the contending cross-traffic from otherwireless stations.

The interaction between probing traffic and contend-ing cross-traffic is not considered at a bit or packet persecond perspective. From the perspective of this paperwe consider that there is a ’virtual scheduler’ (S in thefigure) that regulates channel access (in the context ofthe paper it follows a CSMA/CA mechanism). As willbe further developed later, we are interested in knowingthe characteristics of the access delay of probing pack-ets. That is, the delay since they are at the head of thetransmission (FIFO) queue until they are completelytransmitted (i.e. scheduling + transmission time).

3.2 The rate response curve in steady stateThis section extends the rate response curve of a

CSMA/CA system to account for both types of inter-action between the probing flow and cross-traffic de-scribed above.

0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Probe Traffic Input Rate (in Mbps)

Thr

ough

put (

in M

bps)

Probe TrafficContending Cross−TrafficFIFO cross−traffic

Figure 4: The complete picture

Equation (3) shows that the fair-share that the prob-ing traffic can get out of the wireless medium constitutesa limiting bound to its transmission rate. The interac-tion between FIFO cross-traffic and the probing flow,reduces then, in steady-state, to a FIFO interaction asdescribed in equation (1) but with the fair-share actingas the bandwidth to share between probing and FIFOcross-traffic flows. The following expression describesthis interaction and constitutes the rate response curve,in steady-state, of the system considered.

ro =

{ri ri ≤ BBf

ri

ri+ufifoBfri ≥ B

(4)

In this expressionBf represents the achievable through-put that the probing flow would get if there is no FIFOcross-traffic and ufifo is the mean portion of time thatthe FIFO cross-traffic is using the system. Further, theachievable throughput B can be expressed here as,

B = Bf (1− ufifo) (5)

Figure 4 is an experimental illustration of expression(4). The plot shows how the rate response curve startsdeviation when the aggregate FIFO cross-traffic andprobing traffic achieve the fair-share that the wirelessstation can get out of the wireless medium. After that,as the probing traffic increases its throughput it gainspresence in the FIFO queue in detriment of the FIFOcross-traffic.

4. TRANSIENT-STATE BEHAVIOR OF THEACCESS DELAY

This section analyzes the characteristics of the accessdelay process describing the time that packets wait atthe head of the FIFO transmission queue until they gainchannel access and are completely transmitted. For thisstudy we remove any fifo cross-traffic from the proposedmodel and focus, strictly on the interaction between

4

probing traffic and the contending. Figure 5 illustratesthe scenario considered here.

Figure 5: Model of the interaction betweenprobing traffic and (contending) cross-traffic ina WLAN system

The access delay in CSMA/CA based systems hasbeen repeatedly studied in the literature. Indeed, dif-ferent researchers have analyzed its exact distributionusing using Markov Chains [6, 9]; others show how theexponential distribution provides a good fit [7]. Allthese studies focus on modeling the steady-state dis-tribution of the access delay. However, in general, ac-tive bandwidth measurements are gathered using prob-ing trains of a limited number of packets in order tolimit intrusiveness. As a consequence, for the purposeof this work, we are interested in analyzing how the ac-cess delay evolves over time as an increasing number ofpackets are sent. In other words, we are interested inthe transient-state behavior of the access delay in thesystem we are considering.

In order to illustrate this evolution first consider thefollowing experiment: using NS2 we send 1000 probepackets at a given rate (5Mbps) and with a given loadof contending cross-traffic (4Mbps). We have repeatedthe experiment 25000 times and, for each probe packet(indexed from 1 to 1000), we compute the distributionof the access delay individually (considering all the rep-etitions).

Figure 6 plots the average access delay that each oneof the first 150 packets observes. The figure shows howthe average access delay perceived by the first packets

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 1502.8

3

3.2

3.4

3.6

3.8

4x 10

−3

Probe Packet Number

Ser

vice

Del

ay (

s)

Mean Service Delay

Figure 6: Mean access delay vs. Probe packetnum (simulator)

0 0.002 0.004 0.006 0.008 0.01 0.0120

500

1000

1500

2000

0 0.002 0.004 0.006 0.008 0.01 0.0120

500

1000

1500

2000

2500

3000

Service Delay (ms)

Histogram (Service Delay seen by the first packet)

Histogram (Service delay seen by the 500th packet)

Figure 7: Histogram of the s.d seen by the firstand 500th packet (simulator)

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

Probe Packet Number

KS V

alue

Probe Traffic (8Mbps) Contending Traffic (2Mbps)

KS TestThreshold 95% CI

0 10 20 30 40 50 60 70 80 90 1000.2

0.4

0.6

0.8

1

1.2

Probe Packet Number

Pack

ets

Mean Queue Size (Contending Node)

Figure 8: Analysis of the distribution (8Mbpsprobe-traffic rate, 2Mbps cross-traffic rate (Top)KS-Test (Bottom) Mean queue size (simulator)

is lower than for the rest of them. This suggests that,in fact, the distribution of the access delay changes asmore probe traffic keeps on arriving to the WLAN link.In order to verify this hypothesis, figure 7 plots the his-togram of the access delay as seen by the first probepacket and by the 500th. As the plot shows, the distri-bution changes significantly. The main reason behindthis is that as new probing packets keep on arriving theykeep on increasing the load of the network until reach-ing a steady-state of interaction with the (contending)cross-traffic.

To further illustrate this we use the well-known Kolmogorov-Smirnov2 (KS) goodness-of-fit test [17]. This statisticaltest is used to compare the resemblance of the delaydistribution suffered by every probing packet startingfrom the first one, and the delay distribution once prob-

2Since we are using the KS test to compare two empiricaldiscrete distributions we convert one of them to a continuousone using linear interpolation.

5

0 5 10 15 20 25 30 35 40 45 500

0.1

0.2

0.3

0.4

0.5

Probe Packet Number

KS V

alue

Probe Traffic (0.5Mbps) and Multiple Contending Stations

KS TestThreshold 95% CI

Figure 9: Analysis of the distribution (complexcase) (simulator)

ing packets have reached a steady-state. The KS testis non-parametric and analyzes whether two differentsets come from the same random distribution. Usingthis test we compare the distribution of each individualpacket in the probing sequence with the access delaydistribution of the last 500 probing packets.

Figure 8 -top- shows the evolution of the KS-test ofthe distribution each one of the first 100 probing pack-ets when compared to steady-state distribution. Thefigure reveals clearly how there is a transient-state inthe access delay that the probing packets suffer whencontending for channel access. The KS-test evolutionis put in contrast to the evolution of the mean queuesize of a cross-traffic station that contends for channelaccess (see figure 8 -bottom-). The comparison how thetransient-state takes as long as it takes for the contend-ing queue to reach a stationary size ( 10 packets).

We have also experimented with more complex sce-narios. As an example consider figure 9 that showsthe KS-test for a case with 4 contending stations us-ing different packet sizes (40, 576, 1000 and 1500 bytes)and the following rates respectively (0.1, 0.5, 0.75 and2Mbps). Again, the figure reveals a transitory regimein the distribution of the access delay, also load of thesystem before and after the probing flow enters the sys-tem. As the figure shows, we need to send tens ofpackets until reaching a steady-state. We have simu-lated more cases with different degrees of complexityobtaining similar results. The transient-state is presentwhenever the system is not empty, nor in backlog and ismaximum when either probing traffic and/or contend-ing traffic are exactly sending at their fair-share of thewireless medium.

4.1 Duration of the transient-state of accessdelay

In order to design efficient measurement strategiesover CSMA/CA systems we need to provide some boundson the duration of the transient-state of the access delay.The main hypothesis taken here is that the duration ofthe transient-state has a close relation with the offeredtraffic load that both probing and contending stationsare trying to inject into the network.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

50

100

150

200

250

300

350

400

Offered Cross−traffic Load (in Erlangs)

Est

imat

ed tr

ansi

tory

leng

th (

in p

acke

ts)

Tolerance 0.01Tolerance 0.1

Figure 10: Estimated duration of the transitorywith 0.1 and 0.01 tolerance. offered probingload=1Erlang.

Figure 10 plots a simulation based estimation of theduration of the transitory. To generate the figure wehave fixed an offered probing load of 1 Erlang. Thetransitory is estimated for a range of values of offeredcross-traffic load. In order to estimate the duration ofthe transitory we have conducted extensive repetitionsof the simulation in order to assure proper convergenceof access delay distributions. The figure identifies thefirst packet, for each cross-traffic load, whose averageaccess delay is within 0.1 or 0.01 of the steady-stateaverage value.

The offered cross-traffic load at which the length ofthe transient-state is maximum corresponds in fact toits fair-share. This not only applies to the cross-trafficload but also to the probing load. When the offeredload of the probing flow corresponds to its fair-sharethe duration of the transient-state is also maximum.

In order to provide practical values of the transitorywe have conducted an extensive simulation for a rangeof probing and cross-traffic loads with multiple contend-ing stations. In order to determine the length of thetransitory we find the first packet whose average ac-cess delay lays within 0.1 of the expected access delayin steady-state conditions. We have found that, underthis conditions, the transient-state never exceeds 150packets.

4.2 Consequences of the observationsThis section has shown and characterized the transient-

state behavior of the access delay of probing packetswhen traversing a CSMA/CA link. The results in thissection imply that the first packets of a probing se-quence do not capture the long-term behavior of largerflows but represent deviated samples of the steady-stateinteraction between the probing flow and cross-traffic.This observation has a direct impact on bandwidth mea-surement tools that generally use short trains of packetsto support measurements.

6

5. MODELING PACKET DISPERSION WITHTRANSIENT ACCESS DELAY

5.1 Analytical frameworkHere we introduce the basic analytical framework used

to deal with this problem. This framework was origi-nally proposed in [15] but is extended here to includethe particularities of WLAN transmissions. We havechosen to use this framework as it has been designed tocapture the effects of possible transient-state on disper-sion measurements. Furthermore, the analytical frame-work has been adapted to the particularities of WLANtransmissions and extended to capture the transitoryevolution of the access delay.

5.1.1 The probing sequence: Arrivals, departures andinput gap

The probing sequence consists of a series of n pack-ets that enter the transmission queue at instants {ai, i =1, 2, · · · , n}. Their departure instants, meaning the timeat which they are completely transmitted, form the se-ries {di, i = 1, 2, · · · , n}. Finally, we are consideringhere periodic probing flows with a fixed inter-packet ar-rival time or input gap: gI = ai − ai−1.

5.1.2 The access delay processThe access delay that probing packets experience is a

random process. This process is the result of the inter-action between probing traffic, contending cross-trafficand backoff. To account for this let us define the se-quence {µi, i = 1, 2, · · · , n} to denote the random accessdelay that each one of the n probing packets of a prob-ing sequence experiences when contending for mediumaccess.

5.1.3 Processes associated to cross-traffic in the FIFOpart of model

The cross-traffic that shares the transmission queuewith probing traffic comes associated to the hop-workloadprocess {W (t), 0 ≤ t < ∞}, that is the sum of theservice times of all cross-traffic packets in the FIFOqueue and the remaining service time of any cross-trafficpacket that may be in service. Note that cross-trafficpackets experience also a random access delay implicitin the hop-workload process. Note also that this pro-cess refers to the cross-traffic only, without consideringthe probing flow.

Taking into account the hop-workload process, the uti-lization of the FIFO queue can be defined such that,

ufifo(t) =

{1 W (t) > 00 W (t) = 0

(6)

The evolution of ufifo(t) indicates how the FIFOqueue is being utilized along time. In other words, it

expresses the intensity of the cross-traffic process in theFIFO queue. With some abuse of notation we use theterm ufifo(t, t+ τ) to refer to the average utilization ofthe queue during the period [t, t+ τ ]. That is,

ufifo(t, t+ τ) =1τ

∫ t+τ

t

ufifo(u)du (7)

This paper assumes that the system is stable dur-ing the measurement process. We use the term ufifoto denote the expected utilization that the cross-trafficmakes of the FIFO queue. This value is ,

ufifo = E[ufifo(t)] (8)

Finally, we define the offered workload of cross-traffic{X(t), 0 ≤ t <∞} as the cumulative sum of the servicetime of cross-traffic packets that enters the FIFO queue.We define also the averaging function {Y (t, t + τ), 0 ≤t <∞} as,

Y (t, t+ τ) =X(t+ τ)−X(t)

τ(9)

Note that under the assumption of stability for thesystem,

E[Y (t, t+ τ)] = E[ufifo(t)] = ufifo (10)

5.1.4 Adding probe traffic in the queue: Intrusionresidual

First, we define the utilization of the fifo queue ufifo(t, t+τ) coming from the superposition of fifo cross-traffic andprobing traffic.

Second, we define as W (t), 0 ≤ t <∞ the hop-workloadprocess resulting from the superposition of the servicetime of the FIFO cross-traffic and that of the prob-ing traffic. The intrusion residual Wd(t) accounts forthe sum of the service time of all probing packets inthe FIFO queue and the remaining time to service anyprobing packet that may be in transmission. The intru-sion residual is, then, the difference between W (t) andW (t) at any time,

Wd(t) = W (t)−W (t) (11)

Next, we define the series {Ri, i = 1, 2, · · · , n} whichcaptures the intrusion residual that every probing packetfinds when it enters the transmission queue3,

Ri(a1) = Wd(a−i ) = Wd(a1 + (i− 1)g−I ) (12)

Note that Ri is a recursive process that under theassumptions in this work can be expressed as,3The minus superscript refers to the state of the queue justbefore the arrival, i.e. without counting the new arrival.

7

Figure 11: Inter-relation between probing ar-rival sequence (ai), departure sequence (di) andcross-traffic related processes (Zi).

Ri =

{0 i = 1

max(0, µi−1 +Ri−1 − (1− uFIFO(ai−1, ai))gI) i > 1

(13)

Finally, we define the series {Zi, i = 1, 2, · · · , n} thatencloses the queuing plus access delay that each one ofthe probing packets experiences. Under the assump-tions taken,

Zi = di − ai = µi +Ri +W (ai) (14)

5.2 Dispersion based measurements:The out-put gap and its relation to the probing rate

Dispersion based measurements of bandwidth metricsconsist on measuring the dispersion (or inter-departuretime) of packets at the output of a path (receiving side).This measure is then used to infer the value of band-width related metrics. The output gap (or dispersion)of a train of probing packets is defined as follows,

gO =dn − d1

n− 1(15)

Figure 11 illustrates the contribution of the processesdefined above to the value of the output gap. From thearrival of the first probing packet at the transmissionqueue (a1), probing packets keep on arriving at a con-stant interval of gI . The cross-traffic, access delay andthe intrusion residual of previous probing packets (Zi)randomize the departure times of probing packets (di)and thus, their output dispersion (gO).

Observing figure 11 we can obtain the output gap inrelation to the different processes involved.

gO =dn − d1

n− 1=

(n− 1)gI + Zn − Z1

n− 1(16)

Expanding this expression we get the following,

gO = gI +Rnn− 1

+W (an)−W (a1)

n− 1+µn − µ1

n− 1(17)

The output dispersion can also be formulated takinginto consideration the offered workload of probing trafficas,

gO =1

n− 1

n∑i=2

(µi+Y (ai−1, ai))+(1− ufifo(d1, dn))gI

(18)The intuition behind this last expression is as follows.

We take the departure of first packet as a reference (seed1 in figure 11). The time elapsed until dn comes fromthe addition of the (1) access delay of all probing pack-ets (from second to last), (2) the workload of FIFOtraffic that arrives in between probing arrivals and (3)the remaining ”idle” time that is not being used fortransmissions by either process.

5.3 Problem formulationWe are interested in studying whether dispersion mea-

surements can be used to estimate the steady-state rateresponse curve of a wireless link with CSMA/CA ac-cess. Measurement tools based on dispersion take theassumption that the relation between the input (gI) andoutput (gO) dispersions of a probing train can be usedas estimators of the inter-relation between input (ri)and output (ro) rates of a flow traversing the system.In other words if L is the length of the packets used forprobing, dispersion based measurements assume thatL/gI is a good approximation of ri and L/gO is a con-sistent estimator of ro.

Reformulating equation (4) from a dispersion per-spective, the problem of bandwidth measurement fol-lows,

E[gO] ?=

{gI gI ≥ L

BLBf

+ ufifogI gI ≤ LB

(19)

As (19) states we are interested in analyzing the ex-pected value of the output dispersion (E[gO]).

First, taking expectation over equations (17) we ob-tain,

E[gO] = gI +E[Rn]n− 1

+ κ(n) (20)

with κ(n) = E[W (an)−W (a1)]n−1 + E[µn]−E[µ1]

n−1 .

Further, taking expectation over (18) we get a secondexpression for the output dispersion,

E[gO] =1

n− 1

n∑i=2

(E[µi]+ufifogI)+E[(1−ufifo(d1, dn))gI ]

(21)Expressions (20) and (21) will be used to derive upper

and lower bounds to the expected output dispersion.

6. RATE RESPONSE CURVES IN PRESENCEOF TRANSIENT ACCESS DELAYS

8

This section presents an analysis of the expected valueof the output dispersion when probing a system withCSMA/CA access. The study provides bounds ratherthan closed form expressions.

The basic finding here is that, when using limitednumber of probing packets, the transitory stage in theaccess delay that they suffer induces deviations fromthe steady-state response curve. Further, this devia-tions are, in some sense, opposite to the ones caused bythe FIFO cross-traffic itself (as detected previously in[16]). The reason behind this is that first packets are’accelerated’ in contrast to packets sent in steady-state.This leads, in some cases, to infer optimistic values ofbandwidth metrics.

6.1 Part I: Analysis of the expected output dis-persion

6.1.1 Intrusion residualOn one side, from expression (20), we learn that the

expected output gap depends on the expected value forthe residual that the last packet of the probing train(i.e. with index n) finds in the queue. Recalling therecursive expression (13) there can be defined the fol-lowing bounds for the intrusion residual.

max(0,n−1∑i=1

(µi − gI)) ≤ Rn ≤n−1∑i=1

µi (22)

The lower bound comes from the assumption thatthe probing sequence did not find any cross-traffic inthe FIFO queue. The upper bound considers that theprobing sequence found the FIFO queue with sufficientworkload so that all probing packets find each other inthe queue before transmission.

Taking expectation over Rn, we can differentiate twocases,

E[Rn]n− 1

=

{βn

n−1 gI ≤ 1n−1

∑n−1i=1 (E[µi])

αn

n−1 gI ≥ 1n−1

∑n−1i=1 (E[µi])

(23)

The specific values of αn and βn depend on the spe-cific characteristics of the random cross-traffic (contend-ing and FIFO) and are bounded as follows,

{1

n−1

∑n−1i=1 (E[µi]− gI) ≤ βn

n−1 ≤1

n−1

∑n−1i=1 (E[µi])

0 ≤ αn

n−1 ≤1

n−1

∑n−1i=1 (E[µi])

(24)On the other side, from expression (21), we can see

the dependence of the output dispersion on the timethat the wireless medium is being used considering thesuperposition of probe traffic and FIFO cross-traffic.We can bound this value as follows,

min(1,1gI

1n− 1

n∑i=2

(E[µi]) ≤ ufifo(d1, dn) ≤ 1 (25)

Note that when gI ≤ 1n−1

∑ni=2(E[µi]) the FIFO

queue is being used during the whole measurement pro-cess (i.e. ufifo(d1, dn) = 1), regardless of the amountof FIFO cross-traffic in the queue.

6.1.2 Bounds for the expected output dispersionNow we reconsider expressions (20) and (21) taking

into account the bounds (24) and (25) derived for theresidual processes.

When gI ≤ 1n−1

∑ni=2E[µi], equations (21) and (25)

provide a closed form expression for the output disper-sion,

E[gO] =1

n− 1

n∑i=2

(E[µi] + ufifogI)) (26)

When gI ≥ 1n−1

∑ni=2E[µi] the expected output dis-

persion can bounded as follows,

{max(gI + κ(n), 1

n−1

∑ni=2(E[µi] + ufifogI)) ≤ E[gO]

min(gI + 1n−1

∑n−1i=1 E[µi] + κ(n), (ufifo + 1)gI) ≥ E[gO]

(27)

Rearranging the lower bound in expression (27) wecan differentiate two regions.

E[gO] ≥

gI + κ(n) gI ≥

1n−1

∑ni=2(E[µi])−κ(n)

1−ufifo

1n−1

∑ni=2(E[µi]) + ufifogI) gI ≤

1n−1

∑ni=2(E[µi])−κ(n)

1−ufifo

(28)

We can do the same for the upper bound, that presentsthree differentiated regions

E[gO] ≤

gI + 1n−1

∑n−1i=1 E[µi] + κ(n) gI ≥

1n−1

∑n−1i=1 (E[µi])+κ(n)

ufifo

(ufifo + 1)gI1

n−1

∑ni=2 E[µi] ≤ gI

≤1

n−1∑n−1

i=1 E[µi]+κ(n)

ufifo

1n−1

∑ni=2(E[µi] + ufifogI)) gI ≤ 1

n−1

∑ni=2(E[µi]

(29)

Expressions (28) and (29) constitute upper and lowerbounds of the rate response curve of the system intransient-state. Next section provides insights into theinter-relation between them and the rate response curvesin steady-state. This will help understand rate responsecurves obtained using probing trains with a limited num-ber of packets.

6.2 Part II: Results without FIFO cross-trafficThis section assumes that no cross-traffic is present

in the FIFO queue and analyzes the rate response curvein transient-state. The objective is to provide insightsinto the results obtained, for example, in [3, 5, 28].

9

Figure 12: The system without FIFO cross-traffic

6.2.1 The expected achievable throughputIn this case, probing packets cannot be sent, in aver-

age, faster than 1n

∑ni=1(E[µi]). As a result the achiev-

able throughput in this particular case can be definedas,

L

B=

1n

n∑i=1

(E[µi]) (30)

Note that this expression encloses the transient-statebehavior of the access delay. Note also that as the num-ber of probing packets grows the access delay eventuallyreaches a steady-state and the expected access delay be-comes constant,

L

B

n→ E[µn] (31)

6.2.2 Bounds on expected output dispersion and dis-cussion

We rewrite here (28) and (29) for this study case.Notice that in this particular case κ(n) = E[µn]−E[µ1]

n−1

E[gO] ≥{gI +

E[µn]−E[µ1]n−1

gI ≥ 1n−1

∑n−1i=1 E[µi]

1n−1

∑ni=2 E[µi] gI ≤ 1

n−1

∑n−1i=1 E[µi]

(32)

E[gO] ≤{gI gI ≥ 1

n−1

∑ni=2 E[µi]

1n−1

∑ni=2 E[µi] gI ≤ 1

n−1

∑ni=2 E[µi]

(33)

There are a number of observations that can be donehere. First considering that, as shown in section 4, theaccess delay µi is an increasing function with respect tothe packet index i, the following is true for any value ofn > 2,

1n− 1

n−1∑i=1

(E[µi]) ≤1

n− 1

n∑i=2

(E[µi]) ≤ E[µn] (34)

As a result, we can see that in both expressions (32)and (33) the input rate acting as a ’knee’ separatingdifferent regions of the curve is higher than the (steady-state) achievable throughput.

However, taking into account the lower bound (32)we can observe the following. When probing at ratessuch that gI ≥ 1

n−1

∑n−1i=1 E[µi], the expected output

0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Input Rate (in Mbps)

L/E

[Go]

(in

Mbp

s)

Steady State ResponseTrain of 3 PacketsTrain of 10 PacketsTrain of 50 Packets

Figure 13: Experimental rate response curve ofa system without FIFO cross-traffic (testbed)

dispersion may deviate as much as E[µn]−E[µ1]n−1 . In other

words, when the access delay variation during the transient-state is sufficiently high (in contrast to the probingrate), the output gap (E[gO])deviates (is higher) thanthe steady-state curve.

Finally, notice that when the probing rate is highenough (i.e. when gI ≤ 1

n−1

∑n−1i=1 E[µi]) the output

dispersion is higher than the one in steady-state. Inother words, if we probe the system at a high ratewe might infer optimistic values of the steady-state re-sponse curve.

6.2.3 Experimental resultsFigure 13 plots an experimental result illustrating

these observations. The rate response curves plottedcorrespond to those of packet trains probing a CSMA/CAlink at different rates. The figure clearly illustrate theobservations taken in above.

First, the rate response curve follows the steady-statecurve until a certain point (∼2.5Mbps) when the in-ferred rate response is lower than the steady-state one.

Second, when probing at high rates the transient-state curves tend to overestimate the achievable through-put that can be achieved in steady-state.

6.3 Part III: Reintroducing FIFO cross-traffic.The complete model

Figure 14: Model of the interaction betweenprobing traffic and cross-traffic in a WLAN sys-tem

6.3.1 The expected achievable throughput

10

We can define again a relation between the achievablethroughput and the access delay that probing packetsreceive.

L

B=

1n

∑ni=1(E[µi])

1− uFIFO(35)

Note again that as the number of probing packetsgrows the expected access delay becomes constant andwe can say that,

L

B

n→ E[µn]1− uFIFO

(36)

6.3.2 Bounds on expected output dispersion and dis-cussion

In this specific case, expressions (28) and (29) can-not be reduced. Putting in contrast these expressionswith the ones taken in the previous simplified case (i.e.without FIFO cross-traffic), there are a number of ob-servations to make.

First, the burstiness of the FIFO cross-traffic leads tolooser bounds than before. As a consequence depend-ing on the characteristics of the cross-traffic flow it isreasonable to expect higher deviations from the steady-state curve. This is specially true when probing at lowerrates than the steady-state achievable throughput. Asthe burstiness of cross-traffic flow increases so will dothe variability of dispersion measures, thus leading tohigher deviations from the steady-state behavior.

Second, it can be seen that when probing the systemat high rates dispersion measurements based on shortpacket trains tend to overestimate the steady-state rateresponse curve. Even more, the last region in expression(29) assures that, no matter how bursty the FIFO cross-traffic is, when probing at a sufficient rate the outputdispersion will overestimate the steady-state behavior.

6.3.3 Experimental resultsFigure 15 illustrates these observations. As predicted,

the rate response curve inferred using packet dispersionmeasurements follows the steady-state behavior untilit deviates (∼2Mbps) before reaching the achievablethroughput. When probing at higher rates the figureshows that dispersion measurements continue overesti-mating the steady-state response regardless of the pres-ence of FIFO cross-traffic.

7. DISCUSSION ON CONSEQUENCES ANDAPPLICATIONS OF FINDINGS

This section discusses the main findings of this studyand some consequences and possible applications thatthey entail.

7.1 Summary of findings

0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

3.5

4

Input Rate (in Mbps)

L/E

[Gio

] (in

Mbp

s)

Steady−State ResponseTrain of 3 PacketsTrain of 10 PacketsTrain of 50 Packets

Figure 15: Experimental rate response curve forthe complete system (testbed)

• In section 3 the paper provides a complete steady-state rate response curve of a system with CSMA/CAmedium access. It takes into consideration thatthe probing and cross-traffic flows can interact intwo differentiated manners: (1) sharing a FIFOqueue and (2) contending for channel access in arandom manner following the CSMA/CA proce-dure.

• In section 4 the study provides some insights intothe transient-state behavior of CSMA/CA systems.The study shows how the duration (in number ofpackets) of the transient-state relates to the of-fered load coming from both probing and cross-traffic. We show how including some tolerancein the measurement process allows reducing thetransient-state duration to values that can be usedin practice when designing measurement tools.

• Finally, section 6 analyzes the impact that thetransient-state evolution the access delay has onthe accuracy of dispersion based measurements. Itshows how dispersion measurements based on us-ing short packet trains deviate from steady-statebehavior which may lead to erroneous inferenceson bandwidth metrics.

7.2 A consequence: bandwidth estimation inWLAN links

The rate response curve for FIFO queues or some ofthe ideas that it encloses has been repeatedly used in theliterature to design bandwidth measurement tools. Asdefined here, the achievable throughput corresponds tothe available bandwidth when applied to FIFO queues.However, as we have seen, when applied to CSMA/CAsystems, the achievable throughput and available band-width only coincide under certain conditions.

From the results in this paper it can be argued thata large portion of the tools used to infer the availablebandwidth under FIFO assumptions, follow, instead, the

11

0 2 4 6 8 103

3.5

4

4.5

5

5.5

6

6.5

Cross−Traffic Rate (in Mbps)

Ach

ieva

ble

Thr

ough

put (

in M

bps)

Fluid Response (Actual)Packet Pair Based Inference

Figure 16: Experimental comparison betweenpacket pair based bandwidth measurements andthe actual fluid response in a WLAN link(testbed)

achievable throughput when applied to CSMA/CA sys-tems. This idea is illustrated in figure 4 in [28]. Therethe authors plot the bandwidth estimates gathered us-ing popular tools in an IEEE 802.11 system. The figuresshow how all the tools used tend to follow the achievablethroughput rather than the available bandwidth whenthese two metrics start differing in IEEE 802.11 set-tings.

7.3 Another consequence: packet pair mea-surements in WLAN links

A common approach to measure the capacity of a net-work path is the packet-pair technique[26]. Recently,packet pairs have gained momentum as they have beenextensively used to develop routing metrics in all-wirelessmulti-hop networks [24].

However, as a consequence of the results presented insection 6, packet pairs (understood as probes of infiniterate) target the achievable throughput when used in aWLAN link. Even more, considering the results pre-sented in section 6, one can see that packet pairs tendto overestimate the value of the achievable throughput.Figure 16 illustrates this fact. It plots the actual achiev-able throughput of a WLAN link and the estimation us-ing dispersion measurements of packet-pairs. This isdone for different levels of cross-traffic. The capacity ofthe WLAN link is kept constant for all the measurementprocess at 6.5Mbps (i.e. there are no channel propaga-tion errors). As one can see the packet-pair does notpoint at the capacity in the whole measurement regionexcept when no contending traffic is present.

7.4 An application of results: bandwidth mea-surement as a simulation warm-up prob-lem

The transient-state of the access delay described inthis paper can be understood as a simulation warm-

1 2 3 4 5 6 7 8 9 10

2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

Input Rate (in Mbps)

L/E

[Go]

(in

Mbp

s)

Steady State Response

Train of 20 Packets

Train of 20 Packets (MSER−2)

Figure 17: MSER-2 based measurement

up problem. This is a classical problem in the theory ofsimulation that has been extensively studied (e.g. [36]).

The literature proposes several techniques to get ridof the effects that samples taken during the transient-state period may induce to the measurement results.A common technique is to enlarge the simulation timein order to assure that transient-state observations areaveraged out. This would be equivalent, in our case,to sending longer packet sequences, with the increase ofintrusiveness that this entails.

Another technique is trying to infer the duration ofthe transitory and then truncating the sample sequence.The MSER-m technique is a popular heuristic used toautomate the detection of transient-state durations. Wehave applied this heuristic to our scenario. The idea isto remove from dispersion measurements, those packetsthat the MSER-m selects as part of the transitory.

Figure 17 illustrates this observation. We apply anMSER-2 heuristic to the inter-arrival time of the pack-ets of a 20 packet train sequence. As the figure shows,when we remove the packets that the heuristic reportsas part of the transient-state, the curve better approachesthe steady-state behavior. An this is achieved withoutthe need to enlarge the number of packets sent. Thiscould be applied to existing tools [1, 19, 20, 21, 22, 25,26] in order to improve their accuracy and/or reducetheir convergence time.

8. CONCLUSIONSThis paper presents a study of the bandwidth mea-

surement problem when applied to CSMA/CA basedsystems. On one side the paper presents a completemodel of the rate response curve of the system in steady-state completing state-of-art literature related to thetopic.

On the other side, the paper analyzes the transient-state behavior of the system considered. This study re-veals that the access delay of probing packets undergoesa transitory regime before reaching the steady-state.

12

Additionally, it provides some bounds on the durationof such transient-state regime that can be used, in prac-tice, to design bandwidth measurement tools. Finally,the study provides some insights on how this transient-state regime deviates rate response curves based onshort packet trains, and how the effects of this deviationcan be safely reduced without increasing the intrusive-ness of the measurement process.

9. REFERENCES[1] R.S.Prasad et al. ”Bandwidth Estimation:

Metrics, Measurement Techniques and Tools”,IEEE Network 2003

[2] Mingzhe Li et al. ”Packet Dispersion in IEEE802.11 Wireless Networks”, in Proc. of IEEELocal Computer Networks 2006

[3] Karthik Lakshminarayanan, ”BandwidthEstimation in Broadband Access Networks” InProc. of the ACM SIGCOMM conference onInternet measurement (IMC), 2004

[4] Mingzhe Li, Mark Claypool, and Robert Kinicki,”Packet Dispersion in IEEE 802.11 WirelessNetworks”, in Proc. of PAEWN 2007, November2007

[5] Andreas Johnsson et al. ”An Analysis of activeend-to-end bandwidth measurements in wirelessnetworks” In Proc. of IEEE E2EMon 2006

[6] Issariyakul T. et al., ”Exact Distribution of accessdelay in IEEE 802.11 DCF MAC”, In Proc. ofGlobal Telecommunications Conference(GLOBECOM), 2005

[7] Shahrokh Valaee, ”Bandwidth Estimation andDistributed Traffic Regulation in Wireless LocalArea Networks” In Proc. of the Personal, Indoorand Mobile Radio Communications (PIMRC),2008

[8] de A. Rocha, et al. ”An End-to-End Technique toEstimate the Transmission Rate of an IEEE802.11 WLAN” In Proc. of IEEE ICC 2007

[9] G. Bianchi, ”Performance Analysis of the IEEE802.11 Distributed Coordination Function” IEEEJournal on Selected Areas in Communications,Vol. 18, Num. 3, 2000

[10] Marc Portoles-Comeras et al, ”EXTREME:Combining the ease of management of multi-userexperimental facilities and the flexibility of proofof concept testbeds” In proc. of the IEEETridentCom, 2006

[11] Multi-Generator (MGEN) (online)http://cs.itd.nrl.navy.mil/work/mgen/

[12] Attila Pasztor and Darryl Veitch, ”PC Basedprecision timing without GPS” SIGMETRICSPerform. Eval. Rev. Vol. 30, Num. 1, 2002

[13] The Network Simulator NS2 (online)http://www.isi.edu/nsnam/ns/

[14] Melander B.,Bjorkman M., Gunningberg P.”Regression based available bandwidthmeasurements” in Proc. of SPECTS, July 2002.

[15] Liu X., Ravindran K., Liu B., and Loguinov, D.,”A Queuing-Theoretic Foundation of AvailableBandwidth Estimation: Single-Hop Analysis”IEEE/ACM Transactions on Networking, Vol. 15,Num. 6, 2007

[16] X. Liu, K. Ravindran, and D. Loguinov,”Multi-Hop Probing Asymptotics in AvailableBandwidth Estimation: Stochastic Analysis,” InProc. of USENIX/ACM IMC, October 2005.

[17] NIST/SEMATECH e-Handbook of StatisticalMethods (online)http://www.itl.nist.gov/div898/handbook/(Sec. 1.3.5.6)

[18] P.Haga, K. Diriczi et al, ”Granular model ofpacket pair separation in Poissonian traffic”Elsevier Computer Networks, Vol. 51, Num. 3,2006

[19] M. Jain et al. ”End-to-End Available Bandwidth:Measurment Methodology, Dynamics andRelation with TCP Throughput”, In Proc ofACM Sigcomm 2002

[20] N. Huet et al. ”Evaluation and Characterizationof Available Bandwidth Techniques” IEEE JSAC2003

[21] V. J. Ribeiro, R. H. Riedi, R. G. Baraniuk, J.Navratil, and L. Cottrell, ”pathChirp: Efficientavailable bandwidth Estimation for NetworkPaths” In Proceedings of Passive and ActiveMeasurements (PAM), 2003

[22] J. strauss, ”A Measurement Study of availablebandwidth Estimation tools” In Proc. of theACM SIGCOMM conference on Internetmeasurement (IMC), 2003

[23] Marc Portoles-Comeras et al., ”Framework forcharacterizing hardware deployed in wireless meshnetworking testbeds” In Proc. of Tridentcom2007, 2004

[24] R. Draves et al. ”Routing in Multi-Radio,Multi-Hop Wireless Mesh Networks” In Proc. ofACM Mobicom 2004

[25] Albert Cabellos-Aparicio et al., ”A NovelAvailable Bandwidth Estimation and TrackingAlgorithm”, in Proc. of IEEE E2EMon 2008

[26] Dovrolis C., Ramanathan P., and Moore, D.”Packet dispersion techniques and a capacityestimation methodology” IEEE/ACMTransaction on Networking, Vol. 12, Num. 6, 2004

[27] Marc Portoles-Comeras et al., ”Framework forcharacterizing hardware deployed in wireless meshnetworking testbeds” In Proc. of Tridentcom 2007

[28] Michael Bredel and Markus Fidler, ”AMeasurement Study of Bandwidth Estimation in

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IEEE 802.11g Wireless LANs using the DCF” inProc. of IFIP Networking 2008

[29] Ren Wang, Kenshin Yamada, M. Yahya Sanadidi,and Mario Gerla, ”TCP with sender-sideintelligence to handle dynamic, large, leaky pipes”IEEE Journal on Selected Areas inCommunications, 23(2):235-248, 2005

[30] V. Konda and J. Kaur, ”RAPID: Shrinking theCongestion Control Timescale”, IEEE INFOCOM2009.

[31] Hu, n. et al, ”Improving tcp startup performanceusing active measurements: Algorithm andevaluation” In Proc. of ICNP, 2003

[32] Yong Zhu, Constantinos Dovrolis, MostafaAmmar, ”Dynamic overlay routing based onavailable bandwidth estimation: a simulationstudy” Elsevier Comput. Networks, Vol. 50, No.6. pp. 742-762, April 2006

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[35] R. Carter and M. Crovella, ”Measuring BottleneckLink Speed in Packet-Switched Networks” TRBU-CS-96-006, Boston University, 1996

[36] J. A. Joines, Jr., R. R. Barton, et al., ”AComparison Of Five Steady-State TruncationHeuristics For Simulation”, Winter SimulationConference 2000

APPENDIXA. VALIDATION SETUP

This section introduces the simulation and experi-mentation settings used to gather measurement dataand validate theoretical findings. Experimentation hasbeen carried out within the EXTREME framework (see[10]). This is a multi-purpose networking experimentalplatform. The main advantage of this platform is itshigh automation capabilities that allow automatic ex-ecution, data collection and data processing of severalrepetitions of an experiment.

The WLAN devices used are Z-COM ZDC XI-626cards which carry the popular Prism chipset. Thesewireless devices are controlled using computer nodesof the EXTREME cluster. In all cases these nodesare Pentium IV PCs with a 3GHz processor, 512MBof RAM memory and running Linux OS, with kernel2.4.26. To control these devices, the EXTREME au-tomation system makes use of the wireless extensionsAPI.

In order to generate the traffic (probing and cross-traffic), we make use of the Multi-GENerator toolset[11]. However, in order to increase the accuracy ofthe time-stamping procedure, both at sender and re-ceiver sides, network device drivers have been conve-niently modified to timestamp packets just before theyare laid down to the hardware (sending side) and justafter getting them from the hardware (receiving side).This follows some of the ideas described in [12].

Figure 2 shows the basic setup used throughout thesection for experimentation. The probing traffic is sentbetween two stations that are conveniently synchro-nized. This synchronization is achieved by sending fre-quent NTP updates through a parallel wired interfacebetween the NTP server and the measurement nodes.Using this method we achieve accuracies of delay mea-surement in the order of ten microseconds.

Some of the experiments required a large amount ofrepetitions to achieve accurate convergence of results.Since this is difficult to achieve in a testbed we have alsoused a simulator. Specifically we have replicated thetesbed (figure 2) using NS2 (ver. 2.29 [13]). The maindifference between the testbed and the simulator is thatthe latter includes scenarios with up to 5 contendingnodes. Following some recent research results [27] boththe testbed and the simulator went through a thoroughcalibration process in order to assure that the resultsgathered are comparable.

The simulator uses the NO Ad-Hoc Routing Agent.This agent supports static routing configurations overwireless networks and does not send any routing relatedpackets. This avoids possible interferences with probeor cross-traffic. Regarding the configuration, all the ex-periments use the default MAC and PHY 802.11 layersincluded into the NS2 package. The queues used areinfinite, this way we avoid dealing with packet losses,which are irrelevant for our study. Finally all the wire-less nodes are static and equally spaced from the AccessPoint. The physical transmission rate is set to 11Mbpsand RTS/CTS is not used.

Finally, we have also developed a queuing simulatorusing Matlab. The motivation for this is that the prob-ing process in a WLAN presents multiple componentsthat are difficult to isolate from each other in an exper-imentation setting or even through simulations. Thequeuing simulator convolves a series of packet arrivalswith a series of service times in order to measure sev-eral metrics such as the queuing length distribution andthe output dispersion (inter-arrival) of packets. Theinput parameters are gathered from experimentationmeasurements in order to keep the results as close tothe real behavior as possible.

14