intraONU

Intra-ONU Bandwidth Allocation Gamesin Integrated EPON/WiMAX Networks

Hui-Tang Lin and Ying-You Lin

AbstractIntegrationof Ethernetpassive optical network(EPON) and WiMAX technologies is regarded as a promisingsolution for next-generation broadband access networks. Inimplementing such networks, efficient bandwidth allocationschemes are essential to satisfy quality of service (QoS) andfairness requirements of various traffic classes. Existingproposals for solving the bandwidth allocation problem inEPON/WiMAX networks neglect interactions between theself-interested EPON and WiMAX service providers (WSPs).Accordingly, this study proposes a two-stage game-theoreticframework for the intra-ONU bandwidth allocation processwhere the interactions between the EPON and WSPs aretaken into account. In the first stage of the proposed frame-work, a fair and efficient sharing of the available upstreambandwidth between the EPON and WiMAX networks isdetermined using two market models (i.e., noncooperativeand cooperative). In the second stage, the bandwidth alloca-tion obtained from the first stage is distributed among thedifferent traffic classes within the Ethernet and WiMAX net-works in accordance with their QoS requirements by meansof a Nash bargaining game. Simulation results show that theproposed game-theoretic framework efficiently allocatesbandwidth under different market models while simultane-ously ensuring proportional fairness among the varioustraffic classes for the corresponding networks.

Index TermsAccess network; Differentiated services;EPON; Game theory; Intra-ONU scheduling; WiMAX.

I. INTRODUCTION

E thernet passive optical networks (EPONs) [1,2] haveemerged as a promising solution for resolving thebandwidth bottleneck problem between end users andthe backbone network. However, EPONs cannot supportthe access requirements of mobile users. Furthermore,EPONs are cost prohibitive in areas with low subscriberdensity [3]. To address this, integrated EPON/WiMAX net-works have been proposed where infrastructure owned byan EPON service provider (ESP) is used to provide back-haul service to connect multiple dispersed WiMAX basestations (BSs) operated by a WiMAX service provider(WSP). Such networks offer the ESP many important ad-vantages, including lower infrastructure expenditure and

long-term operating cost [4]. For example, by usingWiMAXBSs to provide wireless access services, the ESP canachieve a significant increase in the EPON coverage area.Such an approach is particularly advantageous in low den-sity suburban and rural areas, where it is more cost-effective to provide shared access to the backbone networkrather than to dedicated connections. Moreover, use ofWiMAX BSs reduces trenching and cabling costs and as-sists in meeting the requirements of green PON planning[5]. In general, EPON/WiMAX networks offer many impor-tant advantages, including high bandwidth, good commu-nication reliability, good deployment flexibility, and lowdeployment cost. As a result, such networks have beenidentified as a promising means of improving the stabilityand versatility of the communications services provided bynext-generation broadband access networks [3,6,7].

Recent literature contains many PON and integratedEPON/WiMAX network proposals. For PONs, most pro-posed two-stage bandwidth allocation algorithms supportquality of service (QoS). For example, the authors in [8]developed a hybrid granting protocol to minimize packetdelay variation and to guarantee bandwidth for EPONs.The delay variation guaranteed polling scheme in [9] pro-vided absolute delay variation and bandwidth guaranteesin PONs. The authors in [10] presented a K-out-of-N pro-tocol for dynamic bandwidth allocation (DBA) that adjuststhe trade-off between network efficiency and average la-tency in next-generation PONs. However, these previousstudies [810] did not consider ESP-WSP interactions sothey may not be able to guarantee system performancefor practical scenarios with factors such as the profit maxi-mizing tendencies of service providers [11,12]. For fiber-wireless access networks, an energy-saving schedulingalgorithm having acceptable packet delay was discussed in[13]. In [14], the authors considered dimensioning and siteplanning to ensure long-term performance in a hybrid PONand wireless cooperative network deployment. In [15] and[16], the authors proposed various ONU selection schemesto improve the survivability of EPON/WiMAX networks.However, in implementing such networks, a central issue ishow to design a scheduling mechanism to ensure hetero-geneous traffic flows within the two networks to obtain effi-cient and fair sharing of the available upstream bandwidth.

To resolve this problem, various traffic scheduling algo-rithms for integrated EPON/WiMAX networks have beenproposed. For example, the authors in [17] presented aDBA scheme designed for smooth data transmission acrossboth networks and to provide end-to-end differentiatedhttp://dx.doi.org/10.1364/JOCN.5.000609

Manuscript received November 26, 2012; revised March 4, 2013; ac-cepted March 29, 2013; published May 30, 2013 (Doc. ID 180590).

H. T. Lin is with the Department of Electrical Engineering, NationalCheng Kung University, 1 University Road, Tainan 701, Taiwan (e-mail:[email protected]).

Y. Y. Lin is with the Institute of Computer and Communication Engi-neering, National Cheng Kung University, 1 University Road, Tainan 701,Taiwan.

Hui-Tang Lin and Ying-You Lin VOL. 5, NO. 6/JUNE 2013/J. OPT. COMMUN. NETW. 609

1943-0620/13/060609-12$15.00/0 2013 Optical Society of America

services to WiMAX subscribers with QoS requirements. In[18], the authors developed a layer 2 virtual private net-working framework consisting of bandwidth allocation andadmission control schemes to support the provision of dif-ferentiated QoS over integrated EPON/WiMAX networks.Meanwhile, in [19], the authors presented an integratedQoS and management framework for bandwidth allocationand admission control of specific service bundles with di-verse QoS requirements in integrated EPON/WiMAX net-works, though EPON user QoS requirements remainunaddressed. Thus, the authors in [20] proposed a frame-work for satisfying the QoS requirements of both WiMAXand EPON subscribers. Overall the frameworks proposedin [1720] focus on scheduling Ethernet andWiMAX trafficin such a way as to satisfy QoS requirements and fairnessfor the user. However, as described previously, these frame-works do not account for interactions between the ESP andWSP and so cannot guarantee network efficiency when ser-vice providers use different market models to allocatebandwidth [11,12].

Game theory has emerged as one of the most promisinginformation theoretic techniques for solving network re-source scheduling [2123]. For example, the authors in [24]applied gamemodels to Internet pricing and showed that forQoS support, a cooperative game provides a better solutionfor both the Internet service provider and the user. In [25],the authors employed a Stackelberg game to obtain theoptimal pricing solution for bandwidth sharing in an inte-grated WiMAX/WiFi network. The authors in [26] appliedboth symmetric and asymmetric bargaining games to solvethe resource sharing problem between network service pro-viders in such a way as to satisfy specified QoS and fairnessrequirements. In general, the studies described show gametheory provides a useful tool for capturing interactionsamong Internet and network service providers to supportfair and efficient resource sharing for wired and wirelessnetworks. It is expected that such frameworks will yieldsimilar benefits for integrated optical-wireless networks.

As discussed above, most existing studies on schedulingin EPON/WiMAX networks focus on the user. In contrast,the present study investigates the intra-ONU bandwidthallocation problem from the perspective of the ESP andWSP (i.e., market-based model). The main contributionsof this study are problem formulation using game theoryand analysis of the interests and strategic interactions ofthe ESP and WSP using a two-stage game-theoreticalframework. In the first stage, the interactions between thetwo service providers for sharing the available upstreambandwidth between the Ethernet and WiMAX traffic areformulated as noncooperative and cooperative games. Inthe former case, the ESP provides backhaul support to theWSP and shares the upstream bandwidth with the WSP ina competitive manner. Thus, a Stackelberg game (i.e., aleaderfollower game) is used to model the interactionsof the ESP (leader) and the WSP (follower) with the aimof maximizing ESP payoff. By contrast, in the latter casea coalition game is used to model the interactions betweenthe ESP andWSP in such a way that both service providersobtain fair revenue [27]. In the second stage of the game-theoretic framework, the allocated bandwidth resulting

from the Stackelberg game or coalition game is furtherdistributed among the various traffic classes in the twonetworks in such a way as to meet the QoS requirements ofeach traffic class using the Nash bargaining game. The sim-ulation results reveal various parameters that impact themarket relationships in the proposed framework, which pro-vides better understanding of the bandwidth market of in-tegrated EPON/WiMAX networks. Furthermore, the resultsconfirm that the proposed framework ensures proportionalfairness among the differentiated traffic classes in an inte-grated EPON/WiMAX network. To the best of the authorsknowledge, this study is the first reported attempt to inves-tigate the bandwidth allocation problem in integratedEPON/WiMAX networks using different market models.

II. SYSTEM MODEL

This section introduces the EPON/WiMAX system con-sidered in this study and describes the queue managementscheme implemented at each ONU [28].

A. Integrated EPON/WiMAX System

Figure 1 illustrates the basic architecture of an integratedEPON/WiMAX access network where the EPON andWiMAX networks are, respectively, operated by an ESPand a WSP. As shown, the trunk fiber fans out to multiplebranches attached to individual ONUs located at differentcurb positions (i.e., fiber-to-the-curb, FTTC). Furthermore,each ONU is attached to its Ethernet end users and aWiMAXBS cell via a twisted pair. The EPON provides back-haul service for both the original Ethernet customers andthe WiMAX BS cells and has a point-to-multipoint opticalnetwork with no active components in the signal path be-tween the source and destination. The data transmissionsin the EPON take place between a single OLT and multipleONUs. For convenience, the traffic from the OLT to theONUs is referred to as downstream traffic,while that fromthe ONUs to the OLT is referred to as upstream traffic. Inthe downstreamdirection, the data packets broadcast by theOLT are received by their respective destination ONUs inaccordance with their media access control addresses.Meanwhile, the upstream transmissions are performed us-ing interleaved polling with adaptive cycle time (IPACT)[29], which arbitrates the access requests of the individualONUs in such a way as to ensure a fair sharing of theavailable bandwidth within the trunk fiber.

In modeling the integrated EPON/WiMAX networkshown in Fig. 1, it is assumed that each ONU providesan autonomous access environment for small-to-mediumscale user groups, such as a residential community area,university campus, or large-scale corporation distributedover adjacent buildings. Furthermore, as described above,each ONU serves both Ethernet end users and a WiMAXBS located within the autonomous access area. In otherwords, the EPON system provides broadband backhaul ac-cess service to the WiMAX BSs deployed within the FTTCinfrastructure.

610 J. OPT. COMMUN. NETW./VOL. 5, NO. 6/JUNE 2013 Hui-Tang Lin and Ying-You Lin

B. Queue Management Scheme

To support the differing QoS requirements of the net-work traffic originating from the Ethernet and WiMAXusers within the autonomous access area, this sectionproposes a priority-based queuing scheme for implementa-tion at each ONU within the EPON.

As in a conventional EPON, the Ethernet traffic from theend users in an EPON/WiMAXnetwork is classified in accor-dance with the Ethernet packet classifier into three differentpriorities, namely, expedited forwarding (EF), assured for-warding (AF), or best effort (BE) [30] [see Fig. 1(b)]. Typi-cally, EF services support delay sensitive applicationssuch as voice-over-IP (VOIP) that require a bounded end-to-end delay specification. Meanwhile, AF services are in-tended for applications that are not delay sensitive butrequire certain bandwidth guarantees. Finally, BE servicessupport applications that are neither delay sensitive norrequire a minimum guaranteed bandwidth. As shown inFig. 1(b), each ONU in the EPON/WiMAX network isequipped with an Ethernet buffering space (SE) containingthree different queues (i.e., one queue for each class of traffic)to satisfy the QoS requirements of these three traffic types.

In WiMAX networks, the traffic is assigned five differentservice priorities, namely, unsolicited grant service (UGS),extended real-time polling service (ertPS), real-time poll-ing service (rtPS), non-real-time polling service (nrtPS),and best effort (BE) [31]. To enable the use of a commonpriority queue structure for EPON and WiMAX traffic ateach ONU and to achieve QoS consistency between theEPON and WiMAX traffic, the WiMAX packet classifierat each ONU must be equipped with a QoS mappingmechanism to map the UGS traffic to EF priority traffic,the ertPS and rtPS traffic to AF priority traffic, and thenrtPS and BE traffic to BE priority traffic, respectively[16]. As a result, each ONU contains two buffering spaces,i.e., buffering space SE for Ethernet traffic and SW forWiMAX BS traffic [see Fig. 1(b)], with each space contain-ing three priority queues. The aim of the present study isto derive a game-theoretic framework for intra-ONU

scheduling. Consequently, the problem of developing a QoSmapping mechanism is not explicitly addressed. However,in practice the mapping function can be implemented usingany of the existing QoS mapping mechanisms proposed inthe literature [7,1618].

III. STAGE I INTRA-ONU BANDWIDTH ALLOCATIONSTRATEGIES WITH HETEROGENEOUS TRAFFIC

In the considered integrated EPON/WiMAX network(Fig. 1), various schemes can be used for inter-ONU DBA.For simplicity, the IPACT scheme is assumed. It enableseach ONU to request the OLT to allocate bandwidth inaccordance with the total buffer occupancy of SE and SWin every polling cycle. However, since new Ethernet packetsor WiMAX frames continuously arrive at the ONU duringthe interval between when the ONU sends its bandwidthrequest to the OLT in polling cycle P and when it receivesthe corresponding transmission grant in the next pollingcycle (P 1), the transmission window granted by theOLT may be too small to satisfy the augmented bandwidthrequirements of the two buffers. (Note that this is referred tohereafter as unexpected bandwidth demand.) In the eventthat such a scenario occurs, SE and SW both seek to maxi-mize their share of the bandwidth allocated by the OLT inorder to satisfy the QoS requirements of their respectivepriority queues. Therefore, supporting QoS transmissionsin a heterogeneous EPON/WiMAX network requires a stageI intra-ONU bandwidth allocation strategy capable ofdistributing the bandwidth granted by the OLT betweenthe Ethernet and WiMAX buffer spaces in a fair manner.

The present study treats the unexpected bandwidthdemand problem in the intra-ONU bandwidth allocationprocess as a bankruptcy problem. In economics, the termbankruptcy describes the situation where a businessentity ceases trading as a result of financial difficultiesand has outstanding debts to one or more (N) creditors.Typically, the sum of the claims from the creditors is largerthan the remaining assets of the corporation, and thusthe problem arises of how to allocate the available assets

Fig. 1. Integrated EPON/WiMAX system. (a) Integrated EPON/WiMAX architecture. (b) Queue management scheme at each ONU.


among the creditors in the fairest manner possible. Thisproblem can be modeled as an N-person bankruptcy game,in which the N players all seek to maximize their share ofthe available assets. (Note that the bankruptcy game is de-tailed in [32].) Most DBA approaches inherently have theunexpected bandwidth demand problem. Thus, althoughIPACT is chosen as the experimental environment in thepresent study, the benefits of the proposed game-theoreticframework are also expected to translate to other DBAalgorithms. However, some DBA algorithms specificallyexclude this condition. For example, the control theoreticextensions of IPACT were proposed in [33,34] to estimatethe bandwidth demand of each ONU using refinement.This ensures the grant bandwidth size is closer to the band-width demand of the ONU. Thus, the proposed bankruptcygame scheme is not suitable for these DBA approaches.

In the current context, the bandwidth allocation problemarising as the result of an unexpected bandwidth demandcan be modeled as a bankruptcy game involving a finite set of two different types of players, namely, ESP players (E,corresponding to buffer space SE) andWSP players (W, cor-responding to buffer space SW ). In other words, fE;Wg.Let BONU be a real positive number corresponding to theamount of bandwidth granted to the ONU by the OLT,and let RjONU be a non-negative number corresponding tothe amount of bandwidth required by player j (j ). (Notethat the number of players in the bankruptcy game isnot fixed and can be extended easily to more than two play-ers.) The bankruptcy problem formulation is subject to thecondition

Xj

RjONU BONU: (1)

In solving the bankruptcy problem (i.e., the bandwidthallocation problem between ESP and WSP traffic), the fol-lowing constraints are imposed:

The bandwidth granted by the OLT must be completelydistributed among the players.

Each player must obtain a non-negative bandwidth notexceeding its bandwidth requirement.

Let BjONU represent the solution to the bankruptcy prob-lem (i.e., the amount of bandwidth allocated to player j).Then the rules of the bankruptcy game can be expressedas follows:

0 BjONU RjONU; j P; (2)

andXj

BjONU BONU: (3)

The stage I intra-ONU bandwidth allocation problemcan be formally defined as the following game.

Definition 1 (Intra-ONU Bandwidth AllocationGame, IBAG). Consider an integrated EPON/WiMAX net-work. The stage I intra-ONU bandwidth allocation game isdefined as the following triplet:

h; BjONUj; Ujji; (4)

where is a finite set of players and BjONUj representsthe set of pure strategies for player j constrained byEqs. (1)(3). By defining B QjBjONU as the set of actionprofiles, Ujj denotes the set of utility functions whereUj:B R is a function from the set of all action profiles Bto real numbers.

Several pertinent issues in the above formulated gameare 1) how to determine efficient bandwidth allocationfor network users considering their differing needs andperformance requirements, 2) implementing fairness be-tween the players, and 3) maximizing the service providersrevenue under different market models while considering1) and 2).

The following subsection presents the Stackelberg andcoalition games. These two game-theoretic approachesrespectively solve the aforementioned issues for nonco-operative and cooperating service providers.

A. Bandwidth Allocation Strategy UsingStackelberg Game

In the Stackelberg game, the leader can commit to a pric-ing strategy before the other player(s) and, thus, the leadercan maximize earned revenue. When the ESP and WSPoperate in a competitive market model, they both seekoptimal strategies to allocate user bandwidth while maxi-mizing their own revenue. The ESP serves as the leadersince it provides wired backhaul access to the WSP. TheESP decides the amount of total bandwidth used byWiMAXusers (i.e., BSW ONU) so as to maximize its own revenue. If theESP offers too much bandwidth by undercharging the WSP,the ability of the ESP to provide wired access to its Ethernetusers will be degraded. At the same time, the ESPs revenueis reduced if it charges more for bandwidth, lowering WSPincentive to buy. Hence, the ESP selects an optimal pricestrategy to maximize its revenue while covering costs.

For simplicity and efficiency, the utility functions of theESP and WSP in the Stackelberg game are defined by thefollowing linear functions [35,36]:

1) Utility function of ESP leader: The leader (ESP E)aims to maximize the revenue received from the Ether-net and WiMAX users with minimal infrastructurecost. Note that the infrastructure costC is estimated as

CE Cinstall Ccabling; (5)

where Cinstall is the total OLT/ONU installation cost andCcabling is the cabling costs of the feeder and distributionfibers [4]. Hence, the utility function of ESP E is given by

UEpW pEBSE ONU pWBSW ONU CE ; (6)

where pE is the price charged by ESP E to the Ethernetusers and pW is the price charged by the ESP E to WSPW. The bandwidth BSW ONU allocated to buffer SW to


transmit data from the WiMAX users can be modeled asa bandwidth demand function dWpW;u, i.e., the totalbandwidth demand of all the WiMAX users under pricepW;u charged by the WSP W. Therefore, B

SW ONU

dWpW;u. User bandwidth demand can be modeled re-specting the complex relationships between queuelength, bandwidth price, and bandwidth requirements.To make subsequent analysis tractable [37,38], the fol-lowing positive linear function can be used to approxi-mate user bandwidth demand:

dWpW;u qW WpW;u WRW ; (7)

where qW is the queue length of SW and RW is the mini-mum bandwidth requirement of all WiMAX users.Furthermore, the function x max0; x, W is the re-duction in bandwidth demand per unit price increasepW;u, and W is a tuning factor used to give theWSP flex-ibility in deciding the amount of additional resourcesto allocate to the WiMAX traffic above the minimumbandwidth requirement. A higher value of W indicatesa lower bandwidth demand from the WiMAX users.Conversely, a higher W value implies the importanceof ensuring that the minimum bandwidth guaranteeis increased, and thus the bandwidth demand of theWiMAX users is raised.

In the IBAG problem, ESP E offers bandwidth to WSPWin exchange for revenue, which can be formulated as anoptimization problem for the leader-level game as follows:

maxfpW g

UEpW pEBSE ONU pWdWpW;u CE

s:t:

pE ; pW 0: (8)

2) Utility function of WSP follower: The WSP W canbe regarded as a buyer whose aim is to earn sufficientrevenue from its WiMAX users to cover its forwardingcosts while simultaneously gaining as much additionalprofit as possible. The WSPs utility function can, thus,be expressed as

UWpW;u pW;udWpW;u CW ; (9)

where CW pW dWpW;u is the forwarding cost (i.e.,the cost paid to the ESP for backbone services). Theoptimization problem for the follower-level game isformulated as follows:

maxfpWg

UWpW;u pW;udWpW;u pWdWpW;u

s:t:

pW ; pW;u 0: (10)

The optimal price pW;u is dependent on both total band-width demand of the WiMAX users and the price pWcharged by the ESP. If the WSP sets too high a price,WiMAX user bandwidth demand will fall and then theWSPs revenue will fall. Conversely, if the WSP sets toolow a price, the revenue obtained in Eq. (9) will be unnec-essarily low. Specifically, if the price is set far below the

optimal price (i.e., pW;u), the resulting utility of ESP Ecan be negative, i.e., UE < 0. As a consequence, WSPW will not be granted any bandwidth since ESP E cannotcover its basic costs.

In the following discussions, the optimal strategiesfor both the ESP and the WSP exist in the form of aStackelberg equilibrium. Note that the Stackelberg equi-librium is defined as follows.

Definition 2 (Stackelberg Equilibrium). [39] A strategyprofile pW ; pW;u represents Stackelberg equilibrium if pWmaximizes the utility of the leader (ESP) and pW;u is the bestresponse of the WSP to the ESP.

In general, the optimal strategy profile can be derivedby backward induction [35]. By taking the derivative ofUWpW;u in Eq. (9) with respect to pW;u, the optimal pricepW;u for the WSP is then given as

pW;u qW WRW WpW

2W: (11)

Substituting Eq. (11) into Eq. (6), the optimal price pWcharged by the ESP can be derived as follows:

pW qW WRW WpE

2W: (12)

Property 1. The utility function UWpW;u of the WSP isjointly concave in pW;u with pW;u 0.

Pf: By taking the second-order derivatives of the WSPsutility UWpW;u, the result is readily derived and is lessthan 0. Thus, UWpW;u is strictly concave for any valueof pW;u.

From Property 1, pW;u in Eq. (11) is the global optimumvalue that maximizes the WSPs utility UWpW;u. Thus,pW;u represents the Stackelberg equilibrium since it satis-fies Definition 2.

Property 2. The ESP utility function UEpW is concave inits own price pW when the price charged by the WSP is theoptimized purchase price determined from Eq. (11).

Pf: As the proof of Property 1, the proof of Property 2 isreadily derived.

The utility functions can be proven to have a concaveproperty due to Properties 1 and 2. Thus, the followingtheorem can be obtained.

Theorem 1. The pair of pW;u in Eq. (11) and pW in Eq. (12)

represents the Stackelberg equilibrium that satisfies Defini-tion 2.

The Stackelberg equilibrium is found when the ESP (i.e.,leader) and WSP (i.e., follower) have optimal strategiesthat lead to an optimal bandwidth demand/allocation forEthernet and WiMAX users. In other words, the ESP andWSP can maximize their utilities and decide the allocatedbandwidth for Ethernet and WiMAX users (i.e., BSE ONU andBSW ONU). Note that the allocated bandwidth B

SE ONU and B

SW ONU

can be computed from Eq. (3) based on the results derivedfrom substituting Eqs. (11) and (12) into Eq. (7).


For the Stackelberg game, the WSP selects a strategyafter the ESP sets a price. The WSP may opt for nonpar-ticipation when it cannot gain any revenue. When thishappens, the WiMAX users are excluded from sharing thebandwidth of the backhaul network (i.e., EPON). To avoidthis extreme condition, the parameters of the Stackelberggame need to be set properly. Thus, the following proposi-tion is asserted to adjust the related parameters W, W ,and pE when considering the Stackelberg equilibrium.

Proposition 1. When condition qW WRW > WpE issatisfied, the WSP has positive revenue and, therefore,accepts the price set by the ESP.

Pf: Regarding Eq. (10), the WSP has positive revenue if theutility of the WSP is greater than zero (i.e., UWpW;u > 0).In this case, the necessary conditions dWpW;u > 0 andpW;u pW > 0 must be satisfied. Since dWpW;u is a non-negative function, only dWpW;u 0 needs consideration.Substituting Eqs. (11) and (12) into condition dWpW;u 0 allows qW WRW WpE to be derived. Similarly,condition qW WRW > WpE can be proved by substitu-tion of Eqs. (11) and (12) into pW;u pW > 0. It is trivialto determine that the WSP has positive revenue and, thus,accepts the price set by the ESP.

B. Bandwidth Allocation Strategy Using CoalitionGame

In the previous section, the IBAG problem is formulatedas a Stackelberg game in which the ESP and WSP deter-mine their strategies in turn and the optimal bandwidthallocation strategy maximizes the ESPs profits. In prac-tice, however, the ESP andWSP may not have a strict hier-archical relationship. For example, the ESP and WSP mayhave a close relationship or the EPON and WiMAX net-works may even belong to the same service provider. Insuch a scenario, the ESP and WSPmay share the availablebandwidth in a cooperative manner so that both partiesobtain an efficient and fair bandwidth allocation. Thus, thissubsection solves the IBAG problem with simultaneousplay using a coalition game approach.

1. Coalition Game Formulation: An N-person coalitiongame can be defined as follows.

Definition 3 (Coalition Game). [39] A coalition C is de-fined as a subset of the total set of players f0;; Ng (i.e.,C ). The members of the coalition willingly cooperatewith one another. The coalition of anN-person game is givenby the pair (, f ), where f is a characteristic function (i.e.,value function) of the game. The value f C is the co-operation for coalition C and has two important properties: f 0. Superadditivity: if C and S are disjoint coalitions

CS , then f C f S f CS.

In an EPON-based system, the bandwidth requirementsof the ONUs are determined in accordance with bufferoccupancy status. Consequently, the required bandwidthfor buffering space j (i.e., player j) is obtained as

RjONU SjONU; (13)

where SjONU is the current occupied buffer size of bufferingspace j. In accordance with the two properties described inDefinition 3, the characteristic function can be defined asfollows [40]:

f C max0; BONU

XjC

RjONU

; (14)

for all possible C.

Many methods are available for solving the IBAG bank-ruptcy game using a coalition game approach, includingthe Shapley value method, the kernel method, and the nu-cleolus method [41]. Of these various methods, the Shapleyvalue method not only induces global Nash equilibria butalso yields solutions that are both unique and fair [41]. As aresult, it represents an ideal solution for the bandwidthallocation problem in the present study.2. Shapley Value: The Shapley value [41] is a game-

theoretic concept for cooperative games. The aim of theShapley value method is to obtain a fair solution for aplayer acting in coalition with one or more collaborativeplayers. The Shapley value f is defined as the worthor value of player j in a game with a characteristicfunction and determines a unique distribution forthe coalition of all players. Therefore, the Shapley valueassigns a vector of real numbers corresponding to eachplayer [i.e., f 1f ;; jf ;; Nf ] and can becomputed by

jf BjONU XCj

jCj!N jCj 1!N!

f Cfjg f C:

(15)

The operational complexity of the conventional Shapleyvaluemethod is lower than that of the kernel method or thenucleolus method. However, its time complexity increasesexponentially with an increasing number of players sincethe Shapley value calculation requires every possible coali-tion C to be evaluated. However, this problem is largely re-solved by the bilateral Shapley value (BSV) method havingcomplexity of ON31 log N1 [42]. (Note that the BSVmethod is detailed in [42] and omitted here.)

IV. STAGE II INTRA-ONU ALLOCATIONSTRATEGY WITH QOS SUPPORT

Once the stage I IBAG solutions (i.e., BjSE ONU and BjSW ONU )

are obtained using the Stackelberg or coalition game for-mulations, the bandwidths allocated to SE and SW for eachONU must be further distributed among the individualpriority queues. In other words, each ONU requires a band-width partitioning scheme that ensures the different prior-ity queues within the two buffering spaces receive a fairshare of the allocated bandwidth BjONU while continuingto satisfy the QoS commitments. Accordingly, this studyapplies a bargaining game approach to make bandwidth


partition decisions in accordance with a sigmoid utilityfunction.

A. Bargaining Game Formulation

Most bargaining theories take root from Nashs seminalstudy [43]. Generally speaking, an N-person bargainingproblem describes a scenario in which N players attemptto reach agreement on trading a limited resource. TheseN individuals have a choice to bargain so that all of themcan gain most benefit as a result of cooperative play.

1) Bargaining Game for SE: Consider the bandwidthallocation problem for SE, where the allocatedbandwidth BSE ONU, obtained from the stage I intra-ONUbandwidth allocation game, is distributed among threeplayers k fEF;AF;BEg. The non-negative number RkSErepresents the bandwidth demand of player k. When sell-ing bandwidth, the ESP must consider fairness for playerBE even though BE traffic is not delay sensitive. As a re-sult, the ESP needs to reserve minimum bandwidthBBE;minSE to ensure fairness for Ethernet users. In general,

BBE;minSE is much less than that required by the averageamount of BE traffic in SE. On the other hand, the EF prior-ity queue in SE contains the highest priority traffic. There-fore, the remaining bandwidth BSE;remONU available forallocation to players AF and BE once the requisite alloca-tion of bandwidth to players EF and BE has been made isgiven by

BSE;remONU BSE ONU BEFSE BBE;minSE

; (16)

where BEFSE REFSE

.

To define the utility (i.e., QoS level) received by individ-ual players in the bargaining game, a sigmoid function isused to quantitatively estimate the relative satisfactionof the AF and BE priority queues having bandwidthsBAFSE and B

BESE

allocated. The utility function is definedas follows:

UBlSE 1

1 expl BlSE glE

; l fAF;BEg;

(17)

where indicates the sensitivity of the performance factor,glE denotes the minimum bandwidth requirement of player

l, and gBEE 0. Hence, the utility for player l is representedby UBlSE with the condition

0 UBlSE 1; (18)

where UBlSE D and D is the set of all possible feasibleresults. In order to prevent player l from disputing any QoSdifferentiation decision (i.e., any possible payoff result), adisagreement point of UminBlSE 0 is imposed so that

any uncooperative player is penalized and loses the rightto compete for bandwidth in the current polling cycle. Thus,the bargaining game problem and solution can be definedas (D, UminBlSE ) and FD;UminB

lSE

D, respectively.The Pareto optimal solution defines an agreement such

that one player cannot increase utility without decreasingthe utilities of any other players. An approach for obtaininga fair bargaining solution is to apply the four axioms pro-posed by Nash [44]. According to the player utility func-tions, the Nash bargaining solution (NBS) of players AFand BE can be obtained as

BAFSE ; BBESE

arg maxBAFSE

;BBESE

fUBAFSE UminBAFSE

UBBESE UminBBESE

g; (19)

where BAFSE and BBESE

are the respective bandwidths allo-cated to the AF and BE priority queues. The solution ofEq. (19) can be obtained by means of a local search method[45]. Note that distinct bargaining solutions for an inte-grated EPON/WiMAX network are available in a previouswork by the authors of this paper in [28].

2) Bargaining Game for SW : As in the SE bargaininggame, the SW bargaining game also has three playersk fEF;AF;BEg, an allocated bandwidthBSW ONU, and a non-negative bandwidth demandRkSW for each player k in bufferspace SW . Unlike the allocation process for SE, the mini-mum bandwidth requirement for BE is not guaranteed.Intuitively, the remaining resource (i.e., bandwidth) avail-able for allocation to players AF and BE is given by

BSW ONU;R BSW ONU BEFSW ; (20)

where BEFSW REFSW

. Note the available bandwidth isshared between AF and BE in SW using the NBS methodsimilar to that used for players AF and BE in bufferspace SE.

Computational Complexity of Intra-ONU Band-width Allocation Game: In the stage I intra-ONU band-width allocation, the Stackelberg game solution can bedirectly derived using the backward induction approachwith complexity of O1. The complexity of the coalitiongame is ON31 log N1 obtained via the BSV method [42]whereN1 is the number of players in the stage I game. Sub-sequently, for cases I and II of stage II, the N2 priorityqueues bandwidth allocation (i.e., N2 players) requiresthe NBS to be calculated by using a local search algorithm[45] with the complexity of ON22WMAX log WMAX N42.WMAX is the maximum window size for each ONU. Thus,the total computational complexity of the proposed schemeis ON31 log N1 N22WMAX log WMAX N42.

V. NUMERICAL RESULTS

To evaluate the performance of the proposed game-theoretic-based intra-ONU scheduling scheme, a simula-tion model was constructed comprising an integrated


EPON/WiMAX access network with 16 ONUs and a singleOLT. The maximum upstream bandwidth was set as1 Gbps, and the guard time between successive ONU trans-missions was 5 s. The round-trip time between the ONUsand the OLT was randomly generated with a uniformdistribution of U[100, 200 s] corresponding to a physicaldistance of 15 30 km [46]. Ethernet traffic arriving ateach ONU from end users is assumed to fit in a singleEthernet buffer, while all WiMAX packets awaiting trans-mission at the ONU are assumed to be stored in a singleWiMAX buffer. The Ethernet andWiMAX buffer size main-tained at each ONU is 10 Mbytes. In simulating the IPACTalgorithm, the limited service scheme proposed in [29]was used where the OLT was assumed to grant the ONUsno more than the maximum window size, WMAX (i.e.,15,000 bytes).

For the Ethernet traffic model, an extensive study showsthat most network traffic (i.e., http, ftp, video applications,etc.) are characterized by self-similarity and long-rangedependence [47]. Hence, this traffic model was applied togenerate highly burstyAF and BE traffic. For both trafficclasses, the packet size was uniformly distributed in therange of 64 1518 bytes. In simulating the high-priorityEthernet traffic (e.g., voice application data), the EF trafficwas modeled using a Poisson distribution with a constantpacket size of 70 bytes [47]. To reflect the nature of WiMAXtraffic, the UGS traffic class was generated using the con-stant bit rate traffic model with a fixed packet size of64 bytes. In addition, the ertPS and rtPS traffic classeswere generated using the variable bit rate traffic model.The nrtPS and BE traffic classes were generated usingthe same self-similar traffic model of the AFand BE Ether-net traffic. The packet sizes of the ertPS, rtPS, nrtPS, andBEWiMAX traffic classes were all assumed to follow a uni-form distribution with a range of 64 1518 bytes. Theguarantee flow rate of the Ethernet and WiMAX AF trafficclasses were assumed to be 4 Mbps. Meanwhile, the guar-antee rate of each flow in the WiMAX BE traffic class wasassumed to be 2Mbps [18,48]. The system parameters werespecified as follows: W 0.1, W 0.03, AF 0.0001,BE 0.00003, and pE 0.382. For both the Ethernetand the WiMAX traffic, the loads of the different traffic pri-orities stored in the corresponding EF, AF, and BE priorityqueues were specified as 20%, 30%, and 50% of the totalEthernet (or WiMAX) traffic load, respectively. Finally,each simulation was run for a total of 30 s.

A. Stage I Intra-ONU Bandwidth Allocation

Figure 2 shows the optimal prices charged by the ESP tothe WSP and the WSP to the WiMAX users, respectively.Meanwhile, Fig. 3 shows the throughputs of buffer spacesSE and SW under Stackelberg equilibrium. In both figures,the results are a function of the network offered load andthe Ethernet-to-WiMAX traffic load ratio. In general,Figs. 2 and 3 show both the optimal price and achievedthroughput increase with increasing network offered load.In Fig. 2, it is seen that the optimal price PW;u chargedby the WSP to its WiMAX users is always higher than

the optimal price PW charged by the ESP to the WSP. Thisis because the WSP compensates for the forwarding costwhile gaining additional revenue from its WiMAX users.In Fig. 3, the bandwidth allocated to WiMAX traffic firstincreases and then decreases as network offered load in-creases. This is reasonable since the ESP can increase rev-enue by allocating more bandwidth toWiMAX traffic undernonsaturated network loads but needs to guarantee a cer-tain QoS for its Ethernet users when the network offeredload is saturated and, therefore, reduces the amount ofbandwidth offered to the WSP. Figures 2 and 3 also showthat the optimal prices and achieved throughput of theEthernet and WiMAX traffic are both strongly affectedby the Ethernet-to-WiMAX traffic load composition.

Figure 4 shows the revenues earned by the ESP andWSPfor various network offered loads and Ethernet-to-WiMAX

Fig. 2. Prices pw;u and pw under Stackelberg equilibrium condi-tions for various network-offered loads and Ethernet-to-WiMAXtraffic load ratios.

Fig. 3. Achieved throughput of ESP and WSP under Stackelbergequilibrium conditions for various network offered loads andEthernet-to-WiMAX traffic load ratios.

Fig. 4. Utilities of SE and SW under Stackelberg equilibrium con-ditions for various network-offered loads and Ethernet-to-WiMAXtraffic load ratios.


traffic load compositions. For both service providers, the rev-enue increases with increasing network offered load. For allvalues of network offered load, ESP revenue is maximized.In other words, the results represent the Stackelberg equi-librium for the stage I intra-ONU bandwidth allocationgame. Note the utilities of the other prices (i.e., non-Stackelberg equilibrium prices) are not shown in Fig. 4 sincethe Stackelberg equilibrium of the formulated game hasbeen proven to be the maximum revenue of the ESP.

Overall, the results presented in Figs. 24 confirm thatthe Stackelberg game provides a viable means of sharingbandwidth between Ethernet and WiMAX traffic in accor-dance with the network conditions and the need of the ESPto maximize its revenue by selling its surplus bandwidth.In response, the WSP makes bandwidth demands accord-ing to the Stackelberg equilibrium.

Figure 5 shows the throughput performance of SE andSW in the coalition game with increasing network-offeredloads under different Ethernet (E):WiMAX (W) trafficload compositions. In contrast to Figs. 24, results arenot presented for an Ethernet-to-WiMAX traffic load ratioof 21 since the results are complementary to those for anEthernet-to-WiMAX traffic ratio of 12. The throughputperformance of both traffic classes increases as thenetwork-offered load increases. Also, the SE and SWthroughputs rely strongly on the Ethernet-to-WiMAX traf-fic load ratio. This is to be expected since the formulatedShapley value distribution in the coalition game dependson the bandwidth demand (i.e., queue length) of the bufferand provides fairness for SE and SW according to the fourNash axioms. The results show the coalition game resultsin a fair sharing of the upstream bandwidth between thetwo networks since the ESP and WSP act as peers indivvying up bandwidth.

B. Stage II Intra-ONU Bandwidth Allocation

The performance of the two proposed game schemes(i.e., Stackelberg NBS and coalition NBS) is compared withthat of the baseline DBA scheme for hybrid ONU BSsknown as VOB DBA [16] specifically designed for WiMAXtraffic. Therefore, the bandwidth allocation issue betweenEthernet and WiMAX traffic is not considered. As a result,in comparing the performance of the three schemes, it is

assumed that the stage I bandwidth allocation processfor the VOB scheme is performed using a coalition game.The resulting scheme is designated as the Co-VoB scheme.

Figures 6 and 7, respectively, compare the mean queuingdelays of the different priority queues within SE and SW ,given various network offered loads and the use of the threeallocation schemes (i.e., Stackelberg NBS, coalition NBS,and coalition VOB). Note the Ethernet-to-WiMAX trafficload ratio is 11 in both cases. For both traffic types, theStackelberg NBS and coalition NBS schemes yield betterdelay performance for AF and BE traffic than thecoalition-VOB scheme for all values of network offeredload. The poor delay performance of coalition VOB forAF and BE traffic arises due to a strict-priority-basedapproach in bandwidth allocation of the different priorityqueues. In other words, the bandwidth requirements of theAF and BE traffic are sacrificed to meet EF traffic require-ments. In addition, Stackelberg NBS yields better delayperformance than coalition NBS for all classes of Ethernettraffic. This finding is to be expected since the ESP is theleader in the Stackelberg game from the stage I allocationprocess, and, thus, Ethernet traffic receives more band-width thanWiMAX traffic under saturated load conditions.However, by adopting this approach, WiMAX traffic delayunder Stackelberg NBS is inevitably higher than that ob-tained under coalition NBS, as shown in Fig. 7.

Figures 8 and 9 compare the mean queuing delay perfor-mance of the three schemes for the SE and SW traffic, re-spectively, given a higher Ethernet-to-WiMAX traffic loadratio of 12. For both Ethernet and WiMAX traffic, the EF

Fig. 5. Achieved throughput of ESP and WSP using the coalitiongame approach for various network-offered loads and Ethernet-to-WiMAX traffic load ratios.

Fig. 7. Mean queuing delay of SW using the Stackelberg NBSscheme, coalition NBS scheme, and Co-VoB scheme for variousnetwork offered loads. Note that the Ethernet traffic and WiMAXtraffic have a 11 load ratio.

Fig. 6. Mean queuing delay of SE using Stackelberg NBS scheme,coalition NBS scheme, and Co-VoB scheme for various network-offered loads. Note that the Ethernet traffic and WiMAX traffichave a 11 load ratio.


delays of all schemes are comparable in all network offeredloads. However, the AF delay performance of the two pro-posed schemes is much better than that of coalition VOBunder saturated loads. Also, Stackelberg NBS yields betterAF delay performance for WiMAX traffic than coalitionNBS. This result arises because when WiMAX traffic ac-counts for a larger proportion of the total traffic, the band-width requirement of Ethernet traffic is correspondinglyreduced, and thus, Stackelberg NBS allocates a greateramount of bandwidth to WiMAX traffic in the stage I allo-cation process in order to increase the revenue earned fromthe WSP.

The results in this section show the proposed two-stagegame-theoretic framework not only accurately captures thevarious interactions in the noncooperative and cooperativebandwidth markets between the ESP and WSP but alsoprovides good QoS support for Ethernet and WiMAXtraffic with different priorities. Also, a noncooperativemarket is more beneficial to the backhaul provider (i.e.,ESP) compared to the cooperative market. In addition,the cooperative market provides proportional fairness forthe Ethernet and WiMAX users according to their QoSrequirements.

VI. CONCLUSION

This study presents a two-stage game-theoretic frame-work for modeling market interactions between Ethernetand WSPs for how best to share upstream bandwidth ateach ONU in an integrated EPON/WiMAX network. In

the first stage, the intra-ONU bandwidth allocation prob-lem is formulated as a bankruptcy problem to distributethe bandwidth granted from the OLT between the Ethernetand WiMAX buffer regions of the ONU. Two differentgames are proposed to solve this bankruptcy problem,namely, a Stackelberg game (noncooperative market) anda coalition game (cooperative market). The simulation re-sults show both schemes yield fair and efficient sharing ofupstream bandwidth under various network dynamics. Inthe second stage, the bandwidth allocated to the Ethernettraffic and WiMAX traffic at the ONU buffer is further dis-tributed among the different traffic classes within eachbuffer by a Nash bargaining game to satisfy the QoS re-quirements specified for each class of traffic by the respec-tive Ethernet end users and WiMAX cell. The simulationresults confirm the Stackelberg NBS and coalition NBSschemes both ensure efficient and fair distribution of thebandwidth among the different traffic classes under differ-entmarketmodels. The results also show that the proposedschemes provide better QoS support than the VOB DBAscheme [17].

ACKNOWLEDGMENTS

This work was supported by the National Science Councilof Taiwan under Grant NSC 100-2218-E-006-030-MY3.The authors thank Chi-YouWang for assisting in collectingdata.

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intraONU

Documents

corresponding networks

wimax service providerwsp

wimax technologies

wimax service providers

high bandwidth

qos requirements

haul service

stage gametheoreticframework