Heterogeneous Access Network(s) Selection inMulti-Interface Radio Devices

Deepak K Tosh, Shamik SenguptaDepartment of Computer Science & Engineering

University of Nevada, RenoEmail: dtosh@unr.edu, ssengupta@unr.edu

Abstract—The advent of multi-interface smart radio devicesbrings the flexibility of simultaneous access to multiple het-erogeneous access networks (ANs) for making a significantimprovement in the network utilization by balancing the networkload and avoiding congestion. However, each heterogeneousaccess technology poses its own constraints in terms of datarate, coverage, availability, latency, packet loss rate, usage priceetc. Thus, a novel selection mechanism must be devised toexploit the “best” available access network(s) to best serve thewireless users. Assuming users can ask for a required amountof bandwidth from the ANs, we model the heterogeneous accessnetwork selection mechanism from a game theoretic perspectiveby formulating a user preference based utility expression usingthree major parameters: expected data rate, latency, and usagecost. Then we analyze the utility model to find the users’ optimalbandwidth demands from the selected ANs that maximize theirnet payoff. Theoretical analysis of the utility expression proves theexistence of optimal bandwidth demand in the single and multiplenetwork selection, and we derive the open/closed form expressionfor optimal bandwidth too. The results from the simulationsconducted corroborate the theoretical optimal bandwidth andnumber of packets assigned for the selected network(s) with thecorresponding experimental values.

Index Terms—Heterogeneous Access Network, Game Theory,Multi-interface Radios, Access Network Selection

I. INTRODUCTION

Proliferation of wireless access technologies (WiFi, UMTS,3G, HSPA, LTE, WiMAX etc.) and ever-growing demand ofnew applications/services is hinting to exploit all the availableaccess networks simultaneously for providing high throughput.As the coexistence of different radio access technologiesis more a reality rather than a hypothesis, the smart radiodevices with multiple radio interfaces, will face the chal-lenge of exploiting multiple available wireless technologiessimultaneously, adapting to the dynamic availability of theaccess networks. The parallel access [1] to multitude of accessnetworks will significantly improve the network utilization,overall network latency, and provide robust and ubiquitousconnectivity for the radio devices. The data-intensive appli-cations [2] can perform parallel data communication usingmultiple flows [3] to various ANs, which thereby improvesthe average throughput, reliability of data delivery, and robustconnectivity of the radio systems at minimum network delay.To provision such services through multiple wireless ANs,effective quantification models are required for classifyingand measuring their offered service opportunities. Using thesemodels, an affordable set of ANs can be selected dynamically

based on users’ requirements by resolving the trade-off be-tween their preferences and profitability of service providers.

As the heterogeneous access networks offer services ofdistinct data rate, interference temperature, reliability, usageprice, etc., the users might not get all favorable conditionsin the period of their service. For instance, one technologymight provide better throughput, but consume more energy,whereas another might offer reliable data delivery but chargea high price. Also, the users might experience high congestionas the number of devices that select the same AN increases,or bandwidth demands for the AN increases. To analyze thisconflict, we model the access network selection mechanismas a non-cooperative game by formulating a user preferencebased payoff function, governed by the following parameters:expected link capacity, cost of usage, and latency. Then, wefind the optimal amount of bandwidth to be asked for a usersuch that its expected overall utility is maximized.

As far as access network selection mechanisms are con-cerned, many works focus on single access network selection,where mobile users face challenges to choose one amongmultiple access networks (see survey [4] and the referencestherein). Dynamic single AN selection among WLAN andcellular system has been studied in [5] using preferencesevaluation techniques such as AHP and GRA. A utility andgame theory based AN selection scheme is proposed in [6]by considering various traffic classes and mobility, where thenetwork preference cooperative game is solved to find theNash Equilibrium (NE) strategy. To receive best services fromcandidate ANs like WCDMA, WLAN and WiMAX, authorsof [7] have presented a game having a weighted-sum payofffunction that considers service type, user preference, trafficstate and signal strength, mobility, and battery drainage. Thenetwork with highest payoff then serves a particular servicerequest of the user. In [8], the authors have proposed an inter-face selection scheme considering battery power consumption,and user mobility parameters of the overlaying networks toimprove users’ quality of service (QoS) at minimum hand-overs. Authors of [9] have modeled the game of AN selectionas a Bayesian game, where the players are the users in aparticular area with actions as the probability with whichthey will be selecting a network and solved for the BayesianNE by analyzing the best response dynamics. An automaticnetwork selection mechanism is designed in [10] by consid-ering the end-user’s preference, link quality, and cost in their

utility function. Authors of [11] have studied the dynamics ofend users and network operators by devising non-cooperativegames with different cost functions and evaluated in terms ofprice of anarchy and price of stability.

The past literatures on heterogeneous AN selection havepresented approaches of single-criteria optimization, and gametheoretic solutions to select the single best suitable AN. Theutility framework presented in previous works are formed byconsidering either bit error rate or interference constraintsof the ANs, however the major parameters such as networklatency, monetary cost of usage, link capacity, etc., have notbeen utilized. Moreover, the scope of simultaneous accessto multiple networks by the multi-interface radio nodes formaximizing the overall data delivery rate is still open toresearch. Also, no work has undertaken the ability of radiodevices to demand a flexible amount of bandwidth basedon their application requirements. Therefore, our first stepto achieve the above untouched goals is to design a robustutility/preference function which involves the above mentioneddecision parameters. As the futuristic multi-interface devicescan access multiple ANs simultaneously with the help of mul-tipath TCP protocol [3][12], the challenges of multi-criteriabased selection of one or more ANs need to be addressedthoroughly. In this paper, we study the dynamic multiple ANselection problem from a game theoretic perspective usingthe robust utility function and find the optimal bandwidthdemands from the selected ANs such that users’ net benefit ismaximized. The game is analyzed to derive the open/closedform expressions for the optimal bandwidth demands and thesimulations are conducted to verify the theoretical analysis.

The rest of the paper is organized as follows: the systemmodel is presented in section II. The network selection gamealong with the individual components of utility expression aredescribed in section III. Section IV presents the theoreticalanalysis to find the optimal bandwidth demand for bothsingle network selection as well as two networks selection.The simulation results are reported in section V. Concludingremarks with future directions are briefed in the section VI.

II. SYSTEM DESCRIPTION AND ASSUMPTIONS

We consider a heterogeneous access network scenario whereM access networks are available and offer distinct servicesat a flexible price. To take advantage of such opportunities,N multi-interface radio devices compete among each otherfor accessing either one or a subset of M access networks(AN). Each radio device i (1 ≤ i ≤ N ) is equippedwith multiple radio interfaces and possesses the capabilityof accessing multiple ANs simultaneously provided that eachinterface can operate on exclusively one wireless AN. Figure 1depicts a scenario, where multiple access networks such asWiFi, WiMAX, and cellular network coexist in a given region,and the radio nodes have options to choose one or multipleANs. Hence the data communication between radio nodescan be parallelized using multiple paths via different accessnetworks, and thereby the individual as well as system levelthroughput can be improved. The reachable ANs provide

Fig. 1: A typical Heterogeneous Access Network Scenario

different service opportunities at different costs; for example,WLAN provides the cheapest shared wireless medium whichis prone to interference, whereas LTE and WiMAX providededicated connectivity with high service cost. Thus, the radionodes face a decision situation of choosing the appropriateANs based on their application requirements and offeredQoS of ANs. Given the flexibility of accessing multiple ANssimultaneously, it is assumed that radio systems can demandflexible amounts of bandwidth from the network operators torun their spectrum sensitive applications efficiently. To resolvethe trade-off between network resource utilization and usersatisfaction, we devise a game theoretic utility model, wherethe candidate access networks are evaluated and selected basedon the users’ rewards obtained for their bandwidth demands.

To limit the bandwidth over-utilization, we assumed a costmodel for each AN as a function of bandwidth demand. Thegreedy nature of radio devices to achieve high data rate bydemanding high bandwidth may not be satisfied due to theprice constraints and high chances of colliding with othercompeting nodes. Hence the expected data rate of an ANdecreases as the total interference (

∑j 6=i Ij) increases due to

many users sharing the same medium. Therefore, the wirelessusers look forward to choosing multiple ANs in such a waythat they receive higher data rate and at the same time thecost of usage is minimized for their bandwidth demands.The expected data rate to user i for accessing network mcan be computed using Shannon’s capacity theorem which ispresented in Eqn.(1), where Pm is the received signal strength,Nawgn is the additive white Gaussian noise (AWGN), and Bimis the allocated bandwidth to user i. Thus the throughput ofthe user i depends on how many other devices choose thesame AN m and the amount of bandwidth asked (Bim). Withthe estimated value of link capacity under a particular signal-to-interference-noise ratio (SINR) value, the factors like end-to-end time delay, and monetary cost of usage per unit databyte and unit time can be computed for finding the overallpreference value of the candidate ANs.

E[Cim] = Bim log

(1 +

PmNawgn +

∑j 6=i, Ij

)(1)

III. NETWORK SELECTION GAME FORMULATION

The problem of single or multiple AN selection is modeledas a non-cooperative game G(N,S, U) in which N multi-interface radio devices act as players, and the strategy profile

S = {S1, S2, ..., SN} represents the strategy set of each player,where Si constitutes the set of ANs, out of M available ANs,that player i chooses to associate with, and 1 ≤ |Si| ≤ M .The game is played in a simultaneous and uncoordinatedmanner, where the players receive a reward at the end of gameinteraction depending on their own action and other players’choices too. If user i’s strategy is same as all other playersj 6= i, then user i either incurs high cost or communicates ina highly congested wireless medium at low cost. Additionally,if all the users demand more bandwidth from the same AN,then they might have to share the medium so that the resourceoutage scenario can be avoided. Hence the utility reward toone player is guided by not only its own action but also actionsof all other players too. Therefore, the trade-off between users’willingness to pay and satisfaction on access link performancehas to be resolved in the network selection game wherethe payoff function for player i can be formulated basedon following network related QoS factors: estimated end-to-end latency, expected capacity, and monetary cost involvedfor using an AN. In a real-world deployment, the formertwo parameters can be estimated using Shannon’s theorem,where SINR can be estimated using awgn SINR estimationtechniques [13], and latency can be computed dependingon the packet size and previously estimated link capacity.In the following subsections, we detail the payoff functionformulation using the above mentioned parameters via a cost-benefit approach and describe the underlying optimizationproblem for the ANs selection.

A. Utility reward

To model the reward function, we assume that user irequires transfer of a file of size F in a cost-effective wayvia the selected subset of access networks. Let’s denote theallowed packet length of AN m as Lm bytes and the user idecides to send T im number of packets via network m, whereT im > 0. For player any radio node i ∈ N , the total file transfertime using network m is indirectly proportional to the expectedlink capacity E[Cim]. Therefore, the end-to-end delivery timeof a packet will be high, if the capacity of the link is low.For successfully delivering a single packet to a destinationradio node using AN m, the estimated duration will be Lm

E[Cim] .

We devise a Sigmoidal QoS function in terms of end-to-end delivery time, which explicitly emphasizes how good thelink capacity is on an average. If the average delivery time(tiavg) of player i to transfer T im packets is close to maximumtime (timax), then the QoS function returns low reward value,whereas the reward gain is high when the average delivery timeis minimal. The reward gain to user i after selecting subset ofANs Si, can be expressed as

Gi(Si, S−i) =1

1 + e

(bitiavg(Si,S−i)−

timax2

) (2)

where, bi > 0 is the weight coefficient that definesthe steepness of the reward function. tiavg(Si, S−i) =1|Si|∑m∈Si

T imLm

E[Cim(m,S−i)]

is the average time spent for sending

the whole file of size F via the set of ANs selected (Si), andtimax is the time taken to send the whole file of size F bytesof data via the weakest link only.

B. Monetary Cost/Price Function

In the current data services scenario, the providers offera minimum bandwidth for a constant price. However, in thefuturistic pricing model, when the radio nodes demand morebandwidth as per their requirements, we assume that the priceper unit bandwidth and unit time will increase depending onANs’ service qualities. For example, the WiFi service offersthe cheapest data service at low usage cost; the increasein bandwidth demand may not drastically increase the cost,rather the SINR value of the wireless medium might decreaseexponentially, due to the shared nature of WLAN medium. Onthe other hand, the cellular or hybrid access networks suchas LTE and WiMAX technologies are more reliable in termsof congestion and interference, so the cost of usage per unitbandwidth demand is very high compared to WLAN.

To design such cost functions for the above mentionedANs, we assume that each AN m asks a constant price ofKm units per bytes of data per unit time, until the player i’sbandwidth usage is under a minimum value (Bminm ). As theradios can demand a flexible amount of bandwidth, the rationalANs will definitely charge high as the demand increases. InWLAN technology, cost of access should not be high ondemanding more bandwidth as it may not drastically increasethe throughput. Therefore, the cost function can be modeledas a slow starting function like linear, or piece-wise linear.However, high bandwidth in LTE and WiMAX networkscan make significant improvements in throughput due to lowcontention probability, hence the providers may model the costfunction as any sharp increasing function, but not only limitedto exponential or quadratic. Assuming a linear cost function forWLAN and exponential cost function for the cellular/hybridaccess networks, when the player i demands bandwidth Bimsuch that Bminm < Bim ≤ Bmaxm , the cost function can beexpressed in Eqn.(3), otherwise Ki

m = Km,∀m ∈M .

Kim =

{Km + cma

αmBim

m if m ∈ {LTE, WiMAX}Km + cmB

im if m ∈ WLAN

(3)

where, cm, αm > 1 are the cost coefficients of AN m, andam is the cost exponent decided by the provider of AN m.

Assuming user i will be charged based on the number ofbytes it pushes onto the selected links, and period of linkusage, the estimated cost of usage charged to user i fortransacting total T imLm bytes of data with AN m can be

Ci(Si, S−i) =∑m∈Si

(T imLm)2

E[Cim(m,S−i)]Kim (4)

C. Overall Payoff Expression

The defined components represent various dimensions ofmeasuring QoS from the users’ perspective, however theseparameters are not only limited to only three. In formulatingthe overall payoff expression, the radio terminals always aim

to find a subset of ANs that can provide better link capacityat a minimum cost, so that the end-to-end delivery delay isminimum. In this work, we assume that the transmit power inindividual access networks is constant and maximum as perstandard. As each player i ∈ N has the privilege of demandingmore bandwidth and can decide what percentage of packets itwants to send through a particular AN, the aggregate utilityfunction of player i (Ui) is a function of demanded bandwidths{Bim : m ∈ Si} and number of packets (T im) it wants topush through network m. The aggregate utility expression aftersubtracting the usage cost for the complete transaction can beexpressed as

Ui(Si, S−i) =ai

1 + e

(bitiavg−

timax2

) −∑m∈Si

(T imLm)2Ki

m

E[Cim(m,S−i)]Ftimax

where, ai is the scaling constant,∑m∈Si

T imLmi= F , and

timax is the maximum time consumed to transfer the completefile. The optimization problem is to find the optimal bandwidthdemand vector {(Bim)

∗: m ∈ Si} for the selected ANs, which

maximizes the aggregated utility Ui(Si, S−i) of player i.

IV. THEORETICAL ANALYSIS

Without loss of generality, here we analyze the aggregatepayoff expression from player i’s perspective to find the opti-mal amount of bandwidth from the set of selected ANs, suchthat the aggregate utility is maximized. First, we analyze tofind the optimal bandwidth demand theoretically by selectingonly single AN from the set of N networks. Then we prove theexistence of an optimal bandwidth demand (Bim)

∗ is provedfor two selected ANs, assuming the number of packets sent(T im) via AN m is constant.

A. Single Network Selection

Considering the single network selection scenario, where theradio node can select one network from the set of available net-works, we now analyze to obtain optimal bandwidth demand(Bim)

∗ for WLAN and LTE/WiMAX scenario. To find (Bim)∗,

we equated the first order partial, ∂Ui

∂Bim

to zero and solved tofind (Bim)

∗. As per our assumption on WLAN environment,the cost is a linear function presented in Eqn.(3), whereasthe SINR degradation varies exponentially. The expression for(Bim)

∗ in WLAN is not in a closed form, rather the open formsolution is given in Eqn.(5).[(

E[Cim]

Bim− Bim10SINRmSINRm log(10)

10(1 + SINRm)κ

)×(

(Rim − 1)

(Rim)2+

Kim

timax

)]− E[Cim]cm

Bdiffm timax= 0 (5)

where, SINRm(dB) varies exponentially according toe(B

maxm −Bm)/κ, Bdiffm = Bmaxm − Bminm and Rim = 1 +

e

(biT

im−

timax2

).

Numerical analysis can be made to find the critical B∗mby varying the bandwidth demand so that Eqn.(5) is satisfied.We also find the generic open form solution for the optimal

bandwidth demand in case of LTE/WiMAX access technologyby equating the first order differential to zero, which ispresented as Eqn.(6).[(

E[Cim]

Bim− Bimκ1

(1 + SINRm)

)×((Rim − 1)

(Rim)2+

Kim

timax

)]−[E[Cim] log(am)a

Bimαm

m

αmadiffm timax

]= 0 (6)

where, SINRm(m ∈ {WiMAX, LTE}) varies linearlyaccording to the following equation, SINRm(dB) =

κ1(Bmaxm − Bm) + κ2 and adiffm = a

αmBmaxm

m − aαmB

minm

m .After finding the critical bandwidth demands using numericalanalysis, we conducted the second derivative test and found

that(

∂2Ui

∂Bim

2

)Bi

m=(Bim)∗

< 0, for both the considered scenar-

ios, which proves the critical points are maxima.

B. Two Network Selection

For the sake of showing the existence of optimal bandwidthdemand while selecting multiple access networks, we considertwo networks for simultaneous access. Using the similarapproach, we equate the first order differential of Ui w.r.tB1, B2 by considering WLAN and LTE/WiMAX to zero forfinding the optimal bandwidth demands and the open formconditions are presented in Eqn.(7) and Eqn.(8).[(

E[Ci1]Bi1

− Bi110SINR1SINR1 log(10)

10(1 + SINR1)κ

)×(

bi(Riavg − 1)

2(Riavg)2

+T i1L1K

i1

timax

)]− T i1L1E[Ci1]c1

Bdiff timax= 0 (7)

[(E[Ci2]Bi2

− Bi2κ1(1 + SINR2)

)×(bi(R

iavg − 1)

2(Riavg)2

+T i2L2K

i2

timax

)]−[T i2L2E[Ci2] log(a2)a

Bi2α2

2

α2adiff2 timax

]= 0 (8)

where, Ravg = 1 + e

(bit

iavg−

timax2

)and using similar nu-

merical analysis approach we can find the optimal bandwidthdemand by keeping the number of packets fixed for bothnetworks. The simulated results have been reported in the nextsection, where we could explicitly find the optimal bandwidthdemands for the selected networks. Similar approach can beused to generalize the theory for selecting more than twonetworks to find the optimal bandwidth demands for theselected ANs.

V. RESULTS AND DISCUSSION

To simulate the heterogeneous access network selection,we consider the following three wireless access technologies:WLAN, LTE, and WiMAX. In the non-cooperative game, weassumed that the multi-interface radio nodes can decide toselect either one or two best networks from the available ANs.The players evaluate the aggregate utility based on the numberof ANs they select. The simulations were conducted in Matlab

0 10 20 30 400

0.2

0.4

0.6

0.8

1

Bandwidth Demand (in MHz)

No

rma

lize

d C

os

t

WLAN

WiMAX

LTE

(a)

0 10 20 30 400

5

10

15

20

25

30

35

Bandwidth Demand (in MHz)

SIN

R (

in d

B)

WLAN

LTE

WiMAX

(b)

Fig. 2: (a) Cost/Pricing function (b) SINR degradation functionper unit bandwidth demand

8.1 with the following set of parameters for individual accessnetworks. The flexibility of bandwidth demand is provided byeach access network in the range of 1.5 MHz to 40 MHz andthe packet length is assumed as the size of a standard TCPpacket. To validate our theoretical analysis, we simulated eachof the scenarios individually, where the radio nodes seek tosend a file of size, F = 60MB via the selected ANs, howeverthe size of file that needs to be transfered is not capped to thementioned value, rather a file of any size can be used here.

The unit pricing function for the considered access networksis shown in Figure 2(a) where, we assume that the cost ofdemanding more bandwidth from LTE and WiMAX accesstechnologies is higher compared to WLAN due to their reliableand congestion-free services. The former ANs provide dedi-cated communication mediums to protect its incumbents frominterferences, whereas WLAN may not provide a guaranteedQoS due to its shared medium access. Hence, high bandwidthdemand in WLAN may not provide high throughput but ratherincreases the possibility of network congestions; whereasLTE is an advanced technology which provides guaranteedhigh data rate with bounded interference temperature. Con-sidering the above intuitions, we assume a linear functionto represent the normalized cost for WLAN access withcoefficients cm = 0.004 and Km = 0.07. For WiMAX andLTE, we assume normalized power functions with coefficients(cwimax = 0.1, awimax = 1.58) and (clte = 0.15, alte = 2.7)respectively. However, any increasing functions other thanlinear/exponential is applicable to model our cost function,provided it satisfy the above described assumptions. Due to thepossibility of cross-channel interference upon rising bandwidthdemand, we assume a linear SINR degradation function forWiMAX and LTE ANs, however the shared medium accessdegrades SINR exponentially in WLAN, which is presentedin Fig. 2(b). Considering these parameters, we report thesimulation results in the following for selecting single as wellas two ANs.

A. Single Network Selection Scenario

When a player selects only one AN, all packets of the cor-responding file will be pushed through that particular network.From the Fig. 3(a), it can be observed that sending the wholefile via WLAN is as good as the other two networks because ofits high link capacity at minimum bandwidth demand, whereprobability of congestion is small. However LTE and WiMAXcharge more price compared to WLAN but provides exclusive

0 5 10 15 20−1

−0.5

0

0.5

1

Bandwidth Demand (in MHz)

Gro

ss U

tility

WLAN

LTE

WiMAX

(a)

0 10 20 30 40−1.5

−1

−0.5

0

0.5

1

Bandwidth Demand (in MHz)

Fir

st

Ord

er

Dif

fere

nti

al

WLAN

LTE

(b)

Fig. 3: (a) Optimal Bandwidth Demands in Single AN Se-lection, (b) Numerical analysis result for theoretical optimalbandwidth demand

access to the spectrum bands and estimated capacity is highat high bandwidth region, due to which the gross utility ismaximized at high bandwidth demand. As bandwidth demandincreases, the shared medium of WLAN becomes congestedand the packet delivery time increases compared to respectivecost of extra bandwidth. Therefore, the overall gross utilitydecreases gradually with increasing bandwidth demand. Theoptimal bandwidth demand for WLAN and LTE found throughthe discrete band simulation are 10.25 MHz and 19.25 MHzrespectively. And to validate the theoretical analysis with theresult found, we performed numerical analysis using equations5 and 6, for WLAN and LTE respectively to find the theoreticaloptimal bandwidths. The result of numerical analysis for singlenetwork selection is presented in Fig. 3(b). The plots of thefirst order differential equations of WLAN and LTE hits zeroat 10.5 MHz and 20.25 MHz respectively, which are closeto the results obtained from simulation. Therefore, demandinghigh bandwidth from WLAN will not be beneficial comparedto LTE/WiMAX.

B. Multiple Network Selection Scenario

We also simulated for the two network selection scenarioof choosing WLAN (net # 1) and WiMAX (net # 2), wherewe varied the percentage of packets sent via WiMAX and itscorresponding bandwidth demand to find the optimal band-width required for each candidate AN. For this experimentthe bandwidth of WLAN technology is kept fixed as 20 MHz.From Fig. 4(a), it can observed that there exists a maxima fordifferent percentage ratio of packet sending via each network,but the gross utility at maxima depends on how the access linksare utilized on an average. Under-utilizing the high efficientlink will reduce the utility, however utilizing both the accesslinks equally gives better utility compared to biased usage ofany single AN.

We simulated another instance of the two network selectionscenario of choosing WLAN (net # 1) and LTE (net # 3)where we varied the percentage of packets sent via WLANand bandwidth demand to find the optimal WLAN bandwidthdemand for ANs selected. For this experiment the bandwidthof LTE technology is kept fixed as 20 MHz. From Fig. 4(b),it can observed that the optimal bandwidth for WLAN is lesscompared to the previous scenario. This happens due to thesevere link degradation as the demand of bandwidth increases.

0 10 20 30 40−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

BW Demand from Net # 2 (in MHz)

Gro

ss U

tility

Fixed BW Demand From Net#1 (B1 = 20 MHz)

T1:T

2=0:4

T1:T

2=1:3

T1:T

2=1:1

T1:T

2=3:1

(a)

0 10 20 30 400.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

BW Demand from Net # 1 (in MHz)

Gro

ss U

tility

Fixed BW Demand From Net#3 (B3 = 20 MHz)

T1:T

3=0:4

T1:T

3=1:3

T1:T

3=1:1

T1:T

3=3:1

(b)

010

2030

40

0

10

20

30

400.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

Bandwidth Demand in MHz (Net # 1)

Maxima at B1 = 10.25MHz, B3 = 16.5 MHz, T1

i = 36MB , T

3

i = 24MB

Bandwidth Demand in MHz (Net # 3)

Gro

ss

Uti

lity

(c)

Fig. 4: (a) Two AN Selection with varying BW demand fromWiMAX and T1 : T2 ratio, (b) Two AN Selection withvarying BW demand from LTE and T1 : T3 ratio, (c) Two ANSelection with varying BW demand from WLAN and LTE

Therefore, LTE network can provide better service in thiscase compared to WLAN, so it is useful to utilize the LTElink maximally. The plot shows clearly that when the packetsending ratio is 1:3, maximum utility can be achieved due tohigh utilization of LTE link.

Finally, we considered two networks WLAN (net # 1) andLTE (net # 3), for the simultaneous communication, whereall parameters such as bandwidth demands and number ofpackets sent via each network need to be optimized. Fromthe Fig. 4(c), we can observe that when bandwidth demandfrom both networks is high, the gross utility decreases dueto high monetary cost and SINR degradation in WLAN. Asper our simulation, it is found that gross utility is maximized,when the bandwidth demands from WLAN and LTE are notmore or less than 16.5MHz and 10.25 MHz respectively,provided 60% of the whole file is sent via WLAN and rest istransferred via LTE. This division of whole file by 3:2 ratio isoptimal because WLAN offers high estimated capacity at lowbandwidth demand, whereas sending large packets via LTEcosts more compared to WLAN, which eventually decreasesthe gross payoff of the radio nodes.

VI. CONCLUSIONS AND FUTURE RESEARCH DIRECTIONS

This paper addresses the heterogeneous access networkselection problem from a game theoretic perspective by de-vising a realistic utility formulation. As most of the priorworks looked into the problem to find a single and “alwaysbest connected” access network, we modeled the problem

from a multiple access network selection point of view. Theplayers are more interested in using multiple access networkssimultaneously with the flexibility to demand more spectrumresources to maximize their overall performance using theselected ANs effectively. We designed an aggregate utilityfunction for the smart radio devices by considering three majorcomponents that a user is concerned about, such as networklatency, estimated capacity under SINR variation, and themonetary cost per unit time and unit data bytes. Theoreticalanalysis of the payoff function for both single as well asmultiple networks is conducted and it is proved that thereexists an explicit maxima for optimal bandwidth request tothe selected AN beyond which the radio node cannot gainmore. We simulated two scenarios of selecting single-best andtwo-best networks to validate our theoretical analysis, whichcorroborates with the simulation results. In the future, we willextend this research to analyze the network selection problem,where multiple parameters can be optimized simultaneouslyunder the constraints of dynamic availability of access net-works spatially as well as temporally, and develop adaptiveheuristics to maximize the network throughput by sendingoptimal amount of packets through each AN.

REFERENCES

[1] N. Himayat, S. Talwar, K. Johnsson, and J. J. Sydir, “Multi-radiocommunication between wireless devices,” Oct. 23 2014, uS Patent20,140,313,979.

[2] T. Cisco, “Cisco visual networking index: Global mobile data trafficforecast update, 2012–2017,” Cisco Public Information, 2013.

[3] A. Ford, C. Raiciu, M. Handley, S. Barre, J. Iyengar et al., “Architecturalguidelines for multipath tcp development,” IETF, Informational RFC,vol. 6182, pp. 2070–1721, 2011.

[4] L. Wang and G.-S. Kuo, “Mathematical modeling for network selec-tion in heterogeneous wireless networks: A tutorial,” CommunicationsSurveys Tutorials, IEEE, vol. 15, no. 1, pp. 271–292, 2013.

[5] Q. Song and A. Jamalipour, “Network selection in an integrated wirelesslan and umts environment using mathematical modeling and computingtechniques,” IEEE Wireless Communications, vol. 12, no. 3, pp. 42–48,2005.

[6] C.-J. Chang, T.-L. Tsai, and Y.-H. Chen, “Utility and game-theorybased network selection scheme in heterogeneous wireless networks,”in Wireless Communications and Networking Conference, 2009. WCNC2009. IEEE, 2009, pp. 1–5.

[7] M. S. Z. Khan, S. Alam, and M. R. H. Khan, “A network selectionmechanism for fourth generation communication networks,” Journal ofAdvances in Information Technology, vol. 1, no. 4, pp. 189–196, 2010.

[8] M. Z. Chowdhury and Y. M. Jang, “Priority based interface selectionfor overlaying heterogeneous networks,” arXiv, arXiv:1103.0837, 2011.

[9] K. Zhu, D. Niyato, and P. Wang, “Network selection in heterogeneouswireless networks: Evolution with incomplete information,” in WirelessCommunications and Networking Conference (WCNC), 2010 IEEE,2010, pp. 1–6.

[10] Q.-T. Nguyen-Vuong, N. Agoulmine, E. Cherkaoui, and L. Toni,“Multicriteria optimization of access selection to improve the qualityof experience in heterogeneous wireless access networks,” VehicularTechnology, IEEE Transactions on, vol. 62, no. 4, pp. 1785–1800, 2013.

[11] I. Malanchini, M. Cesana, and N. Gatti, “Network selection and resourceallocation games for wireless access networks,” IEEE Transactions onMobile Computing, vol. 99, no. PrePrints, p. 1, 2012.

[12] D. Wischik, C. Raiciu, A. Greenhalgh, and M. Handley, “Design,implementation and evaluation of congestion control for multipath tcp,”in Proceedings of the 8th USENIX Conference on Networked SystemsDesign and Implementation, ser. NSDI’11. USENIX Association, 2011,pp. 99–112.

[13] D. Pauluzzi and N. Beaulieu, “A comparison of snr estimation techniquesfor the awgn channel,” Communications, IEEE Transactions on, vol. 48,no. 10, pp. 1681–1691, Oct 2000.