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Combinatorial Reverse Auction Based Scheduling in Multi-Rate Wireless Systems IEEE TRANSACTIONS ON COMPUTERS, VOL. 56, NO. 10, OCTOBER 2007 1329 Combinatorial Reverse Auction-Based Scheduling in Multirate Wireless Systems Sourav Pal, Student Member, IEEE, Sumantra R. Kundu, Student Member, IEEE, Mainak Chatterjee, Member, IEEE, and Sajal K. Das, Member, IEEE Abstract—Opportunistic scheduling algorithms are effective in exploiting channel variations and maximizing system throughput in multirate wireless networks. However, most scheduling algorithms ignore the per-user quality-of-service (QoS) requirements and try to allocate resources (for example, the time slots) among multiple users. This leads to a phenomenon commonly referred to as the exposure problem, wherein the algorithms fail to satisfy the minimum slot requirements of the users due to substitutability and complementarity requirements of user slots. To eliminate this exposure problem, we propose a novel scheduling algorithm based on two-phase combinatorial reverse auction, with the primary objective of maximizing the number of satisfied users in the system. We also consider maximizing the system throughput as a secondary objective. In the proposed scheme, multiple users bid for the required number of time slots and the allocations are done to satisfy the two objectives in a sequential manner. We provide an approximate solution to the proposed scheduling problem, which is NP-complete. The proposed algorithm has an approximation ratio of ð1 þ log mÞ with respect to the optimal solution, where m is the number of slots in a schedule cycle. Simulation results are provided to compare the proposed scheduling algorithm with other competitive schemes. Index Terms—Scheduling, multirate wireless system, reverse auction, performance optimization. Ç 1INTRODUCTION HE concept of opportunistic scheduling in wireless net- which demand that packets be delivered within certain Tworks was first introduced in [23]. The basic idea is to delay bounds so as to comply with the application-level continuously monitor the uncertainty of the underlying quality of service (QoS). We justify that time constraint wireless channel and take decisions opportunistically so as scheduling is a necessity for delay-sensitive applications by to optimize the objective functions under consideration. explaining the timing requirements of VoIP applications. Extensive research has been conducted with varying According to the International Telecommunication Union objectives such as maximizing the system throughput [24], (ITU-T) G.114 specifications [10], for good and pleasing maintaining both long and short-term fairness among users voice quality, the end-to-end delay for both the forward and [26], [27], and maximizing the user utility [23]. In general, reverse paths should not be more than 150 ms. This delay is the goal has been to maximize a concave utility function contributed by various sources: representing the specified objective function. Unfortunately, such concave functions fail to capture the importance of the 1. the voice coder, with a processing delay of 10 ms, timelineness of decision making in user scheduling. 2. the bit compression module, with a delay of up to On the other hand, the next-generation multirate wire- 7.5 ms, less data networks, such as Evolution-Data Optimized 3. the packetization scheme, which introduces a delay (1xEV-DO) [1], High Data Rate (HDR) [2], and Enhanced between 20 and 60 ms, Data Rates for Global Evolution (EDGE) [3], promise to 4. serialization, with varying delay between 0.20 and provide data services and applications with strict timing 15 ms, constraints. Examples of such applications include stream- 5. a queuing/buffering and network switching delay of ing multimedia, voice over Internet Protocol (VoIP), instant around 65 ms, and 6. a dejitter buffer, with a worst-case delay figure of messaging (IM), and real-time videoconferencing, all of 40 ms. Summing up these figures, it is easy to observe that the . S. Pal, S.R. Kundu, and S.K. Das are with the Center for Research in delay budget is already exceeds the acceptable ITU-G.114 Wireless Mobility and Networking (CReWMaN), Department of Compu- ter Science and Engineering, The University of Texas at Arlington, requirements. That, too, is without taking into account the 416 Yates Street Nederman Hall, Room 300, Arlington, TX 76019. last-hop wireless link, where additional delay may occur E-mail: {spal, kundu, das}@cse.uta.edu. due to the uncertainty associated with the underlying . M. Chatterjee is with the School of Electrical and Computer Science, University of Central Florida, Orlando, FL 32816. wireless channel. Thus, to keep the end-to-end delay within E-mail: [email protected]. acceptable limits, the wireless delivery system must Manuscript received 1 May 2006; revised 23 Jan. 2007; accepted 30 Jan. 2007; schedule user data delivery within a strict timing constraint. published online 22 May 2007. Therefore, the objective of scheduling is not only to Recommended for acceptance by A. Zomaya. improve the throughput of the system and enforce fairness For information on obtaining reprints of this article, please send e-mail to: [email protected], and reference IEEECS Log Number TC-0168-0506. among participating users but also to meet the minimum Digital Object Identifier no. 10.1109/TC.2007.1082. data requirements of users at each scheduling time slot. It is 0018-9340/07/$25.00 ß 2007 IEEE Published by the IEEE Computer Society 1330 IEEE TRANSACTIONS ON COMPUTERS, VOL. 56, NO. 10, OCTOBER 2007 not possible to provide such delay-sensitive scheduling with system. In [12], an auction-based algorithm was proposed, the help of existing scheduling techniques. It is worth which allowed users to compete for time slots in a fading pointing out that the challenges associated with delay- wireless channel. Using the second-price auction mechan- sensitive scheduling have been extensively studied in the ism, the users in the system were allocated channel slots context of wired networks (see [20] and references within). and the existence of a Nash equilibrium for such a strategy However, the solutions applicable to wired networks cannot was proven. Later, in [13], the Nash equilibrium strategy be directly ported to wireless networks because of the was found when the channels for two users are uniformly fundamental differences in transmission behavior, which distributed. stem from the physical-layer transmission characteristics. To summarize, existing opportunistic scheduling algo- Moreover, the wireless data systems support incremental rithms aim at maximizing the overall system throughput error-correction mechanisms, medium access control and do not focus on the delay-sensitive requirements of the (MAC) layer retransmission of lost packets, and multirate applications. transmission capabilities, all of which significantly impact the dynamics of the underlying wireless channel. Before 1.2 Contributions of This Paper proceeding further, let us review the related work on In this paper, we take a fresh approach to the delay- multirate wireless systems for multiple users. sensitive scheduling problem by borrowing techniques 1.1 Related Work from the auction theory [22]. We consider a cellular network with one base station and multiple users. The resources Most of the existing opportunistic scheduling schemes available to the base station (for example, time slots, suffer from a syndrome, popularly referred to as the frequency bands, and codes) form the goods, which are exposure problem [5] in auction theory. This refers to the sold to the users in a marketlike environment. The users phenomenon where a bidder who bids straightforwardly value these goods distinctively and express the values in according to his demand schedule is exposed to the terms of a common transaction unit called money.1 We also possibility that he may end up winning a collection of slots consider a time-slotted wireless packet data system where that he does not want at the prices that he bid because the complementary slots have become too expensive. Such a the duration of an individual time slot is smaller than the situation arises when the minimum data requirement of the average fading duration of the received signal. Thus, during users is not met. Since opportunistic scheduling algorithms symbol transmission, we can assume that the underlying make their decisions on a slot-by-slot basis, they fail to wireless channel exhibits time-invariant properties. provide the users with the minimum amount of requested Each user demands a certain number of slots (called a data until the very end oftheschedulecycle.Such bundle and denoted as S) in order to satisfy the minimum limitations in scheduling decisions negatively impact the data requirement within a specific schedule cycle. The performance of delay-sensitive applications. The scheduling number of such slots depends on the condition of the algorithm is an important component that determines the underlying wireless channel. Since the market has multiple performance of multirate wireless systems supporting real- indivisible goods and each user’s individual valuation of time data streams. The scheduler needs to be aware not the goods depends on the bundle of goods received, we only of the wireless channel conditions but also of the QoS formulate the scheduling problem as a specific case of requirements of the users. combinatorial auction. This is due to the fact that a single item In the literature, significant research has focused on transaction of the goods does not suffice since the user is varied
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