Mobile Netw Appl (2012) 17:435–446DOI 10.1007/s11036-012-0382-2

Providing Throughput and Fairness Guaranteesin Virtualized WLANs Through Control Theory

Albert Banchs · Pablo Serrano · Paul Patras ·Marek Natkaniec

Published online: 3 June 2012© Springer Science+Business Media, LLC 2012

AbstractWith the increasing demand for mobile Internet

access, WLAN virtualization is becoming a promis-ing solution for sharing wireless infrastructure amongmultiple service providers. Unfortunately, few mech-anisms have been devised to tackle this problem andthe existing approaches fail in optimizing the limitedbandwidth and providing virtual networks with fairnessguarantees. In this paper, we propose a novel algo-rithm based on control theory to configure the virtualWLANs with the goal of ensuring fairness in the re-source distribution, while maximizing the total through-put. Our algorithm works by adapting the contentionwindow configuration of each virtual WLAN to thechannel activity in order to ensure optimal operation.We conduct a control-theoretic analysis of our systemto appropriately design the parameters of the controllerand prove system stability, and undertake an extensive

A. Banchs (B)Institute IMDEA Networks, Avenida del Mar Mediteraneo,22, 28918 Leganés (Madrid), Spaine-mail: albert.banchs@imdea.org

P. Serrano · A. BanchsUniversidad Carlos III de Madrid, Leganés, Spain

P. Serranoe-mail: pablo@it.uc3m.es

P. PatrasHamilton Institute of the National University of Ireland,Maynooth, Ireland

M. NatkaniecAGH University of Science and Technology,Krakow, Poland

simulation study to show that our proposal optimizesperformance under different types of traffic. The re-sults show that the mechanism provides a fair resourcedistribution independent of the number of stations andtheir level of activity, and is able to react promptly tochanges in the network conditions while ensuring stableoperation.

Keywords wireless LAN · virtualization · 802.11 ·control theory · throughput optimization · fairness

1 Introduction

As portable devices are becoming widespread and usersincreasingly prefer connecting to the Internet thoughwireless access points (APs), Internet Service Providers(ISPs) are competing to provide wireless broadbandservices in popular locations such as airports, cafés,hotels, etc. As the infrastructure on such premises isusually managed by local businesses, network operatorsseeking to enable roaming services for their existingcustomers or to gain additional revenue from tempo-rary users are often required to share the resources of asingle AP with other parties. The solutions range fromsetting up a unique client authentication mechanism onthe AP [1], which enables virtual networking for eachprovider across the AP’s gateway connection, to estab-lishing virtual APs (VAP) on the same device, that willmanage the operation of independent virtual WLANs,exposing a unique service set identifier (SSID) for theusers of each operator. The latter is enabled by therecent hardware/software advances that allow the virtu-alization of a single physical interface and the creationof multiple logical AP entities [2–4].

436 Mobile Netw Appl (2012) 17:435–446

Although the existing virtualization techniques solvethe problem of sharing a single wireless resource, theydo not provide fairness guarantees among VAPs thatserve different number of clients, as in the case il-lustrated in Fig. 1. Specifically, as the IEEE 802.11MAC protocol [5] grants stations equal opportunities ofaccessing the channel [6], in such scenarios the through-put performance of the VAPs will be proportionalto their number of users, and thus overloaded virtualWLANs will significantly affect the performance ofthe coexisting networks. Considering the example ofFig. 1 with saturated stations running standard EDCA,WLAN2 will be taking 50% of the network through-put, while WLAN1 will receive 66% of the remainingbandwidth. Hence, the default configuration of the802.11 protocol yields significant inter-VAP unfairness.If operators decide to share a given Access Point usingvirtualization, and they evenly share the deploymentand maintenance cost of the infrastructure, this defaultbehavior is highly undesirable, as those VAPs withfew stations will obtain a small share of the wirelessresource for the same cost. Based on this observation,we argue that a fair distribution of wireless resourcesbetween VAPs is required. Recent work [7] addressesthis problem by proposing an architecture to deployalgorithms that enforce equal airtime among groupsof stations. However, the solution requires clients torun a software application that involves non-negligiblesignaling with a central controller located at the APand employ traffic shaping to limit the sending rates,which challenges its practical use. Additionally, this andprevious proposals [7–10] do not address throughputoptimization in virtualized WLANs, which is essentialgiven the scarce nature of the wireless medium.

In this paper, we propose C-VAP (Control-theoreticoptimization of Virtual APs), a novel algorithm that

Fig. 1 Scenario under study: a single Access Point hosting mul-tiple virtual Wireless LANs on the same channel, each withdifferent number of users

maximizes the total throughput shared by virtual APswhile providing fairness guarantees. The key techniqueof C-VAP is to employ control-theoretic tools to ad-just the contention window (CW) configuration of thestations within each VAP, to drive the WLAN to theoptimal point of operation and evenly share the re-sources among the virtual networks. Specifically, withour approach the AP runs an independent proportionalintegrator (PI) controller for each VAP, which mon-itors the channel activity and drives the empty slotprobability to the optimal value that maximizes perfor-mance, while simultaneously equalizing the probabili-ties of successful transmissions among the VAPs. Tothis end, each controller computes the optimal CW tobe used by the clients of the VAP and broadcasts itto the stations by means of beacon frames, a featurespecified in the current standard [5].

We conduct a performance analysis of the virtualizedWLAN to characterize the optimal point of opera-tion, which provides the foundations for the designof our algorithm. We configure the parameters of thePI controllers and prove system stability by under-taking a control-theoretic analysis of the WLAN. Thekey advantages of our solution are that (i) it is fullycompliant with the 802.11 standard as it requires nomodifications at the client side, while solely relyingon existing AP functionality, (ii) it provides the samethroughput performance for all the VAPs sharing thewireless resources irrespective of their number of usersand their traffic patterns, (iii) it guarantees that non-saturated stations see all of their traffic served, and(iv) it maximizes the total throughput of the network.

The performance of the algorithm has been eval-uated by means of simulation experiments underdifferent network scenarios. The results show that ourproposal significantly outperforms the default 802.11scheme in terms of throughput, while providing fairnessgains of up to 50% as compared to both EDCA and thestatic configuration of the CW that maximizes through-put in the whole system. Furthermore, we show that ourapproach maximizes performance even when not allthe stations are backlogged; in this case, non-saturatedVAPs see their throughput demand satisfied whilethe remaining resources are equally shared among themore demanding VAPs.

The rest of the paper is organized as follows. InSection 2 we present our system model and derive theoptimal point of operation of a virtualized WLAN,Section 3 describes the proposed algorithm, a control-theoretic analysis is conducted in Section 4 to configurethe algorithm’s parameters and in Section 5 we evaluatethe performance of our proposal through simulation

Mobile Netw Appl (2012) 17:435–446 437

experiments. Section 6 summarizes the related workand, finally, Section 7 concludes the paper.

2 System model and optimization

We consider the case of N different virtual WLANssharing the resources of a single AP and operating onthe same carrier frequency.1 We assume ideal channelconditions, and that all stations are in carrier-sensingrange of each other, regardless of the virtual AP theyare associated with. In this way, collisions are the onlysource of frame losses. Such ideal channel conditionshave been widely used in the past (see e.g. [6, 12, 13])and been proven to yield a good level of accuracy inexperimental scenarios [14]. We consider stations areusing a single transmission queue (note that following[15] the analysis can be easily extended to accountfor multiple active EDCA queues per station). Giventhat our approach computes the optimal point of op-eration according to the observed network conditions,the exponential backoff scheme is not required, (fur-thermore, this would increase jitter) and therefore weset CWmin,i = CWmax,i = CWi (we refer the reader to[15] for a detailed discussion and validation of thisargument). We denote with CWi the configuration ofthe contention window parameter that the virtual AP i(VAPi) announces to its ni associated stations, with i ∈{1, . . . , N}. Assuming that all clients operate in satura-tion conditions, i.e., they always have a frame ready fortransmission,2 the probability that a station transmits ata randomly chosen slot time is given by[12],

τi = 21 + CWi

, (1)

and the total throughput obtained by clients associatedwith VAPi, denoted as Ri, can be computed as [13]

Ri = E[paylod VAPi/slot]E[slot length] = Si L

PeTe + (1 − Pe)To, (2)

where Si is the probability that a slot contains a suc-cessful transmission from VAPi, L is the average framelength, Pe is the probability that a slot is empty, Te isthe corresponding slot length in this case and To is the

1In case of overlapping BSS scenarios, our mechanism can beindependently implemented on each AP, as long as they em-ploy appropriate dynamic channel assignment schemes such as,e.g., [11].2Later on we relax this assumption and demonstrate that perfor-mance is optimized even when some stations are not saturated.

average length of an occupied slot, as derived in [12].3

Pe is expressed as

Pe =N∏

k=1

(1 − τk)nk , (3)

while Si can be computed as

Si = niτi(1 − τi)ni−1

N∏

k=1,k�=i

(1 − τk)nk = niτi

1 − τiPe. (4)

The above completes our throughput analysis. Basedon this model, we next address the optimization of theCWi parameters of all VAPs in order to fulfill two keyobjectives. Namely, our goal is to design an algorithmthat ensures the following two requirements:

1. All VAPs obtain the same performance when thenetwork is fully loaded, regardless of their numberof stations, i.e.,

Ri = R j ∀i, j

2. The overall network performance is maximized,i.e.,

max∑

Ri

To derive the condition that guarantees the firstobjective is achieved, we rewrite Eq. 2 as

Ri =niτi1−τi

PeL

To − (To − Te)Pe. (5)

With the above, it can be easily seen that the firstobjective imposes the following constraint on the trans-mission probabilities:

niτi

1 − τi= n jτ j

1 − τ j, (6)

which, assuming τi � 1∀i, can be approximated by4

niτi ≈ n jτ j. (7)

Based on this result, we next address the secondobjective of our algorithm, namely, maximizing thethroughput obtained by any VAPi (given the firstobjective, this is equivalent to maximizing the total

3Although for simplicity reasons we assume throughout thepaper a fixed frame length, this assumption could be relaxedfollowing our previous work [13].4Note that this assumption is reasonable, as large values of thetransmission probability would lead to high collision probabilityand hence to an inefficient utilization of the WLAN.

438 Mobile Netw Appl (2012) 17:435–446

throughput). Using the same approximation τ � 1 onEq. 5 yields

Ri ≈ niτi LTo/Pe − (To − Te)

= niτi LTo

∏k(1 − τk)−nk − (To − Te)

,

which can be further approximated as

Ri ≈ niτi LToe

∑τknk − (To − Te)

= niτi LToeNτini − (To − Te)

.

The optimal τi, denoted as τ ∗i , can be obtained by

solving

dRi

dτi= 0,

which leads to the following non-linear equation:

ni[ToeNτini − (To − Te)

] − (niτi)ToeNτini Nni = 0.

To solve this equation, we proceed as in [12, 16] and usea Taylor expansion to approximate the exponential, i.e.,ex = 1 + x + x2/2 + . . . , and, given τi � 1, we neglectthe τi terms above second order, which leads to thefollowing expression for τ ∗

i :

τ ∗i = 1

Nni

√2Te

To(8)

Thus, we obtain the optimal CW configuration by sub-stituting the above in Eq. 1,

CWi = 2τ ∗

i− 1. (9)

Finally, we compute the probability of an empty slot,Pe, when all stations are configured as above, which willcharacterize the point of operation of the WLAN underoptimal configuration. To this end, we substitute Eq. 8in Eq. 3, which results in

P∗e =

∏

k

(1 − 1

Nnk

√2Te

To

)nk

, (10)

This expression can be approximated as

P∗e ≈

∏

k

e− 1N

√2TeTo = e−

√2TeTo . (11)

The above shows that, under optimal operation withsaturated stations, the probability of an empty slot is aconstant independent of the number of VAPs and sta-tions. The key approximation of this paper is to assumethat this also holds when there are non-saturated sta-tions in the system. The accuracy of this approximationwill be assessed in Section 5.

3 C-VAP algorithm

From the analysis of Section 2 we know that the optimalpoint of operation of the system as given by P∗

e doesnot depend on the number of VAPs, the number of sta-tions, or their activity. This suggests that P∗

e can be usedas a reference signal, to assess how far the network isoperating from this optimal point and react accordingly.A key challenge, though, is to appropriately react whenthe system deviates from P∗

e : if the reaction is not quickenough, this will result in wastage of channel time; onthe other hand if the reaction is too prompt, the systemmay turn unstable due to the inherent randomness ofthe EDCA mechanism.

Control theory is a particularly suitable tool to ad-dress this challenge, since it provides the necessaryapparatus to guarantee the convergence and stability ofadaptive algorithms. Therefore, in this paper we pro-pose C-VAP (Control-theoretic optimization of Vir-tual APs), a mechanism based on the classic controlsystem depicted in Fig. 2, where each VAP runs anindependent controller in order to compute the CWconfiguration of its clients.5 Specifically, we employ aproportional integral (PI) controller [17], a well-knowndevice from classic control theory that has been previ-ously applied to a number of networking algorithms inthe literature [16, 18, 19]. A key advantage of using aPI controller is that it is simple to design, configure andimplement with existing hardware [16].

As shown in the figure, the PI controller of VAPi

takes the error signal ei as input and provides the con-trol signal oi as output, which is then used to computethe CWi announced by VAPi, thereby controlling theaggressiveness of the ni stations. The error signal servesto evaluate the state of the system. If the system is op-erating at the desired point, the error signal of all VAPswill be zero. Otherwise, a non-zero error will drivethe system from its current state towards the optimalstate. In our approach, the error signal ei is designed tofulfill the two objectives identified previously, namely(i) VAPs fairly share the system resources, and (ii) theoverall throughput is maximized.

In order to satisfy the above requirements, we takethe error signal as the sum of two terms. The first one isgiven by:

eopt = P∗e − Pe, (12)

5Although in the figure we represent each VAP as a differentblock, they all run o the same physical device and therefore theycan easily share operation parameters, e.g., sniffed frames.

Mobile Netw Appl (2012) 17:435–446 439

Fig. 2 Use of a different PI controller per Virtual AP

where Pe is the estimated probability of an empty slotand P∗

e is the optimal value resulting from our analy-sis. This term ensures that if the network operationyields an empty slot probability higher than the desiredvalue (corresponding to a suboptimal utilization of thechannel), the error will be negative, thus triggering adecrease of the CWi and therefore an increase in thechannel activity.

The second term of the error signal is:

efair,i = (N − 1)Si −∑

j�=i

S j. (13)

This term of the error ensures that if VAPi is ob-taining a share of the total bandwidth larger than theaverage of the other (N − 1) VAPs due to employinga smaller CW configuration, the error will be positive,thus reducing the aggressiveness of the stations associ-ated to VAPi.

The combination of Eqs. 12 and 13 leads to thefollowing error signal:

ei = eopt + efair,i = P∗e − Pe + (N − 1)Si −

∑

j�=i

S j (14)

Theorem 1 included in the Appendix guaranteesthat there exists an unique point of operation at whichboth terms of the above error signal are equal to zero,this being our target configuration specified by Eq. 8.Note that this result is of particular importance, as itensures that there exists a single point of operation forthe whole system despite the independent PI instancesrunning at each VAP.

4 Control-theoretic analysis

To appropriately configure our PI controllers, we con-duct a control-theoretic analysis of the closed-loop sys-tem depicted in Fig. 2, which can be expressed in theform of Fig. 3, where

E =

⎛

⎜⎜⎜⎝

e1

e2...

eN

⎞

⎟⎟⎟⎠

=

⎛

⎜⎜⎜⎝

P∗e − Pe + (N − 1)S1 − ∑

j�=1 S j

P∗e − Pe + (N − 1)S2 − ∑

j�=2 S j...

P∗e − Pe + (N − 1)SN − ∑

j�=N S j

⎞

⎟⎟⎟⎠ , (15)

O =

⎛

⎜⎜⎜⎝

o1

o2...

oN

⎞

⎟⎟⎟⎠ , (16)

and

W =

⎛

⎜⎜⎜⎝

CW1

CW2...

CWN

⎞

⎟⎟⎟⎠ . (17)

Our control system consists of one PI controllerresponsible for each VAPi, which takes ei as input andgives oi as output. Each VAP takes this output signaland multiplies it by the number of associated stationsni, and the resulting value is broadcast to the associatedstations as the CW to use during the next interval.Following this behavior, we can express the relationshipbetween E and W as follows:

W(z) = N · O = N · C · E(z), (18)

Fig. 3 Control system

440 Mobile Netw Appl (2012) 17:435–446

where

N =

⎛

⎜⎜⎜⎝

n1 0 · · · 00 n2 · · · 0...

.... . .

...

0 0 · · · nN

⎞

⎟⎟⎟⎠ , (19)

and

C =

⎛

⎜⎜⎜⎝

CPI(z) 0 · · · 00 CPI(z) · · · 0...

.... . .

...

0 0 · · · CPI(z)

⎞

⎟⎟⎟⎠ , (20)

with CPI(z) being the z-transform of a PI controller,i.e.,

CPI(z) = KP + KI

z − 1. (21)

In order to analyze this closed loop we need to char-acterize the cluster of VAPs as a system with a transferfunction H that takes as input the oi’s and providesas output the error signals ei’s. Since our system actswith beacon frequency, typically 100 ms, we can safelyassume that the channel measurements obtained overa beacon interval correspond to stationary conditions.This implies that the error does not depend on theprevious values, but only on the output value computedin the previous interval; this is modeled by the termz−1 in the figure, which shows that the error signal ata given instance is computed with the output signal ofthe previous interval.

Following the above, E can be computed from Oby multiplying its elements by their respective ni’s toobtain the W vector, using Eq. 1 to compute the respec-tive τi’s, and expressing Pe and the Si’s as a function ofthe τi’s, following Eqs. 4 and 3. This gives a nonlinearrelationship between E and O. In order to expressthis relationship as a transfer function, we linearize itwhen the system suffers small perturbations around itsstable point of operation. Note that the stability of thelinearized model guarantees that our system is locallystable [18], which is confirmed by the performanceevaluation results presented in Section 5.

We express the perturbations around the point ofoperation as follows:

oi = oi,opt + δoi, (22)

where oi,opt is the oi value that yields τ ∗i .

With the above, the perturbations suffered by E canbe approximated by

δE = H · δO, (23)

where

H =

⎛

⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝

∂e1

∂o1

∂e1

∂o2· · · ∂e1

∂oN∂e2

∂o1

∂e2

∂o2· · · ∂e2

∂oN...

.... . .

...

∂eN

∂o1

∂eN

∂o2· · · ∂eN

∂oN

⎞

⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠

. (24)

The above partial derivatives can be computed as

∂ei

∂o j= ∂ei

∂τ j

∂τ j

∂CW j

∂CW j

∂o j, (25)

where we have, according to our system,

∂CW j

∂o j= n j, (26)

while Eq. 1, evaluated at the stable point of operation,yields,

∂τ j

∂CW j= −1

2τ 2

j . (27)

We next compute ∂ei/∂τ j for j �= i that, after someoperations, yields the following

∂ei

∂τ j= n j Pe

1 − τ j

(1 − (N − 1)

niτi

1 − τi− 1

1 − τ j

+∑

k�=i

nkτk

1 − τk

⎞

⎠ , (28)

which, evaluated at the stable point of operation (withniτi ≈ n jτ j) and assuming τ j � 1, results in the follow-ing

∂ei

∂τ j≈ 0. (29)

If we now compute ∂ei/∂τi, we obtain

∂ei

∂τi= ni Pe

1 − τi

⎛

⎝1 + N − 11 − τi

− (N − 1)niτi

1 − τi+

∑

k�=i

nkτk

1 − τk

⎞

⎠,

(30)

which, evaluated at the stable point of operation, resultsin

∂ei

∂τi≈ Nni Pe. (31)

Combining all the above yields

H = KH I, (32)

Mobile Netw Appl (2012) 17:435–446 441

where

KH = − P∗e Te

NTo. (33)

Thus, our system is now fully characterized by thematrices C and H. The next step is to configure the KP

and KI parameters of the PI controller. Following The-orem 2 (provided in the Appendix), we have that the{KP, KI} setting has to fulfill the following conditionfor the system to be stable:

KI < KP <NTo

P∗e Te

+ 12

KI . (34)

In addition to guaranteeing stability, our goal in theconfiguration of the PI parameters is to find the righttrade-off between speed of reaction to changes and os-cillation under stable conditions. To find this trade-offwe use the Ziegler-Nichols rules [20] as follows: (i) wefirst compute the KP value that leads to instability whenKI = 0, denoted as KU , and configure KP = 0.4KU ;(ii) we then compute the oscillation period TI when thesystem is unstable, and configure KI = KP/(0.85TI).

To compute KU we set KI = 0 in Eq. 34, whichgives

KP <NTo

P∗e Te

. (35)

Since the above is a function of N, to find a boundindependent of the number of VAPs we set N = 1, asthis constitutes the most restrictive case on KP, whichleads to

KU = To

P∗e Te

. (36)

During unstable operation, a given set of input val-ues may change their sign up to every time interval,yielding an oscillation period of two (TI = 2). Thus, weobtain the following configuration for the KP and KI

parameters:

KP = 0.4To

P∗e Te

,

KI = 0.20.85

To

P∗e Te

. (37)

It is easy to verify that this configuration meetsthe condition of Eq. 34 and therefore guarantees thestability of the system.

5 Performance evaluation

To evaluate the performance of the proposed algo-rithm, we conducted an extensive set of simulation

experiments. For this purpose, we have extended thesimulator used in [13, 16],6 which is an event-driven net-work simulator based on the OMNeT++7 frameworkthat closely follows the details of the MAC protocol of802.11 EDCA for each contending station. The simu-lations are performed with the system parameters ofthe IEEE 802.11a physical layer [21] and the 54 MbpsPHY rate, assuming a channel in which frames are onlylost due to collisions and considering stations transmitframes with a payload size of 1000 bytes. We presentaverages over 10 simulation runs, each lasting 300 s.We also compute 95% confidence intervals for thethroughput figures, and confirm that in all cases theirwidth is well below 1% of the average.

Unless otherwise specified, we assume that all sta-tions are saturated. We compare the performance ofour proposal, C-VAP, against the following two alter-natives: (i) the standard default configuration, denotedas ‘EDCA’ [5], and (ii) the static CW configuration thatmaximizes total throughput of the WLAN (regardlessof VAPs associations) under saturation conditions [12],labeled as ‘Bianchi’ in the plots.

5.1 Throughput & fairness

Our first aim is to validate that C-VAP is able to max-imize the throughput performance in the WLAN whileproviding all VAPs with a fair share of the resources.To this end, we consider the case of three VAPs withni = {2, 4, 6} saturated stations, respectively, and com-pute the throughput obtained by each station. Theresults, grouped by VAP, are presented in Fig. 4.

The figure shows that C-VAP succeeds in providingall VAPs with the same throughput (8.9 Mbps approxi-mately) regardless of their number of users (the stackedboxes show the throughput attained by each station).In contrast, the other two alternatives fail to providefairness among VAPs, and instead favor the VAPs withhigher number of associated stations. Precisely, the JainFairness Index (JFI) [22] for the per-VAP throughputdistribution yields values of 1, 0.85 and 0.86 for C-VAP,Bianchi and EDCA, respectively. Note that C-VAPis able not only to enforce fairness among VAPs, butalso to maximize the overall throughput in the system;indeed, the total throughput obtained with C-VAP andBianchi is approximately 26.7 Mbps, while the defaultEDCA configuration proves to be too aggressive forthe considered number of stations and yields a totalthroughput of 24.6 Mbps.

6The source code of the simulator used in [13, 16] is available athttp://enjambre.it.uc3m.es/∼ppatras/owsim/.7http://www.omnetpp.org

442 Mobile Netw Appl (2012) 17:435–446

0

5

10

15

VAP1 VAP2 VAP3

EDCARtotal = 24.64 Mbps

0

5

10

15

Thr

ough

put [

Mbp

s]

BianchiRtotal = 26.69 Mbps

0

5

10

15 C-VAPRtotal = 26.75 Mbps

Fig. 4 Throughput distribution among VAPs

We next analyze how the performance of the threeapproaches varies when the number of stations asso-ciated with the VAPs changes. For this purpose, weconsider the case of two VAPs, with n1 = 5 stations andan increasing number of saturated stations associatedwith VAP2. For each considered case, we obtain thetotal throughput in the system and the Inter-VAP JFI asin the previous case. The results are depicted in Fig. 5.

The figure confirms the results obtained in the pre-vious scenario. First, it can be seen that as the totalnumber of stations increases, the EDCA configurationresults overly aggressive and therefore the overallthroughput performance is degraded; in contrast, bothC-VAP and Bianchi’s approach are able to maximizethe total throughput. On the other hand, only C-VAPis able to provide a fair resource distribution withJFI≈1 in all cases, while the other two approachesexcessively favor VAP2 as its number of users increases,which results in JFI values significantly smaller than

0.7

0.8

0.9

1

1 2 3 4 5 6

Inte

r-V

AP

JF

I

VAP dissimilarity (n2/n1)

C-VAPBianchiEDCA

20

22

24

26

Tota

l thr

ough

put [

Mbp

s]

Fig. 5 Throughput performance and inter-VAP fairness

one. More specifically, although Bianchi’s approachoptimally configures the CW and maximizes the overallthroughput, it does not take into account users associ-ations and therefore penalizes the VAP with the leastnumber of stations.

The above results confirm that, in saturation condi-tions, our mechanism is able to maximize the overallthroughput in the system while guaranteeing a fairdistribution of the resources among VAPs. In whatfollows, we study the case of non-saturation scenariosand assess the effectiveness of the configuration of thePI controller under both steady operation and dynamicconditions.

5.2 Non-saturation scenarios

We next analyze the behavior of the proposed algo-rithm in non-saturated traffic conditions, to confirmthat the good properties of C-VAP are maintainedeven when stations are not constantly backlogged withframes to transmit. Note that under non-saturationconditions our goals are the following: (i) non-saturatedstations see all their traffic served, as long as theygenerate less than the saturation rate; (ii) VAPs withsaturated stations fairly share resources regardless ofthe number of stations; and (iii) the overall networkperformance is maximized.

In our first set of experiments, we consider the caseof one VAP with n0 = 5 stations generating 500 kbpsPoisson traffic, and an increasing number of VAPs,each having ni = 5 · i saturated stations, i.e., the firstVAP with saturated stations associated has n1 = 5, thesecond VAP that we add has n2 = 10, and so on. Theaggregated throughput per VAP is depicted in Fig. 6 for

0

8

16

24

1 2 3 4 5

Number of saturated VAPs

EDCA 0

8

16

24

Thr

ough

put [

Mbp

s]

Bianchi 0

8

16

24C-VAP

Fig. 6 Throughput performance with non-saturated stations as-sociated to one VAP

Mobile Netw Appl (2012) 17:435–446 443

the three considered mechanisms. We mark with solidblack the throughput obtained by the non-saturatedVAP, while the other boxes depict the throughput ofthe saturated VAPs. The results can be summarized asfollows:

– C-VAP satisfies all the considered objectives, asthe non-saturated VAP always sees all of its trafficserved, while the other VAPs fairly share the avail-able bandwidth, which is furthermore maximized.

– The optimal-throughout configuration (Bianchi)only satisfies the non-saturated VAP as long as thenumber of saturated VAPs is below 5. Otherwise,despite the overall throughput is maximized as withC-VAP, the uneven distribution of resources harmsthe performance of non-saturated traffic and favorsthe VAPs with more associated stations.

– Finally, EDCA fails to fulfill all the above objec-tives, as it does not serve non-saturation trafficappropriately, the throughput is not maximized, andresources are unevenly shared.

The above scenario confirms that C-VAP is able toguarantee a fair sharing of resources when a VAP withnon-saturated stations is contending vs. other VAPswith saturated stations. We next analyze the case whenthere are saturated and non-saturated stations associ-ated with the same VAP. For this purpose, we considerthe case of two VAPs, with VAP1 having n1 = 5 sat-urated stations, and VAP2 having 5 saturated stationsand a varying number of non-saturated stations associ-ated (like in the previous case, non-saturated stationsgenerate 500 kbps Poisson traffic). We compute theaggregated throughput per VAP, and the throughputdistribution within VAP2, and depict the results inFig. 7.

0

4

8

12

16

0 5 10 15 20 25 30

VA

P2

thro

ughp

ut [M

bps]

Number of non-saturated stations

Saturated stationsNon-saturated stations

10

12

14

16

Tot

al

thro

ughp

ut [M

bps]

VAP1VAP2

Fig. 7 Performance vs. increasing number of non-saturatedstations

The figure shows that the good properties of thethroughput distribution are maintained also in this case.Indeed, in all cases the VAPs fairly share the resourceslike in the previous cases, each one getting about13.5 Mbps (top subplot of the figure). Examining thethroughput distribution within VAP2 (bottom subplotof the figure), again we see that saturated stations areable to maximize their performance as long as non-saturated stations see their traffic served. Once thenumber of non-saturated stations increases above 20,the resources are fairly distributed among the stationswithin the VAP.

5.3 Configuration of the controller

The main objective in the setting of the KP and KI

parameters proposed in Section 4 is to achieve a goodtradeoff between stability and speed of reaction tochanges in the system.

To validate that our system guarantees a stablebehavior, we consider the case of three VAPs, withni = {5, 10, 15} saturated stations each, and analyzethe evolution over time of the CW announced byeach virtual AP for our {KP, KI} setting proposed inEq. 37 and a configuration of these parameters 10 timeslarger. The results are depicted in Fig. 8. We observefrom the figure that with the proposed setting (labeled“KP, KI”) the systems performs stably with minor de-viations of the CWs around their average values; incontrast, for the other setting (labeled “KP ∗ 10, KI ∗10”) the announced values drastically oscillate and thesystem shows unstable behavior.

We next investigate the speed with which the systemreacts to changes in the working conditions. To this end,we consider the case of two VAPs, namely VAP1 andVAP2. The first one has associated n1 = 5 saturated

0

250

500

750

0 10 20 30 40 50 60

CW

Time (s)

KP*10,KI*10

0

250

500

750

CW

KP,KI

VAP1VAP2VAP3

Fig. 8 Stability of the PI controller configuration

444 Mobile Netw Appl (2012) 17:435–446

0

100

200

300

0 30 60 90 120 150

CW

Time (s)

KP/10,KI/10

VAP1VAP2

0

100

200

300

CW

KP,KI

VAP1VAP2

Fig. 9 Speed of reaction to changes

stations, while for VAP2 the number of associatedstations varies over time as follows: in the beginningthere are n2 = 5 stations, at t = 30 s 5 more stations jointhe network, and subsequently 5 more stations join theVAP at t = 60 s, resulting in a total of n2 = 15 stations.Then, after 30 s, 5 stations leave VAP2, and again 5more stations leave at t = 120 s, the WLAN returningto the initial state with n1 = 5 and n2 = 5. For thisexperiment, we examine the evolution over time of theCW announced by each VAP for our {KP, KI} setting,as well as for a configuration of these parameters 10times smaller. The results are depicted in Fig. 9.

The figure shows that with our setting (“KP, KI”),the system reacts fast to the changes described above,as the CW announced by VAP2 reaches the new valuealmost immediately. In contrast, for the other setting(“KP/10, KI/10”), the system cannot keep up with thechanges and reacts too slowly.

We conclude that the proposed setting of {KP, KI}provides a good tradeoff between stability and speedof reaction to changes, since with a larger setting thesystem suffers from instability and with a smaller one itreacts too slowly to changes.

6 Related work

WLAN virtualization has recently become an impor-tant issue addressed by the research community. Wire-less networks virtualization architectures are proposedin [23–25] and a virtual networking infrastructure usingopen source techniques is introduced in [3]. Design andimplementation of solutions for supporting multiplevirtual WiFi interfaces with a single physical deviceare discussed in [2, 4]. TDMA-based approaches toWLAN virtualization are studied in [8] and [9], while

the strengths and drawbacks of space and time basedvirtualization techniques are compared in [26]. AP vir-tualization for enabling efficient mobility managementis described in [27, 28]. Client virtualization is employedfor supporting simultaneous connectivity to multipleAPs and achieving bandwidth aggregating in [29–32],while [10] exploits virtualization and multi-AP connec-tivity to improve video streaming performance. In [7]the problem of fair sharing of the uplink airtime acrossgroups of users is considered in a network virtualizationscenario.

However, none of the above works address the prob-lem of throughput optimization in virtualized WLANswhile providing fairness guarantees to virtual APs,which significantly limits their applicability to practicalscenarios where service providers seek to maximizerevenue from their wireless subscribers. In contrast tothese works, we propose a standard compliant solu-tion that can be easily deployed at the AP and whichsuccessfully maximizes the network performance whileevenly sharing the resources among the virtual net-works, irrespective of their number of users.

7 Conclusions

It is becoming increasingly common that operatorsshare a physical device to create different virtualWLANs, for reasons varying from lack of availablechannels (and therefore to increase efficiency in coordi-nating with competitors), to infrastructure being ownedby local businesses. In such circumstances, it is criticalto guarantee fair sharing of resources between virtualWLANs while maximizing throughput and, therefore,revenue. While previous approaches have provided themeans to enable virtualization or to optimally configurea single-owner WLAN, the problem of an optimalyet fair configuration has not been addressed. Fur-thermore, without a proper configuration, the defaultaccess scheme favors those operators with more clients,thus degrading the performance of the users attachedto lightly loaded networks.

In this paper we proposed C-VAP, a novel mech-anism that maximizes performance in virtualizedWLANs scenarios while ensuring fairness among com-peting providers. In contrast to previous work thatintroduces non-trivial changes to both the AP andthe stations, our approach runs exclusively at the APand relies only on standard functionality. Furthermore,by building on foundations from control theory, C-VAP is able to adapt to changes in the WLANswhile guaranteeing system stability. Extensive simula-tions confirm the good properties of our mechanism,

Mobile Netw Appl (2012) 17:435–446 445

and results show that (i) our scheme outperforms thestandard configuration in terms of throughput, (ii) itmaintains fairness among virtual WLANs regardless ofthe network conditions, either in terms of number ofstations or traffic patters (in contrast to the standardor the throughput-optimal configurations), and (iii) itpromptly reacts to changes in network conditions whileensuring stable operation. Following our implementa-tion experiences [14], we plan as part of our futurework to assess the performance of C-VAP in a real-lifetestbed.

Acknowledgements This work has been partly supported bythe European Community’s Seventh Framework Programme(FP7-ICT-2009-5) under grant agreement n. 257263 (FLAVIAproject), and by the Spanish Government, MICINN, under re-search grant TIN2010-20136-C03.

Appendix

Theorem 1 Given the def inition of ei in Eq. 14, thereexists an unique solution to the system def ined by ei =0 ∀i that satisf ies eopt = 0 and efair,i = 0 ∀i.

Proof By subtracting e j from ei we obtain

ei − e j = (N − 1)Si − S j − (N − 1)S j + Si

= N(Si − S j), (38)

and therefore, given that ei = 0 ∀i, j, the above resultsin Si = S j ∀i, j, and therefore we have that efair,i = 0 ∀i.Furthermore, this results in the following relation (asalready expressed in Eq. 6),

niτi

1 − τi= n jτ j

1 − τ j, (39)

which specifies, for a given (ni, n j) pair, a one-to-onerelationship between τ j and τi ∀i, j, and therefore wecan take e.g. τ1 as reference. In this way, if we expresseopt = 0 as

∏(1 − τk)

nk = P∗e , (40)

we have that the rhs of the above equation is a constantbetween 0 and 1, while the lhs is a decreasing functionof τ1 from 1 to 0. Therefore there exists a uniquesolution that solves the above equation, thus ensuringalso that eopt = 0.

Theorem 2 The KP and KI relationship specif ied byEq. 34 guarantees stability.

Proof According to [33], we need to check that thefollowing transfer function is stable

(I − z−1CH)−1C. (41)

Computing the above yields

(I − z−1CKH I)−1C = KP + KIz−1

1 − z−1(KP + KI

z−1

)KH

I, (42)

which can be expressed as

(I − z−1CKH I)−1C = P(z)

z2 + za1 + a2I, (43)

where P(z) is a polynomial and

a1 = −1(1 + KP KH), (44)

a2 = KH(KP − KI). (45)

According to [33], a sufficient condition for stabilityis that the zeros of the pole polynomial fall withinthe unit circle. This can be ensured by choosing thecoefficients {a1, a2} that belong to the stability triangle[17]:

a2 < 1, (46)

a1 < a2 + 1, (47)

a1 > −1 − a2. (48)

Equation 46 is satisfied as long as KP > KI , whileEq. 48 is satisfied if KI > 0. By operating in Eq. 47we obtain the relationship KP < −K−1

H + KI/2, whichcombined with the previous relations results in theconditions expressed by Eq. 34.

References

1. Janevski T, Tudzarov A, Stojanovski P, Temkov D (2007)Applicative solution for easy introduction of WLAN asvalue-added service in mobile networks. In: IEEE vehiculartechnology conference (VTC) spring, pp 1096–1100

2. Hamaguchi T, Komata T, Nagai T, Shigeno H (2010) Aframework of better deployment for WLAN access pointusing virtualization technique. In: IEEE international confer-ence on advanced information networking and applicationsworkshops (WAINA), pp 968–973

3. Aljabari G, Eren E (2011) Virtualization of wireless LANinfrastructures. In: IEEE international conference on in-telligent data acquisition and advanced computing systems(IDAACS), vol 2, pp 837–841

4. Xia L, Kumar S, Yang X, Gopalakrishnan P, Liu Y, Schoen-berg S, Guo X (2011) Virtual WiFi: bring virtualization fromwired to wireless. In: ACM SIGPLAN/SIGOPS internationalconference on virtual execution environments, ser. VEE ’11.Newport Beach, California, USA, pp 181–192

446 Mobile Netw Appl (2012) 17:435–446

5. IEEE 802.11 WG (2007) Information technology—telecommunications and information exchange betweensystems. Local and metropolitan area networks. Specificrequirements. Part 11: Wireless LAN medium access control(MAC) and physical layer (PHY) specifications. IEEE Std802.11

6. Berger-Sabbatel G, Duda A, Gaudoin O, Heusse M,Rousseau F (2004) Fairness and its impact on delay in 802.11networks. In: IEEE global telecommunications conference(GLOBECOM), vol 5, pp 2967–2973

7. Bhanage G, Vete D, Seskar I, Raychaudhuri D (2010) Spli-tAP: leveraging wireless network virtualization for flexiblesharing of WLANs. In: GLOBECOM 2010, 2010 IEEEglobal telecommunications conference, pp 1–6

8. Smith G, Chaturvedi A, Mishra A, Banerjee S (2007) Wire-less virtualization on commodity 802.11 hardware. In: ACMinternational workshop on wireless network testbeds, exper-imental evaluation and characterization, ser. WinTECH ’07.Montreal, Quebec, Canada, pp 75–82

9. Perez S, Cabero J, Miguel E (2009) Virtualization of the wire-less medium: a simulation-based study. In: IEEE vehiculartechnology conference (VTC) Spring, pp 1–5

10. Ahn S-W, Yoo C (2011) Network interface virtualizationin wireless communication for multi-streaming service. In:IEEE international symposium on consumer electronics(ISCE), pp 67–70

11. Akl R, Arepally A (2007) Dynamic channel assignment inIEEE 802.11 networks. In: IEEE international conference onportable information devices (PORTABLE), pp 1–5

12. Bianchi G (2000) Performance analysis of the IEEE 802.11distributed coordination function. IEEE J Sel Areas Com-mun 18(3):535–547

13. Serrano P, Banchs A, Patras P, Azcorra A (2010) Optimalconfiguration of 802.11e EDCA for real-time and data traffic.IEEE Trans Veh Technol 59(5):2511–2528

14. Serrano P, Patras P, Mannocci A, Mancuso V, Banchs A(2012) Control theoretic optimization of 802.11 WLANs: im-plementation and experimental evaluation. [Online]. Avail-able: http://arxiv.org/abs/1203.2970v1

15. Banchs A, Vollero L (2006) Throughput analysis and op-timal configuration of 802.11e EDCA. Comput Networks50(11):1749–1768

16. Patras P, Banchs A, Serrano P, Azcorra A (2011) A control-theoretic approach to distributed optimal configuration of802.11 WLANs. IEEE Trans Mob Comput 10:897–910

17. Aström K, Wittenmark B (1990) Computer-controlled sys-tems, theory and design, 2nd edn. Prentice Hall InternationalEditions

18. Hollot C, Misra V, Towsley D, Gong W-B (2001) A controltheoretic analysis of RED. In: Proceedings of IEEE INFO-COM 2001. Anchorage, Alaska

19. Grieco L, Boggia G, Mascolo S, Camarda P (2003)A controltheoretic approach for supporting quality of service in IEEE

802.11e WLANs with HCF. In: IEEE conference on decisionand control, vol 2, pp 1586–1591

20. Franklin GF, Powell JD, Workman ML (1990) Digital controlof dynamic systems, 2nd edn. Addison-Wesley

21. IEEE 802.11 (1999) Supplement to wireless LAN mediumaccess control and physical layer specifications: high-speedphysical layer in the 5 GHz band. IEEE Std 802.11a

22. Jain R, Chiu DM, Hawe W (1984) A quantitative measure offairness and discrimination for resource allocation in sharedsystems. DEC Research Report TR-301

23. He Y, Fang J, Zhang J, Shen H, Tan K, Zhang Y(2010) MPAP: virtualization architecture for heterogenouswireless APs. SIGCOMM Comput Commun Rev 41:475–476

24. Yap K-K, Kobayashi M, Sherwood R, Huang T-Y, Chan M,Handigol N, McKeown N (2010) OpenRoads: empoweringresearch in mobile networks. SIGCOMM Comput CommunRev 40:125–126

25. Matos R, Sargento S, Hummel K, Hess A, Tutschku K,de Meer H (2011) Context-based wireless mesh networks: acase for network virtualization. Telecommun Syst 1–14

26. Mahindra R, Bhanage G, Hadjichristofi G, Seskar I,Raychaudhuri D, Zhang Y (2008) Space versus time sepa-ration for wireless virtualization on an indoor grid. In: Nextgeneration internet networks (NGI), pp 215–222

27. Grunenberger Y, Rousseau F (2010) Virtual access pointsfor transparent mobility in wireless LANs. In: IEEE wire-less communications and networking conference (WCNC),pp 1–6

28. Berezin M, Rousseau F, Duda A (2011) Multichannel virtualaccess points for seamless handoffs in IEEE 802.11 wirelessnetworks. In: IEEE vehicular technology conference (VTCSpring), pp 1–5

29. Chandra R, Bahl P (2004) MultiNet: connecting to multipleIEEE 802.11 networks using a single wireless card. In: INFO-COM 2004, vol 2

30. Kandula S, Lin KC-J, Badirkhanli T, Katabi D (2008)FatVAP: aggregating AP backhaul capacity to maximizethroughput. In: USENIX symposium on networked sys-tems design and implementation (NSDI), San Francisco,California

31. Giustiniano D, Goma E, Lopez A, Rodriguez P (2009)WiSwitcher: an efficient client for managing multiple APs.In: SIGCOMM workshop on programmable routers for ex-tensible services of tomorrow (PRESTO). Barcelona, Spain,pp 43–48

32. Giustiniano D, Goma E, Lopez Toledo A, Dangerfield I,Morillo J, Rodriguez P (2010) Fair WLAN backhaul aggrega-tion. In: ACM international conference on mobile computingand networking (MobiCom). Chicago, Illinois, USA, pp 269–280

33. Glad T, Ljung L (2000) Control theory: multivariable andnonlinear methods. Taylor & Francis