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Handover Incentives for Self-Interested WLANswith Overlapping Coverage

Xenofon Fafoutis, Student Member, IEEE, and Vasilios A. Siris, Member, IEEE

Abstract—We consider an environment where self-interestedIEEE 802.11 wireless local area networks (WLANs) have over-lapping coverage, and investigate the incentives that can triggerhandovers between the WLANs. Our focus is on the incentives forsupporting handovers due solely to the improved performance forall wireless networks. Such incentives arise due to a well-knownproperty of 802.11 networks, where low rate users that sendtraffic significantly degrade the performance of high rate usersthat are associated to the same access point. A key differenceof this paper compared to other works is that WLANs areself-interested, seeking to improve the performance of theirown clients. We develop a comprehensive analytical model foraccurately identifying and quantifying the handover gains. Themodel captures cases such as uplink and downlink traffic, wiredlink capacity constraints, and non-saturated traffic conditions,and yields a practical handover decision policy. Simulationsand experiments on a real test-bed verify the accuracy of themodel, and indicate that significant gains can be achieved throughperformance-induced handover incentives.

Index Terms—multi-rate wireless networks, handovers, incen-tives

I. INTRODUCTION

Consider an environment where multiple wireless local areanetworks (WLANs) have overlapping coverage and operateon the same channel. The WLANs are assumed to be self-interested, meaning that they seek to improve the performanceof their clients. The problem we address in this paper iswhether there are cases where the self-interested WLANs haveincentives to support handovers, based solely on the improvedperformance they can achieve for their clients. We developa comprehensive analytical model to investigate the aboveproblem. Using the model, we can accurately identify the caseswhere such performance-induced incentives for supportinghandovers arise, and quantify the potential improvements forthe WLANs involved.

Handover incentives arise due to a well-known property ofIEEE 802.11 networks, where the assignment of low and hightransmission rate users to the same access point significantlydegrades the performance of the high rate users [1]. Thisoccurs because IEEE 802.11’s medium access control protocolgives both high and low rate nodes equal chances for accessingthe shared wireless channel. However, low rate nodes needmore time to send the same amount of data. As a result, when

Xenofon Fafoutis is with DTU Informatics, Technical University of Den-mark, Email: xefa@imm.dtu.dk. He was with the Institute of ComputerScience, Foundation for Research and Technology - Hellas (FORTH) whenthis work was conducted.

Vasilios A. Siris is with the Institute of Computer Science, Foundation forResearch and Technology - Hellas (FORTH), 71110, Heraklion, Greece andthe Department of Informatics, Athens University of Economics and Business,Greece. Email: vsiris@aueb.gr

low rate nodes send traffic, high rate nodes suffer significantperformance degradation, achieving throughput equal to thatof low rate nodes. There have been a number of works thataddress the above problem. The handover of nodes that areassociated with an access point at a low rate, to another accesspoint with which they can associate with at a high rate is onepossible solution to the problem; this is the approach taken byworks such as [2] [3] [4], which assume cooperation betweenaccess points. Alternatively, relays can be used for forwardingtraffic that cannot be transmitted directly at high rates [5][6] [7] [8] [9]. The distinctive feature of the current paper isthat we investigate the above problem in the context of self-interested WLANs, which seek to improve the performance oftheir own clients. Our analytical framework can identify whensuch handovers can be induced solely by the performanceimprovements that the self-interested WLANs can achieve.The work in this paper also differs from works such as [10],[11], [12], which deal with the problem of access point andnetwork selection using a game theoretic approach; the keydifference is that the above works investigate the problemfrom the viewpoint of the individual users, namely users seekto maximize their benefit, whereas in our work we considerthe gains of WLANs which seek to improve the aggregateperformance of their clients, by supporting handovers ofclients that belong to other WLANs.

In the case of operator-owned networks, handovers may besupported by cooperation agreements between the operators,which require detailed accounting. On the other hand, ourfocus is on the incentives for supporting handovers, due solelyto the improved performance that handovers yield for bothnetworks without involving any monetary or virtual currencyexchange, such as in token-based systems [13] [14] [15], orreputation systems [16] [17]. Moreover, similar performanceincentives arise in the case of overlapping wireless homenetworks where cooperation agreements are unrealistic. Al-though this paper focuses on performance-oriented incentivesfor triggering handovers, such incentives can also arise in otherareas, such as when forwarding traffic in multihop wirelessnetworks; the key property of wireless networks that can giverise to performance-oriented cooperation incentives is that thetransmission rate for different nodes depends on the pathattenuation, hence the transmission rate can be different fordifferent nodes.

An assumption about the environment we consider is thattwo or more WLANs operate on the same channel. Indeed, itis common that there are more than three WLANs within therange of each other [18]. Hence, the number of orthogonalchannels available in 802.11b/g or even 802.11a are notenough to assign different orthogonal channels to the dif-

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ferent access points. Moreover, the available non-overlappingchannels will be further reduced as more wireless networksoperating in unlicensed bands are deployed and as channelbonding techniques, e.g., in 802.11n, are used to increase thebandwidth hence the transmission speeds.

In order to identify and quantify the potential gain of han-dovers, we propose a comprehensive model that estimates thethroughput of each overlapping WLAN in different scenarios.Throughput approximations that account for rate diversity havebeen used in [19], [20], [21], [22] and, [23]. Our modellingframework captures more complicated scenarios, such as caseswhere the wired connection of access points, rather than thewireless channel, is the bottleneck for the end-to-end through-put. Moreover, our main contribution lies in the application ofthe above throughput model to predict the impact of handoversand decide whether handing over the nodes that communicateat low rates leads to higher performance for the clients ofthe overlapping WLANs. The analysis suggests that there arecases where such handovers can yield significant performanceimprovements. Additionally, based on the necessary conditionsfor a handover to be beneficial for all overlapping WLANs,we propose a simple policy that can be used by access pointsin order to decide whether to accept the handover.

In summary, the contributions of the paper include thefollowing:

• We present an analytical model that can approximate theaggregate performance of each WLAN, for a comprehen-sive set of cases which include the case where the capac-ity of a wired link constrains the end-to-end throughput,unsaturated traffic conditions, and client differentiation.

• We apply the model to predict when handovers betweenself-interested WLANs with overlapping coverage arebeneficial for all parties, giving all WLANs the incentiveto support handovers.

• We present a comprehensive series of numerical evalu-ations that identify and quantify the performance gainsfor handovers, we evaluate the proposed model withsimulation and test-bed experiments, and we discuss theimplementation of the proposed handover decision policyin our prototype.

The definition of the incentive problem introduced and ana-lyzed in detail in this paper, to the best of our knowledge, hasnot appeared in the same form previously in the literature.

The rest of this paper is organized as follows. Section IIformulates the handover incentives problem, and defines thehandover performance gains. Section III presents a compre-hensive model for estimating the throughput, and the cor-responding handover gains; the model includes the case fordownlink and uplink traffic, wired link capacity constraints,non-saturated traffic conditions, and client differentiation. Sec-tion IV describes some variations, such as swapping of lowrate clients, multiple low rates, and three access points. Sec-tion V presents investigations based on the analytical model toidentify and quantify the handover gains. Section VI investi-gates the accuracy of the model using simulation and test-bedexperimentation. Section VII discusses the implementation ofthe proposed model. Finally, Section VIII concludes the paper.

Fig. 1. No handover (case a): AP0 serves both high rate (N0) and low rate(Nx

0 ) nodes, that are clients of WLAN0. AP1 serves high rate nodes (N1)that are clients of WLAN1.

Fig. 2. Handover (case b): WLAN0’s low rate clients (Nx0 ) are handed off

to AP1.

II. THE HANDOVER INCENTIVES PROBLEM

In this section we first discuss the handover incentivesproblem, and then define the corresponding performance gainsthat will determine whether the overlapping WLANs have theincentive to support handovers.

Consider two wireless networks, WLAN0 and WLAN1, con-taining access points AP0 and AP1 respectively, Fig. 1. Weassume that both access points operate on the same channeland are in the same contention area. The clients of WLAN0

include the nodes in sets N0 and Nx0 : the nodes in N0 are

associated with AP0 at a high transmission rate R, whereasnodes in Nx

0 are associated with AP0 at a low transmissionrate r. The clients of WLAN1 are the nodes in set N1, whichare associated with AP1 at a high transmission rate R. Forsimplicity, we will use the notation N0, N

x0 , N1 to also denote

the number of nodes in the corresponding sets.Due to the low transmission rate of the nodes in Nx

0 , andsince both APs operate on the same channel, the performancefor the clients of both networks is low. The nodes in Nx

0 arecloser to AP1, hence could associate with this access point ata high transmission rate R. WLAN0 would gain if its clients inNx

0 are handed off to AP1, Fig. 2, because the throughput of itsclients in both N0 and Nx

0 would increase, since there will nolonger be low rate nodes. However, whether the performanceof WLAN1’s clients N1 improves or not if the nodes in Nx

0

are handed off to AP1 will depend on two opposite factors:On one hand, there will be a gain because the transmissionrate of nodes in Nx

0 will increase. On the other hand, therewill be a loss in throughput since now the resources of AP1

are shared by the clients of WLAN1 (N1) and some clientsof WLAN0 (Nx

0 ). The magnitude of the two opposite factorswill determine whether their combination results in an overallperformance improvement or reduction.

Based on the above discussion, we make the following tworemarks:• We consider that the performance of WLAN0 includes

the performance of nodes in both sets N0 and Nx0 ,

independent of whether the nodes in the latter set areconnected to AP0 or AP1. In other words, the nodes in

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Nx0 remain clients of WLAN0 even when they are handed

over to AP1.• Each WLAN is a self-interested party, seeking to improve

the performance of its clients. Hence, a WLAN willsupport handovers only if they improve the performanceof its clients. Moreover, handovers will eventually occuronly if both WLANs have the incentive to support them,which occurs if handovers improve the performance ofthe clients for both WLANs.

The motivation and importance of the above problem becomesclear if we consider the following application scenario: As-sume two neighboring homes, each with its own WLAN. Theusers of each home can have a number of wireless stations,which are the clients of that home’s WLAN. The problem thatwe investigate is whether there are incentives, based solely onperformance improvements, for the WLAN of one home tosupport handovers so that its AP serves wireless stations thatbelong to its neighbor. Handovers will eventually occur onlyif they improve the performance of the clients for both homenetworks. Moreover, the performance of each home’s WLANinvolves the performance of wireless stations belonging tothat home, independent of whether they are associated to thehome’s or a neighbor’s AP.

A. Handover gainsNext we define the gains that can arise from handovers.

The performance gain of WLANi is defined as the ratio of theaggregate utility for all clients of WLANi when a handoveroccurs, i.e., when the Nx

0 clients are handed off to AP1, Fig. 2,over the aggregate utility when there are no handovers, i.e., theNx

0 clients are associated at a low rate to their home accesspoint AP0. When the gain for both access points is greater thanone, then it is to the advantage of both access points to supporthandovers, since they will both increase the performance oftheir clients; these are the cases we seek to identify, and toquantify the corresponding gains for both WLANs.

For WLAN0, the handover gain is given by

GainWLAN0=N0 · u(Xb

N0) +Nx

0 · u(XbNx0

)

N0 · u(XaN0

) +Nx0 · u(Xa

Nx0), (1)

where the utility u(·) is a function of the achieved throughput.XaNx0

and XbNx0

are, respectively, the throughput achieved byeach of the Nx

0 nodes when there are no handovers and theNx

0 nodes are associated to AP0 at a low rate (case a, Fig. 1),and when there are handovers and these nodes are associatedto AP1 at a high rate (case b, Fig. 2). Similarly, Xa

N0and

XbN0

are, respectively, the throughput achieved by each of theN0 clients in the case of no handovers and in the case ofhandovers.

As discussed above, the Nx0 nodes are clients of WLAN0

even when they are associated to AP1. For WLAN1, thehandover gain is given by

GainWLAN1=u(Xb

N1)

u(XaN1

), (2)

where XaN1

and XbN1

are, respectively, the throughput for eachof the N1 clients of WLAN1 in the case of no handovers (casea, Fig. 1) and in the case of handovers (case b, Fig. 2).

In the above discussion, we have assumed that when han-dovers are performed, all low rate nodes associated to AP0

are handed off to AP1. In the next section we prove that ifhandovers of some low rate nodes provide performance gains,then the gains are maximized if all low rate nodes are handedoff to AP1.

The utility u(·) is a linear function of the throughput, ifthe WLANs value the aggregate throughput achieved by theirclients. Alternatively, if the utility is a concave function, thenmore value is given to low throughput clients, compared tohigh throughput clients.

Based on the estimated gains, WLANi decides to accepthandovers from clients of a neighboring WLAN if its gains arepositive, i.e., GainWLANi > 1. For the scenario in Figs. 1 and2, which involve two WLANs, handovers will be performedif the gains for both WLANs are positive.

III. MODELLING FRAMEWORK

In this section we begin with the analysis of the scenariodiscussed in the previous section for long-lived downlink flowswith saturated traffic, presenting a model for estimating thethroughput per node X that appears in the gain given by(1) and (2). Then, we extend the model for the case wherethe throughput is limited by the capacity of the wired linkthat connects an access point to an external network, forunsaturated traffic conditions, for client differentiation, and forthe case of uplink traffic.

A. Model for Downlink

A simple approach for estimating the throughput for thescenario with two access points shown in Fig. 1 is to assumethat each access point sends one frame in consecutive rounds.This is a reasonable approximation for long-lived flows withsaturated traffic, and assuming that the 802.11’s DCF (Dis-tributed Coordination Function) protocol provides long-termfair channel access; the latter is true when all access pointsare in the same contention area, hence there are no hiddenterminals or contention asymmetries.

Case a (no handover): When Nx0 low rate nodes are assigned

to AP0, the expected time interval that AP0 needs to transmita frame depends on the percentage of traffic sent to the N0

and Nx0 nodes, since the transmission duration is different

due to their different rates. On the other hand, the expectedtime interval that AP1 needs to transmit a frame is the samefor all nodes associated to it, since they all have the samerate. We initially assume that N0, N

x0 , N1 > 0. The long term

throughput Xa that each access point will achieve, assumingboth access points transmit frames of the same size, can beapproximated by

Xa =p

N0

N0+Nx0T (p,R) +

Nx0N0+Nx0

T (p, r) + T (p,R), (3)

where T (p,R) is the time for transmitting a packet of size pat rate R. The throughput of a node in N0, Nx

0 , and N1 isthen

XaN0

= XaNx0

=1

N0 +Nx0

Xa , XaN1

=1

N1Xa . (4)

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Case b (handover of low rate users): The low rate nodesNx

0 are handed over to AP1 and all transmissions are at a highrate. Hence, the throughput Xb of each access point can beapproximated by

Xb =p

2 · T (p,R). (5)

The above holds because all transmissions occur at a highrate R, hence the time for transmitting a packet is the samefor both access points. The throughput of a node in N0, Nx

0 ,and N1 is

XbN0

=1

N0Xb , Xb

Nx0= Xb

N1=

1

Nx0 +N1

Xb . (6)

If we substitute the throughput estimates (3)-(6), in expressions(1) and (2), we can obtain the handover gains for WLAN0

and WLAN1, respectively. If N0 > 0 and u(x) = x, i.e.,the WLANs value only the aggregate throughput their clientsachieve, then the above substitution yields the following han-dover gains:

GainWLAN0 =Xb +

Nx0Nx0 +N1

Xb

Xa, (7)

GainWLAN1=

N1

Nx0 +N1Xb

Xa. (8)

The above indicate that handovers are always beneficial forWLAN0, i.e. GainWLAN0 > 1, since with handovers WLAN0’sclients in Nx

0 obtain resources from AP1 hence WLAN0’sclients utilize the channel more than half the time, andXb > Xa because there are no low rate nodes.

Unlike WLAN0, the performance of WLAN1 depends onthe following tradeoff: On one hand, the aggregate throughputachieved by AP1 increases, i.e. Xb > Xa, due to removinglow rate nodes. On the other hand, when nodes in Nx

0 arehanded over to AP1, the later’s resources are now sharedby WLAN1’s clients N1 and WLAN0’s clients Nx

0 . Whetherhandovers improve the performance of WLAN1 depends onthe magnitude of the above two factors.

The throughput estimation in (3) and (5) considers thefunction T (p,R), which denotes the time for transmitting aframe of size p, at transmission rate R. In Section V-A wepresent an expression for T (p,R) that includes all protocoloverheads. For the discussion in this section, we consider thesimple expression T (p,R) = p

R which does not account forprotocol overheads; this expression captures a key propertyof wireless networks, namely that the duration of a packettransmission is higher for nodes with a smaller transmissionrate. Considering the above simple expression for T (p,R),from (8) the inequality GainWLAN1

> 1 which indicates whenhandovers are beneficial for WLAN1 is equivalent to

N1

N0 +Nx0

> c , where c =2

Rr − 1

. (9)

Hence, to decide whether handovers are beneficial WLAN1

simply needs to compare the ratio of its clients and the clientsof its neighboring WLAN, with a factor c, which depends onthe ratio of the high and low transmission rate. Note that thehandover acceptance condition (9) for the case of downlink

traffic depends only on the total number of WLAN0 clientsN0 +Nx

0 , and not separately on the number of high and lowrate clients. This in general is not the case for the extensions tothe model we present below, where the handover gains dependseparately on the number of high and the number of low rateclients. Nevertheless, what is important to note is that forall the extensions, the handover gains can be estimated usingsimple mathematical formulas that take as input the numberof neighboring clients and their respective transmission rates.

As noted above, the handover decision policy for WLAN1

given by (9) does not take into account the protocol overheads.Interestingly, the simple form of the inequality in (9) remainsthe same, even when the protocol overheads, described inSection V-A, are taken into account.

Up to now we have assumed that when handovers aresupported, all low rate nodes are handed over to the visitingaccess point, AP1. The following theorem shows that whentheir is a gain from handing over some number of low ratenodes, then this gain is maximized if all low rate nodes arehanded over. The above has important practical implications.Namely, in order to identify if handovers are beneficial,WLAN1 needs to only check if it gains from accepting alllow rate clients of WLAN0.

Theorem. Assume that N0, Nx0 , N1 > 1. If there are gains

for WLAN1 when a subset of WLAN0’s low rate clients arehanded over to AP1, then these gains are maximized if all ofWLAN0’s low rate clients Nx

0 are handed over to AP1.

The proof of the theorem is given in the Appendix.

Special case N0 = 0: We now assume that N0 = 0, i.e., thereare no clients of WLAN0 operating at high rate R. Equations(3) and (4) still apply, with N0 = 0.

In the case of handovers, all WLAN0 clients will be asso-ciated with AP1, hence only AP1 will be transmitting. Thus,the throughput for AP1 can be estimated by

Xb,N0=0 =p

T (p,R). (10)

From the last expression, equations (1), (2), and assumingu(x) = x, we obtain the following expressions for thehandover gains:

GainWLAN0=

Nx0Nx0 +N1

Xb,N0=0

Xa,N0=0,

GainWLAN1=

N1

Nx0 +N1Xb,N0=0

Xa,N0=0,

where Xa,N0=0 is given by (3) with N0 = 0. Recall fromthe above discussion, when N0 > 0 handovers are alwaysbeneficial to WLAN0 because half of the wireless resourcesare used by the N0 clients of WLAN0. If N0 = 0, thenhandovers are not always beneficial for WLAN0; whether theyare beneficial for WLAN0 depends on the share of AP1’sresources that are used by the Nx

0 clients of WLAN0 that arehanded over to AP1, and on the improved throughput achievedby removing low rate nodes.

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B. Wired Link Capacity Constraints

An important application of WLANs is to provide access toa wired networks, such as the Internet. It is not uncommon thatthe wired link connecting a WLAN to an external network isa bottleneck. This can be the case for DSL (Digital SubscriberLink) connections, whose speed depends on the distance of thesubscriber to the provider’s office. Specifically, for distanceslarger than 3 Km, the capacity for ADSL+ (Asymmetric Digi-tal Subscriber Link) falls below 8 Mbps, which is significantlylower than the maximum throughput supported by 802.11a/g.In this section we extend the throughput model to accountfor wired capacity constraints. We denote CAP0 , CAP1 as thecapacity of the wired link connecting AP0, AP1 respectively tothe external network. In the analysis that follows we considervarious cases involving the values of CAP0

, CAP1in relation

to the throughput values Xa, Xb estimated in the previoussubsection.

Case CAP0 ≤ CAP1 : The aggregate throughput of AP0 is

XCAP0= min(CAP0 , X) , (11)

where X is the throughput that is estimated by the modelin Section III-A, for either the case of no handovers (3) orhandovers (5).

If CAP0 < X , then AP0 uses less than its maximum shareof the wireless channel, and as a result AP1 can potentiallyobtain a larger share. Hence, the aggregate throughput of AP1

isXCAP1

= min(CAP1, θ ·XCAP0

) , (12)

where factor θ ≥ 1 is the ratio of the number of frames sent byAP1 over the number sent by AP0, in the same time interval.If AP0 is not constrained by CAP0 then θ = 1. On the otherhand, if AP0 is constrained by CAP0

, then part of AP0’s shareof the medium is available and can be used by AP1. Whenthere are no handovers, factor θ satisfies

XaCAP0

=p

N0N0+Nx0

T (p,R) +Nx0

N0+Nx0T (p, r) + θ · T (p,R)

, (13)

where XaCAP0

is given by (11) for X ≡ Xa. In the case ofhandovers, factor θ satisfies

XbCAP0

=p

T (p,R) + θ · T (p,R), (14)

where as before, XbCAP0

is given by (11) with X ≡ Xb.XaCAP1

, XbCAP1

can be estimated from (12), where XCAP0is

substituted with XaCAP0

given by (13), XbCAP0

given by (14),respectively.

From the above expressions forXaCAP0

, XbCAP0

, XaCAP1

, XbCAP1

, equations (1), (2), andassuming u(x) = x, we obtain the following expressions forthe handover gains:

GainWLAN0 =XbCAP0

+Nx0

Nx0 +N1XbCAP1

XaCAP0

,

GainWLAN1=

N1

Nx0 +N1XbCAP1

XaCAP1

.

Case CAP0 > CAP1 : The aggregate throughput of AP1 is

XCAP1= min(CAP1

, X) , (15)

where X is the throughput that is estimated by the modelin Section III-A, for either the case of no handovers (3) orhandovers (5). The aggregate throughput of AP0 is

XCAP0= min(CAP0

, θ ·XCAP1) ,

where factor θ ≥ 1 is the ratio of the number of frames sent byAP0 over the number sent by AP1, in the same time interval.When there are no handovers, factor θ satisfies

XaCAP1

=p

θ[

N0N0+Nx0

T (p,R) +Nx0

N0+Nx0T (p, r)

]+ T (p,R)

(16)

where XaCAP1

is given by (15) for X ≡ Xa. In the case ofhandovers, all nodes are connected at high rate R and factorθ satisfies

XbCAP1

=p

θ · T (p,R) + T (p,R), (17)

where as before, XbCAP1

is given by (15) with X ≡ Xb. Asabove, from the values of XCAP0

and XCAP1for the case of

no-handovers and handovers, using equations (1) and (2) wecan derive the corresponding handover gains.

Case CAP0 , CAP1 < Xa, given by (3): In this case, han-dovers are always beneficial for WLAN0, but not beneficial forWLAN1. Specifically, in the case of no handovers the aggregatethroughput for WLAN0,WLAN1 is CAP0

, CAP1respectively,

whereas in the case of handovers the aggregate through-put for each access point is CAP0 + Nx

0CAP1/(Nx0 + N1),

N1CAP1/(Nx

0 +N1), respectively.

Case CAP0 , CAP1 ≥ Xb, given by (5): In this case the wiredlink capacity constraints do not affect handovers, and the gainscan be estimated using the model in Section III-A.

C. Non-Saturated Traffic Conditions

Next we investigate the case where the flow to one of thenodes is not saturated, and has a maximum sending rate cx.As in the previous subsections, we assume that traffic flowsin the downlink direction. We derive the equations when theunsaturated node is in set Nx

0 ; a similar approach can be usedto derive the equations when the unsaturated node is in setN0. Consider Xa

Nx0given by (4) and Xb

Nx0given by (6). We

identify the following cases:

Case XaNx0≤ cx < Xb

Nx0: In this case Xa and Xb are the

same as the downlink model in Section III-A, and are givenby (3) and (5), respectively.

Case cx < XaNx0

: In this case Xb is given by (5). Next, weestimate Xa.

Let µ < 1 be the ratio of the throughput of the saturatednode cx, over the throughput of an unsaturated node Xa−cx

N0+Nx0−1.

Parameter µ can also be seen as the percentage of frames sentto the unsaturated node, over the frames sent to a saturatednode in the same time interval. The throughput of AP0 andAP1 when there are no handovers is

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Xa=

p

N0N0+Nx0 −1+µ

T (p,R) +Nx0 −1+µ

N0+Nx0 −1+µT (p, r) + T (p,R)

The handover gains are given by

GainWLAN0=Xb +

Nx0−1Nx0−1+N1

(Xb − cx) + cx

Xa,

GainWLAN1=

N1

Nx0−1+N1(Xb − cx)Xa

.

If there are more than one unsaturated flows with the samesending rate cx, the above expressions can be extended in astraightforward manner by replacing Nx

0 −1 with Nx0 −n and

cx with n · cx, where n is the number of unsaturated flows.If the flows have a different sending rate, then the extensionis more detailed and an iterative procedure such as the onedescribed in [24] applied to the case of single hop flows canbe used.

D. Client Differentiation

The model in the previous subsections assumed that thehanded over nodes are treated by AP1 identical to the clientsof WLAN1. From equations (1) and (2) it is easy to see thatthe gains for WLAN0 are always higher than the gains forWLAN1. Hence, WLAN1 may wish to differentiate the guestnodes of AP1 from its own clients. Such differentiation canbe supported by standards such as IEEE 802.11e.

Consider that AP1 sends η ≥ 1 frames to the clients ofWLAN1 for every frame it sends to the guest clients, whichbelong to WLAN1. The handover gains for each WLAN,assuming that each WLAN seeks to improve the aggregatethroughput of its clients, are given by the following:

GainWLAN0 =Xb + 1

η+1Xb

Xa, GainWLAN1

=

ηη+1X

b

Xa

where Xa and Xb are given by (3) and (5), respectively.Observe that by increasing η, WLAN1 can increase the gains

it achieves, and simultaneously reduce the gains of WLAN0.Moreover, as η → ∞ both WLANs achieve the same gain,equal to Xb/Xa.

If we consider a logarithmic utility u(x) = log(x), then thegains for WLAN0 and WLAN1 are the following:

GainWLAN0=N0 log

Xb

N0+Nx

0 log(

1η+1

Xb

Nx0

)(N0 +Nx

0 ) logXa

N0+Nx0

,

GainWLAN1=

log(

ηη+1

Xb

N1

)log Xa

N1

.

As we will see in the numerical investigations of Section V-C,unlike the case of a linear utility where WLANs value only theaggregate throughput of their clients, in the case of logarithmicutility, for large values of η, the handover gains for WLAN1

can be higher than the gains of WLAN0; this occurs becauseincreasing η reduces the throughput of WLAN0’s clients thatare handed off to AP1.

E. Model for Uplink

In the uplink direction, each node contends for accessingthe wireless channel. If we assume fair channel access, theneach node transmits one frame in consecutive rounds. Hence,in the case of no handovers the throughput of each node is

XaN =

p

N0 · T (p,R) +Nx0 · T (p, r) +N1 · T (p,R)

,

whereas in the case of handover the throughput is

XbN =

p

N0 · T (p,R) +Nx0 · T (p,R) +N1 · T (p,R)

.

From the above equations, assuming that R > r, handoverswill always be beneficial for both WLANs.

IV. MODEL VARIATIONS

In this section we discuss variations of the model presentedin the previous section. The variations include the case whenboth WLANs have low rate clients which are close to theneighboring access point, when a WLAN has clients withdifferent low rates, and when there are three access pointsin the same area.

A. Swapping Low Rate Nodes

Next we assume that both WLAN0 and WLAN1 have lowrate clients, Nx

0 and Nx1 respectively. These low rate nodes

connect at rate r when they are associated to their homeAP, but can connect at rate R if they are handed off to theneighboring access point.

Case a (no handover): The throughput of each access pointis

Xa=

p

g(N0)T (p,R) + g(Nx0 )T (p, r) + h(N1)T (p,R) + h(Nx1 )T (p, r),

(18)where g(x) = x/(N0 +Nx

0 ) and h(x) = x/(N1 +Nx1 ). The

throughput of a node in N0, Nx0 and N1, N

x1 is

XaN0

= XaNx0

=1

N0 +Nx0

Xa , XaN1

= XaNx1

=1

N1 +Nx1

Xa .

Case b (handover of low rate nodes): When low rate nodesare handed over to the neighboring AP, then all nodes operateat a high rate R, hence the throughput of each AP is given by(5). The throughput of a node in N0, N

x0 and N1, N

x1 is

XaN0

= XaNx1

=1

N0 +Nx1

Xb , XaN1

= XaNx0

=1

N1 +Nx0

Xb .

Finally, the handover gains are

GainWLAN0=

N0

N0+Nx1Xb +

Nx0Nx0 +N1

Xb

Xa,

GainWLAN1=

N1

Nx0 +N1Xb +

Nx1N0+Nx1

Xb

Xa.

7

Fig. 3. Mix of low rate nodes. No handovers.

B. Mix of Different Low Rates

Next we investigate the case where a mix of different lowrate nodes co-exist in the same contention area. Specifically,we assume that WLAN0 has three sets of clients: clients in N0

associate to AP0 at a high rate R, clients in Nx10 associate at

a low rate r1, and clients in Nx20 associate at a low rate r2,

Fig. 3. We also assume that r1 < r2.

Case a (no handover): The throughput of each access pointis

Xa=

p

f(N0)T (p,R) + f(Nx10 )T (p, r1) + f(N

x20 )T (p, r2) + T (p,R)

(19)

where f(x) = x/(N0 + Nx10 + Nx2

0 ). The throughput of anode in N0, Nx1

0 , Nx20 , and N1 is

XaN0

= XaNx10

= XaNx20

=1

N0 +Nx10 +Nx2

0

Xa ,

and XaN1

=1

N1Xa ,

where Xa is estimated from (19).

Case b (handover of low rate r1 and r2 nodes): Whenboth low rate r1 and r2 nodes in Nx1

0 and Nx20 are handed

over to AP1, Fig. 4, then all nodes transmit at high rate R,and the throughput of each access point is given by (5). Thethroughput of a node in N0, and Nx1

0 , Nx20 , N1 is

XaN0

=1

N0Xb and

XbNx10

= XbNx20

= XbN1

=1

N1 +Nx10 +Nx2

0

Xb ,

where Xb is given by (5). The handover gains are

GainWLAN0 =Xb +

Nx10 +N

x20

Nx10 +N

x20 +N1

Xb

Xa,

GainWLAN1=

N1

Nx10 +N

x20 +N1

Xb

Xa.

Note that, when N0 > 0, the handover of all low rate nodesis always beneficial for WLAN0.

Case b’ (handover only of low rate r1 nodes): When onlynodes with the lowest rate r1 in Nx1

0 are handed over to AP1,Fig. 5, the throughput of each access point is

Xb =p

N0

N0+Nx20

T (p,R) +Nx20

N0+Nx20

T (p, r2) + T (p,R).

Fig. 4. Mix of low rate nodes. Handover of all r1 and r2 low rate nodes.

Fig. 5. Mix of low rate nodes. Handover only of r1 low rate nodes, r1 < r2.

The throughput of a node in N0, Nx20 , and Nx1

0 , N1 isrespectively

XaN0

= XbNx20

=1

N0 +Nx20

Xb ,

XbNx10

= XbN1

=1

N1 +Nx10

Xb .

The handover gains are

GainWLAN0=Xb +

Nx20

Nx20 +N1

Xb

Xa,

GainWLAN1=

N1

Nx20 +N1

Xb

Xa.

Note that in the case we have two values for the low rate,then it might be beneficial for both WLANs to hand overnodes with both low rates, or it might be beneficial to handover only nodes with the lowest rate; this is illustrated in theinvestigations of Section V-C. The model presented above canbe used to calculate the gains for both cases, and select theoption that is better.

Moreover, although we do not provide a formal proof ofa theorem similar to the one in Section III-A, based onnumerical investigations, we conjecture that a similar resultholds. Namely, if there are gains in supporting handovers forsome subset of low rate nodes with a specific rate, then thesegain are maximized if handovers are supported for all low ratenodes with the same rate.

C. Three Access Points

We now consider the case where three access points, oper-ating on the same channel, are in the same contention area.Nodes Ny

0 that are clients of WLAN0 are closer to AP1, hencecan associate with it at high rate R, compared to the rate theyassociate to AP0. Also, nodes Nz

0 = Nx0 −N

y0 are closer to

AP2, hence can associate to it at a high rate R. In this scenario,there are three contending transmitters in the downlink, whichshare the channel in a fair manner.

8

Case a (no handover): The throughput of each access pointis

Xa =p

N0

N0+Nx0T (p,R) +

Nx0N0+Nx0

T (p, r) + 2 · T (p,R). (20)

Since all clients associated with AP2 are served at the samerate R, the duration that AP2 uses the wireless channel isequal to T (p,R); the same holds for AP1. On the other hand,the duration of time that AP0 uses the channel depends on themix of nodes with different transmission rates.

The throughput of a node in N0, Nx0 , N1, and N2 is

XaN0

= XaNx0

=1

N0 +Nx0

Xa ,

XaN1

=1

N1Xa , Xa

N2=

1

N2Xa ,

where Xa is estimated by (20).

Case b (handover of low rate nodes): Now we consider thecase where AP1 and AP2 serve the clients of WLAN0 whichare close to them. Hence, nodes Ny

0 are handed off to AP1

and nodes Nz0 are handed off to AP2. All nodes now connect

at rate R, hence the aggregate throughput of each access pointis

Xb =p

3 · T (p,R). (21)

The throughput of a node in N0, Ny0 , N1, and Nz

0 , N2 is

XbN0

=1

N0Xb , Xb

Ny0= Xb

N1=

1

Ny0 +N1

Xb ,

XbNz0

= XbN2

=1

Nz0 +N2

Xb ,

where Xb is estimated by (21).The handover gains are

GainWLAN0=Xb +

Ny0Ny0 +N1

Xb +Nz0

Nz0+N2Xb

Xa> 1 ,

GainWLAN1=

N1

Ny0 +N1Xb

Xa> 1 ,

GainWLAN2=

N2

Nz0+N2Xb

Xa> 1 .

Note that, as in previous scenarios, when N0 > 0 the handoverof all low rate nodes is always beneficial for WLAN0.

V. ANALYTICAL INVESTIGATIONS

In this section we present a series of analytical investigationsthat aim to identify the performance gains of handoversin different scenarios. First, we describe a more accurateestimation of the protocol overhead. Then we describe thenormalized gain metric used to evaluate the models presentedin the previous sections. Finally, we present numerical investi-gations identifying how various factors influence the incentivesfor supporting handovers and the corresponding gains. Thediscussion of the results also show how the model can beused to provide intuitive and insightful explanations for variousbehaviors.

A. Protocol Overhead Estimation

The 802.11 protocol overhead is estimated based on thetheoretical maximum throughput [25], which is more accuratethan the simple approximation in Section III-A. We considerthe standard DCF protocol without RTS/CTS (Request ToSend/Clear To Send)1. The time for transmitting one frameconsists of five components: TDIFS , TSIFS , TACK , TBO,and TDATA. The duration of the DIFS (DCF InterfameSpacing) and SIFS (Short Interframe Spacing) intervals aredefined by the standard. TACK is the time for transmitting anacknowledgement, which in 802.11a is transmitted with thesame transmission rate as a data frame, while in 802.11b it istransmitted at the minimum rate. TBO is the duration of thebackoff, which we discuss below. Finally, TDATA is the timefor transmitting one frame, which includes the MAC (MediaAccess Control) and physical layer headers, and the framepayload.

Based on the above, we can define T (p,R) that appears inthe models of the previous section as:

T (p,R) = TDIFS + TSIFS + TRACK + T p,RDATA .

Note that the backoff time TBO is not included in the aboveexpression, since the backoff from multiple frame transmis-sions are not independent, hence the backoff time is not anadditive quantity; this occurs because the backoff counter ofmultiple contending transmitters decreases simultaneously.

More specifically, when there is a single transmitter, theexpected backoff delay is equal to CWmin/2 time slots, wherethe minimum contention window CWmin and the time slotduration are defined by the standard. When there are multi-ple contending transmitters, their backoff counter decreasessimultaneously, since the backoff counter freezes when atransmission is sensed. Based on the above observation, whenthere are no collisions, the total backoff delay is independentof the number of contending transmitters, and depends onlyon the maximum number of frames a single transmitter sendsin the time interval over which the throughput is estimated.Hence, the backoff delay can be expressed as q · T 1

BO, whereT 1BO = CWmin/2 is the average backoff delay when there is

only one transmitter, and q is the maximum number of framessent by a single transmitter, in each transmission round of ourapproximation. The value of q is 1 for all the equations inSection III and Section IV, except for (13), (14) where q = θ.

Table I shows the values of TDIFS , TSIFS , T 1BO, TACK and

TDATA according to [25]. In all the experiments we considerpayload size p = 1500 bytes.

B. Evaluation Metric

The modelling framework presented in the previous sectionsestimates the gain that can be achieved when a WLAN acceptshandovers. The handover of low rate nodes is performed whenall of the involved WLANs improve their performance if theysupport handovers. In our evaluations we seek to determinehow well such a policy based on the models presented inthe previous sections performs. Hence, the evaluation metric

1The model can easily be extended to the case of RTS/CTS exchange.

9

TABLE IDELAY COMPONENTS FOR TRANSMITTING ONE FRAME (p IN BYTES, R IN MBPS).

TDIFS TSIFS T 1BO TACK TDATA

802.11b 50 10 310 304 192 + 8 · (34 + p)/R802.11a 34 9 67.5 20 + 4d22 + 8 · 14/(4 ·R)e 20 + 4d22 + 8 · (34 + p)/(4 ·R)e

should account both for accuracy of the handover decision,and the corresponding gains. Specifically, if we perform Kruns, then the normalized gain for WLANi is given by

NormGainWLANi =1

K

K∑k=1

xik , (22)

where xik is equal to the gain GainWLANi for run k ifhandovers are performed, and equal to 1 otherwise; hence, theabove metric captures both the performance of the handoverdecision policy and the corresponding handover gains. More-over, note that handovers are performed only if both WLANsobtain gains hence have the incentives to support them.

C. Investigations

In this section we perform a series of analytical investi-gations in order to identify the gains that can be obtainedusing handovers in different scenarios. The number of clientsof each WLAN is assumed to follow a normal distribution,whose average has default value µ = 6. If a WLAN has bothhigh and low rate clients, then the average number for eachis µ/2 = 3. For all types of clients, the variance is σ2 = 2.Also, we use equation (22) to compute the normalized gain,and consider K = 2000 runs for the same scenario.

1) Downlink traffic: Fig. 6 depicts the normalized gain for802.11b and 802.11a and various values of the low rate r, inthe case of downlink traffic (Section III-A). The rate R is equalto the highest rate supported by each protocol, 11 Mbps and54 Mbps for 802.11b and 802.11a, respectively. Both protocolsyield similar gains for the two WLANs, and the differences aredue to the different overheads. The handover gains for valuesof r smaller than 2 Mbps and 12 Mbps in 802.11b and 802.11arespectively, are significant. Moreover, observe that the gainsfor WLAN0, which is the WLAN with the low rate clients,Fig. 1, are significantly higher than the gains for WLAN1;this occurs because WLAN0’s low rate clients use WLAN1’sresources when they are handed over to AP1, Fig. 2.

Fig. 7 depicts the acceptance policy shown in (9) for802.11b, where however the factor c is estimated taking intoaccount the more accurate overhead estimation discussed inSection V-A. The slope of the lines in Fig. 7 corresponds tothe value of c. All combinations of N0, Nx

0 , N1 denotingpoints that are above the line are scenarios where handoversare beneficial for both WLANs. Observe that the numberof combinations for which handovers are beneficial becomessmaller, as the low transmission rate r increases.

Fig. 8 shows the normalized gain for WLAN1 as a functionof the number of WLAN0’s low rate clients that are handedover to AP1. Observe that the dependence is not monotonous,and it can happen that the gain initially decreases and thenincrease as more low rate nodes are handed over to AP1;

Fig. 6. Downlink traffic in 802.11a/b. WLAN0 gains more than WLAN1

which accepts the handed over nodes.

Fig. 7. Acceptance policy for downlink traffic in 802.11b. Combinations ofnodes above the line correspond to scenarios where handovers are beneficial.

this behavior is a result of two factors: Improved performancewhen the number of low rate nodes is reduced and increasedshare of WLAN1’s resources used by the handed over nodes.Figure 8 shows that, for N0 = 10, Nx

0 = 4, N1 = 10, whenone or two low rate nodes are handed over to AP1 the secondfactor is more significant, resulting in a reduction of WLAN1’sperformance. On the other hand, when three or four nodes arehanded over the first factor becomes more significant, resultingin an improvement of WLAN1’s performance.

2) Case where WLAN0 has only low rate clients: Fig. 9shows the normalized gain when WLAN0 has only low rateclients, which is the special N0 = 0 considered in Sec-tion III-A. The figures show that the handover gains in thiscase are significantly higher compared to the case whereWLAN0 had both high and low rate clients; this occurs becausewhen WLAN0 has only low rate clients, all transmissionsfrom AP0 involve low rate transmissions, which results in asignificant reduction of the throughput for all nodes. Moreover,Fig. 9 shows that the gains for both WLAN0 and WLAN1 isthe same; this occurs because in this case, when handovers aresupported, all nodes are served by AP1.

10

Fig. 8. Normalized gain for WLAN1 as a function of the number of WLAN0’slow rate nodes handed over to AP1.

Fig. 9. Case when WLAN0 has only low rate clients, downlink traffic,802.11b. The gains for both WLANs are the same and significantly highercompared to where WLAN0 has both high and low rate clients.

3) Uplink traffic: Fig. 10 shows the normalized gain inthe case of uplink traffic (Section III-E). Unlike the caseof downlink traffic, in the uplink case the normalized gainis the same for both WLANs. This occurs because in theuplink direction all nodes contend for the channel and thebandwidth is shared among the nodes associated to bothAPs. Additionally, note that the normalized gain in the uplinkdirection is closer to the higher of the two normalized gains(that of WLAN0) in the downlink direction.

4) Effects of the node density: Next, we investigate how thenode density affects the handover gains. In this scenario weconsider the case of downlink traffic, and that only WLAN0

Fig. 10. Uplink traffic in 802.11a/b. The gains for both WLANs are thesame.

(a) Effects of the average node density. σ2 = 2

(b) Effect of the variance of the node density. µ = 6

Fig. 11. Effect of the node density.

has low rate nodes with r = 1 Mbps.Fig. 11(a) shows how the normalized gain is influenced

by the average node density, when the variance is σ2 = 2.Observe that the normalized gain increases slightly when theaverage number of nodes is small, and then remains constant.On the other hand, Fig. 11(b) shows that the normalized gaininitially decreases when the variance increases, but remains thesame for a variance higher than σ2 = 10. The above resultssuggest that the handover gains remain significant for differentnode densities.

5) Wired capacity constraints: Fig. 12(a) shows the han-dover gains for different capacity constraints of AP1’s wiredconnection to an external network, when AP0 does not havesuch a constraint (Section III-B). When the capacity constraintCAP1

is small, then the handover gain for WLAN1 is verysmall. On the other hand, when CAP1

is higher than ap-proximately 17 Mbps, which is larger than AP1 throughputshare when there are two contending access points, then thewireless network is the bottleneck, and the wired capacityconstraint does not influence the gains. For intermediate valuesof the capacity constraint CAP1

, the gain for both WLAN0 andWLAN1 increases as the constraint increases.

Fig. 12(b) shows the opposite case, where only AP0 hascapacity constraints. The normalized gain for WLAN0 stillhas a monotonous behavior as CAP0 increases. On the otherhand, the normalized gain for WLAN1 now depends on twofactors that have an opposite influence: The first is the increaseof the traffic transmitted by AP0 as its capacity constraintincreases, which results in more low rate traffic transmitted in

11

(a) Capacity constraint CAP1for AP1.

(b) Capacity constraint CAP0for AP0.

Fig. 12. Influence of capacity constraints. 802.11a, r = 6 Mbps.

Fig. 13. Client differentiation by AP1 in 802.11b.

the network, which in turn makes handovers more beneficial.The second is that as the capacity constraint CAP0 increases,then AP1 uses a smaller percentage of the wireless resources.The first factor has a larger effect when CAP0

is smaller thanapproximately 9 Mbps, whereas the latter factor has a largereffect when CAP0

larger than 9 Mbps.6) Client differentiation: Fig. 13 shows the normalized

gain when AP1 differentiates WLAN1 and WLAN0 clientsthat are handed over, by transmitting η > 1 frames fromclients of WLAN1 for every frame from clients of WLAN0

that are handed over to it (Section III-D). The results includethe case of a linear utility, where the WLANs value theaggregate throughput achieved by their clients, and for the caseof a logarithmic utility where more value is given to lowerthroughputs. As expected, the normalized gain for WLAN1

Fig. 14. Swapping low rate nodes. 802.11b.

increases as η increases, since more traffic from WLAN1

clients are transmitted. When the utility is a linear function ofthe throughput, then as η increases, the gains for both WLANsconverge to the same value. However, when the utility is alogarithmic function of the throughput, the gains for WLAN1

can exceed those of WLAN0 as η increases; this is because asη increases, the throughput achieved by the clients of WLAN0

that are handed over to AP1 is reduced, resulting in a loweraggregate utility for WLAN0, compared to that of WLAN1.

7) Swapping low rate nodes: Fig. 14 shows the symmetricscenario where the access points swap low rate nodes (Sec-tion IV-A). Comparison of this figure with Fig. 6 shows thatwhen WLANs swap low rate nodes, the gains they can achieveare higher and more balanced.

8) Two low rates: In Fig. 15 we show the gains for thescenario where there are two sets of low rate nodes, with adifferent rate (Section IV-B). We assume that the nodes inthe first set connect at r1 = 1 Mbps while those in the otherset connect at either r2 = 2 Mbps or r2 = 5.5 Mbps. Weinvestigate whether it is better to hand over all low rate nodesor only the nodes that connect at the lowest rate r1. The resultsshows that it is best for WLAN1 is to accept all low rate nodeswhen r2 = 2 Mbps, and to accept only the nodes that connectat r1 = 1 Mbps when r2 = 5.5 Mbps. On the other hand, forWLAN0 it is always better to hand over all its low rate clientsto the neighboring AP.

The above results show that, in the case of multiple lowrates, it is not always beneficial to handover nodes with allthe different low rates; the model presented in Section IV-Bcan be used to decide which low rates are beneficial for anaccess point to accept.

9) Three access points: Fig. 16 depicts the results for thecase of three access points (Section IV-C). The performancegains are higher compared to the case of two access points,Fig. 6, since both WLANs now have low rate clients, andbenefit from handing off these clients.

10) Estimation error: The handover decision model pre-sented in Section III-A requires estimating the transmissionrate with which low rate clients can associate to the visitingaccess point. Errors in estimating this transmission rate canaffect the performance gains. To investigate this influence, weconsider the scenario in Figs. 1 and 2, where the high ratenodes in N0 and N1 are associated with access points AP0

12

Fig. 15. Mix of low rate nodes where r1 = 1 Mbps in 802.11b.

Fig. 16. Three access points in 802.11b.

and AP1 at transmission rate 54 Mbps, where nodes in Nx0

are associated to AP0 at rate 6 Mbps.Access point AP1 estimates the rate at which nodes in

Nx0 can associate to it, by measuring the received signal

strength and inferring the corresponding transmission rate;The minimum signal strength to achieve transmission rate6,9,12,18,24,36,48,54 Mbps is considered to be -88,-87,-85,-84,-83,-80,-76,-71 dBm respectively. Errors are modelled byassuming that the measured signal strength follows a normaldistribution, with an average equal to the above minimumsignal strength for the corresponding transmission rate, anddifferent values of the standard deviation. Fig. 17 shows howthe errors in estimating the received signal strength, hence theerrors in estimating the transmission rate with which the nodesin Nx

0 can associate to AP1, influence the gain for WLAN1.Observe that the average gains show a small dependence on theerror in estimating the received signal strength; this is the casebecause errors in deciding when to support handovers occurwhen the corresponding gains are small, hence the overallinfluence on the normalized gain is small.

VI. EVALUATION

In this section we evaluate the accuracy of the proposedmodel using simulation and test-bed experiments.

A. Simulations

First, we present simulation results using NS-2 (NetworkSimulator 2). The default version of NS-2 does not supportmultiple rates for transmissions between one transmitter and

Fig. 17. Gain for WLAN1 as a function of the standard deviation of the errorin estimating the received signal strength.

multiple receivers. Hence, we extended NS-2 to support mul-tiple rates by adapting the transmission rate according to thesignal strength of the last received frame. We simulate thetopology in Figs. 1 and 2 for 802.11b. The low rate r is 1 Mbpsand the high rate R is 11 Mbps. We performed experimentsfor a different number of nodes in N0, Nx

0 and N1, assumingthat each AP serves up to 10 nodes; this resulted in a total450 scenarios. Fig. 18(a) compares the normalized gain givenby NS-2 when using the handover policy given by (9), wherehowever the factor c is computed using the more accurateprotocol overhead estimation discussed in Section V-A, withthe gain given by NS-2 when using an oracle that accuratelypredicts when a handover is beneficial, and with the analyticalmodel; this figure shows that both the analytical model andthe proposed handover acceptance policy achieve performancethat is very close to that optimal performance achieved by anoracle, that accurately knows beforehand when handovers arebeneficial. Fig. 18(b) shows the gain for WLAN1 for each ofthe scenarios. This figure also shows that using the proposedmodel for deciding whether to support handovers results inonly 9 false negatives and 2 false positives; moreover, thecorresponding gain in the scenarios with a false prediction isvery close to one, hence the false predictions have a smallinfluence on the average performance across all scenarios.Finally, Fig. 18(c) shows the cumulative distribution of thenormalized gains for WLAN0 and WLAN1; note that morethan 60% of the scenarios yield a gain of more than 230%for WLAN0, and 50% for WLAN1.

B. Test-bed experiments

Next we evaluate the accuracy of the proposed modelusing experiments in an actual test-bed. We implemented thescenario shown in Figs. 1 and 2, for 802.11b and N0 = Nx

0 =N1 = 1; this involved three wireless clients and two Cisco’sAironet 1240AG access points. The low rate r was manuallyset to 1, 2 and 5.5 Mbps, and the high rate R was set to11 Mbps. Fig. 19 compares the average gain of WLAN1, fordifferent values of the low rate r, measured on the test-bedand estimated using the analytical model; the figure showsthe average of five runs, and the 90% confidence interval.The experimental results show that there is an excellent matchbetween the two. Although the experiments presented above

13

(a) Comparison from NS-2 with handover prediction model, NS-2 withoracle, and analytical model.

(b) Gain for WLAN1, and false positives and false negatives.

(c) Cumulative distribution function for the handover gains.

Fig. 18. Evaluation of proposed model using simulation.

are for a small number of nodes, the scenario consideredcan be common in practical situations; moreover, in the caseof downlink traffic, the access points contend for channelaccess, hence the number of contending devices (access points)remains the same when the number of end nodes increases.

VII. IMPLEMENTATION

The handover decision model presented in Sections II andIII requires knowledge of the number of nodes associatedwith a WLAN’s access point, the nodes that are in the samecontention area, their transmission rate, and the transmissionrate if low rate nodes associate with a visiting access point. Thenumber of nodes, assuming there are no hidden terminals, canbe obtained using passive measurements, Fig. 20, by countingthe number of unique MAC addresses. The transmission rateto/from nodes can be obtained from 802.11’s PLCP (PhysicalLayer Convergence Protocol) header, when nodes are inside an

Fig. 19. Comparison of test-bed results with analytical model.

Fig. 20. Handover decision procedure.

access point’s range. If some nodes are hidden from an accesspoint, then the information for these hidden nodes needs tobe communicated, either directly between access points, orthrough some central server; the latter can be the case, e.g.,when home users are subscribers of the same provider, whichmanages the wireless access points on behalf of its subscribers.

The last parameter that needs to be estimated is the transmis-sion rate if low rate nodes are associated with a visiting accesspoint. This can be estimated by measuring the received signalstrength of packets to estimate the corresponding transmissionrate. To perform the above passive measurements, an accesspoint can either use a virtual interface or a separate wirelessadapter, set to monitoring mode.

Upon identifying that handovers are beneficial, an accesspoint can proceed to allow nearby clients of other WLAN’s toassociate to it. This can be achieved, without a change at thewireless nodes, by using the same SSID (Service Set Identifier)as the neighboring/home access point. Moreover, to addresssecurity concerns, access to visiting nodes can be offered usinga virtual interface at the access point, whereas normal securitymechanisms can be used for a WLAN’s own clients.

The handover decision procedure depicted in Fig. 20 hasbeen implemented in a prototype, which supports the prac-ticality of the implementation approach described in thissection, and demonstrates2 the handover gains presented inthe previous section.

VIII. CONCLUSION AND FUTURE WORK

The key contribution of the paper is to develop and evaluatea model for identifying and estimating the incentives andgains for supporting handovers in an environment where self-interested WLANs coexist in the same area. The self-interestedWLANs seek to improve the performance of their clients,hence the incentives for supporting handovers are induced

2The prototype implementation was demonstrated at the 5th ACM Interna-tional Workshop on Wireless Network Testbeds, Experimental evaluation andCharacterization (WiNTECH 2010), collocated with ACM Mobicom 2010.

14

solely by the corresponding performance gains. We havepresented results from numerical investigations, simulation in-vestigations, and experiments showing that significant perfor-mance gains can be achieved by exploiting the performance-induced incentives for supporting handovers. Finally, our pro-totype implementation verifies the practicality of the proposedhandover decision policy.

An assumption we have made is that access points are inthe same contention area. If this does not hold then there canbe hidden terminals and contention asymmetries, which fordownlink traffic require a more detailed throughput estimationmodel than the one considered in this paper. Note, however,that for uplink traffic handovers are always beneficial, hencethe corresponding handover decision policy is not affected byhidden terminals or contention asymmetries.

Future work involves investigating other environmentswhere performance-induced incentives arise, such as in thecase of relaying traffic in multihop wireless networks. Akey requirement in such an investigation is the developmentof a simple and accurate model for estimating the end-to-end throughput, while capturing contention asymmetries [26];initial work in developing such a simple end-to-end throughputmodel is presented in [24]. Also interesting is to investigatehow technologies such as 802.11n, which exploits channelbonding to increase the wireless bandwidth, and cognitiveradio, which allows opportunistic access of the wirelessspectrum, influence the incentives for cooperation and thecorresponding performance gains.

ACKNOWLEDGMENTS

This work was supported in part by the European Commis-sion in the 7th Framework Program through project EU-MESH(Enhanced, Ubiquitous, and Dependable Broadband Accessusing MESH Networks), ICT-215320, http://www.eu-mesh.eu

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15

APPENDIX

Theorem. Consider the model presented in Section III-A,Figs. 1 and 2, and assume that N0, N

x0 , N1 > 1. If there are

gains for WLAN1 when a subset of WLAN0’s low rate clientsare handed over to AP1, then these gains are maximized if allof WLAN0’s low rate clients Nx

0 are handed over to AP1.

Proof: Let Ny0 , Nz

0 be two non-overlapping and non-empty sets of low rate clients of WLAN0, which satisfy Nx

0 =Ny

0

⋃Nz

0 .Let Gainall

WLAN1be the gain for WLAN1 when all low rate

clients Nx0 of WLAN0 are handed over to AP1. Gainall

WLAN1is

given by (8).Let Gainsome

WLAN1be the gain for WLAN1 when only the Ny

0 ⊂Nx

0 low rate clients of WLAN0 are handed over to AP1. Thethroughput Xb,some of each access point when only the Ny

0 ⊂Nx

0 low rate clients of WLAN0 are handed over to AP1 isgiven by

Xb,some =p

N0

N0+Nz0T (p,R) +

Nz0N0+Nz0

T (p, r) + T (p,R),

and the corresponding gain GainsomeWLAN1

is

GainsomeWLAN1

=

N1

Ny0 +N1Xb,some

Xa,

where Xa is given by (3). Handing over a subset of the lowrate clients is beneficial if Gainsome

WLAN1> 1, which after some

simplifications gives

GainsomeWLAN1

> 1⇔

N1

(N0 +Ny0 +Nz

0 )>

(2N0 +Nz

0

(T (p,r)T (p,R) + 1

))N0

(T (p,r)T (p,R) − 1

) ,

which is equivalent to

N1

(T (p, r)

T (p,R)− 1

)>

2(N0 +Ny0 +N

z0 ) +

Nz0N0 +Nz0Ny0 +Nz0

2

N0

(T (p, r)

T (p,R)+ 1

)(23)

We want to prove that if GainsomeWLAN1

> 1, then GainallWLAN1

>Gainsome

WLAN1. The latter is equivalent to

GainallWLAN1

GainsomeWLAN1

> 1⇔

(Ny0 +N1)[

N0N0+Nz0

T (p,R) +Nz0

N0+Nz0T (p, r) + T (p,R)

]2T (p,R)(Ny0 +Nz0 +N1)

> 1⇔

(Ny0 +N1)[2N0 +Nz0

(T (p,r)T (p,R)

+ 1)]

2(Ny0 +Nz0 +N1)(N0 +Nz0 )> 1⇔

N1

(T (p, r)

T (p,R)+ 1

)> 2(N0 +N

y0 +N

z0 )−N

y0

(T (p, r)

T (p,R)+ 1

).

Note that all variables are positive numbers. Hence, it iseasy to see that the last inequality, which is equivalent toGainall

WLAN1> Gainsome

WLAN1, is true if the inequality (23), which

is equivalent to GainsomeWLAN1

> 1, is true.