IN recent years, broadband wireless access (BWA) networks

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1 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 8, NO. 9, SEPTEMBER Efficient Uplink Bandwidth Request with Delay Regulation for Real-Time Service in Mobile WiMAX Networks Eun-Chan Park, Member, IEEE Abstract The emerging broadband wireless access technology based on IEEE is one of the most promising solutions to provide ubiquitous wireless access to the broadband service at low cost. This paper proposes an efficient uplink bandwidth requestallocation algorithm for real-time services in Mobile WiMAX networks based on IEEE e. In order to minimize bandwidth wastage without degrading quality of service (QoS), we introduce a notion of target delay and propose dual feedback architecture. The proposed algorithm calculates the amount of bandwidth request such that the delay is regulated around the desired level to minimize delay violation and delay jitter for real-time services. Also, it can increase utilization of wireless channel by making use of dual feedback, where the bandwidth request is adjusted based on the information about the backlogged amount of traffic in the queue and the rate mismatch between packet arrival and service rates. Due to the target delay and dual feedback, the proposed scheme can control delay and allocate bandwidth efficiently while satisfying QoS requirement. The stability of the proposed algorithm is analyzed from a control-theoretic viewpoint, and a simple design guideline is derived based on this analysis. By implementing the algorithm in OPNET simulator, its performance is evaluated in terms of queue regulation, optimal bandwidth allocation, delay controllability, and robustness to traffic characteristics. Index Terms Mobile WiMAX networks, IEEE , uplink scheduling, bandwidth request, quality of service, real-time service. Ç 1 INTRODUCTION IN recent years, broadband wireless access (BWA) networks have been rapidly evolved to satisfy the increasing demands of users for ubiquitous and seamless access to the broadband service, such as video conferencing, real-time multimedia streaming, IPTV, as well as traditional Internet services under mobile wireless environments. The emerging IEEE e BWA network [1], called Mobile WiMAX, is one of the most promising solutions for the last mile broadband wireless access to support high data rate, high mobility, and wide coverage at low cost. International Telecommunication Union (ITU) approved Mobile WiMAX as one of International Mobile Telecommunication (IMT) advanced technologies in October According to the recent report in WiMAX forum [2], there are about 180 WiMAX (both Mobile and Fixed WiMAX) operators in over 94 countries globally at the end of 2007 and the number of WiMAX users in the world is expected to grow up to 134 millions by Along with wide deployment of WiMAX networks, the real-time service (e.g., VoIP, VoD, and IPTV) is growing rapidly in the Internet. Thus, providing quality of service (QoS) for realtime service in BWA networks is an imperative and challenging issue. In order to support QoS for various types of traffic, IEEE medium access control (MAC) protocol [1] defines. The author is with the Department of Information and Communication Engineering, Dongguk University, 26 Pildong3-Ga, Jung-Gu, Seoul , Republic of Korea. ecpark@ieee.org. Manuscript received 4 Jan. 2008; revised 24 Oct. 2008; accepted 27 Jan. 2009; published online 6 Feb For information on obtaining reprints of this article, please send to: tmc@computer.org, and reference IEEECS Log Number TMC Digital Object Identifier no /TMC several bandwidth request-allocation mechanisms and five types of scheduling classes: Unsolicited Grant Service (UGS), real-time Polling Service (rtps), non-real-time Polling Service (nrtps), Best-Effort (BE), and extended real-time Polling Service (ertps). Both UGS and rtps are proposed to support real-time service generating packets periodically. While UGS is suitable for constant bit rate (CBR) traffic such as VoIP, rtps is for variable bit rate (VBR) traffic such as MPEG video. The UGS scheduling mechanism can minimize delay in bandwidth request-allocation process; however, at the same time, it might waste bandwidth or suffer from insufficient bandwidth with VBR traffic. On the other hand, the rtps mechanism effectively utilizes bandwidth at the cost of additional delay due to on-demand bandwidth request. To strike a balance between delay and utilization, ertps is introduced in IEEE e [1], an amendment of IEEE [3]. Like UGS, the ertps scheduling mechanism allocates bandwidth periodically without any request so as to decrease delay. Also, in a similar way to rtps, it can adjust the size of bandwidth allocation to increase utilization. However, any specific bandwidth request-allocation algorithm is not standardized so that proprietary implementations may be used by equipment vendors. Although there have been several proposals for QoS scheduling frameworks and algorithms for IEEE BWA networks in the literature [4], [5], [6], [7], [8], [9], they mainly focus on the QoS architecture and scheduling algorithm (i.e., bandwidth allocation algorithm) in a base station, rather than bandwidth request algorithm in a subscriber station. In this paper, we propose a simple and efficient uplink bandwidth request algorithm for the ertps scheduling mechanism, aiming to minimize bandwidth wastage without /09/$25.00 ß 2009 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS

2 1236 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 8, NO. 9, SEPTEMBER 2009 violating QoS requirements. The key idea for this algorithm is twofold: 1) In order to maintain satisfactory QoS, we introduce a notion of target delay, i.e., tolerable delay in the MAC layer, which can be interpreted as a target value of the transmission queue length. 2) Moreover, to improve utilization, we propose to deploy dual feedback architecture: one for difference between the backlogged amount of traffic in the transmission queue and its target value and the other for the mismatch between packet 1 arrival and service rates. Using the dual feedback, the proposed algorithm dynamically calculates the amount of bandwidth request so that the bandwidth wastage is minimized. At the same time, it can decrease delay violation probability and delay jitter, by controlling the MAC-layer service delay around the desired level. Moreover, it responds quickly to the variation of traffic load and is robust to the change of network condition, due to the dual feedback. Based on a control-theoretic approach, we analyze the performance and stability of the proposed algorithm and derive a simple design guideline. Also, we implement this algorithm using OPNET [10] simulator and perform extensive simulations. The simulation results confirm that the proposed algorithm can control delay to the desired level with significantly reduced jitter and bandwidth wastage, and its performance is robust to various traffic patterns. In this paper, we restrict out attention on the uplink bandwidth request mechanism for VBR traffic, since downlink scheduling does not involve any bandwidth request-allocation process and adjusting the size of bandwidth request is not necessary for CBR traffic. The contributions of this study include:. The proposed algorithm strikes a balance between utilization and QoS, i.e., it increases efficiency of bandwidth allocation without violating QoS requirements.. This algorithm provides a control knob for the delay. By setting the target delay appropriately, it can control delay to the desired level while minimizing delay jitter.. Although this algorithm is developed for the ertps scheduling class, it can be applied to the rtps class without any significant changes. Moreover, it can be extended to a generalized uplink bandwidth request mechanism for real-time service under centralized scheduling framework. The rest of this paper is organized as follows: In Section 2, we briefly introduce QoS scheduling architecture and uplink bandwidth request-allocation mechanisms standardized in IEEE e. In Section 3, we propose a dynamic bandwidth request mechanism, which makes use of target delay and dual feedback. In Section 4, we analyze the proposed algorithm and provide a design guideline to make the system stable. Section 5 presents extensive simulation results to evaluate the performance of the proposed scheme. Additionally, we discuss about previous work related to QoS scheduling issue in IEEE networks in Section 6. Finally, we conclude the paper in Section In this paper, packet denotes MAC-layer payload that does not include MAC-layer header overhead, i.e., MAC service data unit (MSDU), unless otherwise stated. 2 QOS ARCHITECTURE OF IEEE NETWORKS 2.1 Scheduling Framework This paper considers point-to-multipoint (PMP) architecture of IEEE BWA networks, where transmission only occurs between a base station (BS) and subscriber stations (SSs) and the BS controls all the communications between BS and SSs. All the transmissions are associated with a unidirectional connection, which is associated with a service flow characterized by a set of QoS parameters, e.g., tolerable delay and minimum/maximum traffic rate. The connection can be either downlink (from BS to SS) or uplink (from SS to BS), each of which is denoted as DL and UL, respectively. The DL and UL connections are scheduled independently and served in the separate region of physical (PHY) layer frame, e.g., orthogonal frequency division multiple access (OFDMA) frame. The DL channel is a broadcast channel, while the UL channel is shared by several SSs in a manner that an SS requests its required bandwidth and the BS allocates it by scheduling all the requests from the SSs. Fig. 1 shows the UL scheduling architecture. Note that the DL scheduling is not shown in Fig. 1 for the sake of simplicity. When establishing a connection, a proper connection admission control is performed at the BS. Once the connection is admitted, the BS scheduler in Fig. 1 allocates bandwidth to the connection in a periodical way or ondemand basis, depending on the service class of the connection. As a result of uplink scheduling, 2 the BS generates and broadcasts UL MAP message containing two-dimensional (time and frequency) channel allocation information. The MAP message indicates the time when an SS can transmit and how long it can do, and which subchannel it can occupy. After receiving the UL MAP, the SS can transmit packets in the predefined time slots and subchannel. It is important to note that the BS scheduler allocates bandwidth on SS basis, although the bandwidth request is performed on connection basis. Therefore, the SS needs to redistribute the allocated bandwidth to the connections, which is done by an SS scheduler depicted in Fig. 1. Depending on the scheduling class, there are several ways for an SS to request bandwidth. The details about uplink bandwidth request-allocation mechanisms defined in the IEEE e will be discussed in the next section. 2.2 Uplink Bandwidth Request-Allocation Mechanisms In the standard of IEEE [3], four uplink scheduling classes are defined:. UGS: This class has the highest service priority and is designed to support CBR traffic generating constant-sized packets in a constant period, e.g., VoIP traffic. On establishing UGS connection, the SS declares its required bandwidth, bandwidth allocation interval, and maximum tolerable delay. Then, BS allocates the requested amount of bandwidth periodically in an unsolicited way. Therefore, UGS can eliminate overhead and delay resulting from the bandwidth request-allocation process. 2. In this paper, the term of uplink scheduling indicates the bandwidth allocation mechanism for the uplink connections, and the uplink scheduler is deployed in the BS.

3 PARK: EFFICIENT UPLINK BANDWIDTH REQUEST WITH DELAY REGULATION FOR REAL-TIME SERVICE IN MOBILE WIMAX NETWORKS 1237 Fig. 1. Schematic diagram of IEEE uplink scheduling framework.. rtps: This is for real-time VBR traffic generating variable-sized packets periodically, e.g., MPEG video. By issuing polls at every given interval, the BS gives request opportunities to SSs and the SS requests bandwidth without contending with other SSs. While UGS is proactive to the bandwidth requirement, rtps is reactive to the bandwidth demand. Therefore, rtps involves an additional delay in the bandwidth request-allocation process.. nrtps: This scheduling class is designed to support non-real-time VBR traffic that requires minimum bandwidth guarantee but is insensitive to delay, e.g., FTP. The nrtps scheduling class uses the same polling mechanism as rtps; however, it is allowed to contend for bandwidth request opportunity.. BE: This is for the best effort traffic that does not have any specific QoS requirements, e.g., or Web. The BS does not give any dedicated request opportunity to the SSs. Thus, the SS contends for the bandwidth request opportunity. After getting the opportunity, it sends a bandwidth request message. This class has the lowest service priority. In addition to these four types of service classes, IEEE e introduces another service class, ertps.. ertps: This is basically identical to UGS, except that ertps can change the allocated bandwidth dynamically depending on the traffic characteristics. On detecting that the allocated bandwidth is insufficient to serve packets in time, the SS requests an additional bandwidth by piggybacking its amount on the packet header. Otherwise, if the connection becomes inactive or traffic input rate decreases, the SS can request stopping or decreasing the bandwidth allocation. Therefore, the ertps is suitable for real-time VBR traffic and VoIP traffic with silence suppression. In summary, the bandwidth request for UGS is done in an unsolicited manner and that for rtps and nrtps is achieved in a polling-based way, and the BE service contends for bandwidth request opportunity. On the other hand, the bandwidth allocation for UGS is performed based on reservation and that for rtps, nrtps, and BE is done on a demand basis. The ertps class employs hybrid approach in bandwidth request and allocation. 3 DYNAMIC BANDWIDTH REQUEST ALGORITHM In this section, we propose an efficient uplink bandwidth request-allocation algorithm for real-time service. First, we explain key design rationales of the proposed algorithm. Then, we describe the detailed algorithm and discuss several issues. 3.1 Design Rationale The design objectives of the optimal bandwidth requestallocation algorithm for real-time service are as follows:. It should estimate the required bandwidth timely and accurately.. It should neither waste bandwidth nor suffer from lack of bandwidth.. It should satisfy delay requirement and minimize jitter.

4 1238 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 8, NO. 9, SEPTEMBER 2009 Fig. 2. Several functions to calculate additional bandwidth request depending on the queue length. (a) Step function, (b) linear function, and (c) nonlinear function. To achieve these purposes, we introduce target delay and dual feedback Introduction of Target Delay The target delay plays a key role in determining the amount of bandwidth request. Instead of minimizing delay, we allow delay up to its target value in order to increase the efficiency of bandwidth usage. Most real-time services have a tolerable end-to-end delay up to which QoS is little deteriorated, e.g., ms for VoIP service and a few hundreds of milliseconds for streaming service. Taking this tolerable delay into account, we can set a target MAC-to-MAC delay, T ref, between BS and SS. It is noteworthy that T ref does not include codec delay and playout buffer delay in the application layer. In order to translate T ref into the target length of transmission queue in SS, Q ref, we make the following reasonable assumptions: A1. A connection admission control is applied to the real-time services so that they are served with the guaranteed bandwidth (in an average sense) once admitted. A2. The BS scheduler employs a priority scheduling algorithm to serve real-time services with high priority. A3. The capacity of link connecting wireless access network to wired network is large enough not to incur any queuing delay in the BS for UL transmission. A4. The retransmission mechanisms (e.g., automatic repeat request (ARQ) or hybrid ARQ (HARQ)) are not employed for real-time traffic. A5. A QoS policy server dynamically establishes an ertps connection for real-time service and sets its bandwidth allocation interval to be equal to the packetization interval, 3 which is constant. The tolerable queuing delay in SS can be considered as T q ¼ T ref T o, where T o represents an additional delay at the MAC layer except queuing delay, e.g., transmission delay over wireless link and processing delay. With these assumptions, we can consider that T o is nearly constant. By 3. The most of common codecs for voice and video applications (e.g., G.711, G.729, H.264, or MPEG) generate packets periodically, even though the bit rate is variable. taking the average packet size l (byte) into account, we can represent Q ref (byte) in terms of T ref and as Q ref ¼ l T ref T o : ð1þ Let us denote the size of transmission queue as qðtþ and the required additional bandwidth due to qðtþ as b q ðtþ. As qðtþ increases over Q ref ; b q ðtþ needs to be increased accordingly to satisfy delay requirement. We can consider several approaches to calculate b q ðtþ. The primitive way, as shown in Fig. 2a, is to ask for additional bandwidth at the amount of b if qðtþ exceeds a maximum threshold value, qth max (>Q ref ), and to reduce the allocated bandwidth by amount of b if qðtþ falls below a minimum threshold value, qth min (<Q ref ). Alternatively, we can calculate b q ðtþ in proportion to the difference between qðtþ and Q ref, as depicted in Fig. 2b. In this approach, we can set the upper and lower limit on b q ðtþ, denoted as max ð>0þ and min ð<0þ, respectively, to avoid a sudden change of b q ðtþ. Also, we can consider a nonlinear function to calculate b q ðtþ, as shown in Fig. 2c. In this approach, the rate of b q ðtþ increases as the discrepancy between qðtþ and Q ref increases, to make fast compensation for bandwidth surplus/deficit Dual Feedback Approach The bandwidth request control based on the queue length, b q ðtþ, reacts slowly to the variation of packet arrival rate because b q ðtþ changes after detecting the deviation of queue length from the desired level. To make the response fast, we introduce the dual feedback consisting of two feedback loops for queue length and rate. Let us define packet arrival rate and service rate as aðtþ and sðtþ, respectively, and an additional bandwidth request due to rate mismatch as b r ðtþ. As the information of queue length mismatch, e q ðtþ ¼qðtÞ Q ref, is used in calculating b q ðtþ, the information of rate mismatch, e r ðtþ ¼aðtÞ sðtþ, is utilized in calculating b r ðtþ. As the packet arrival rate exceeds the service rate, packets are accumulated in the queue. Then, b r ðtþ needs to be positive to serve these packets timely. On the other hand, if aðtþ <sðtþ, the queue length tends to decrease. In this case, less bandwidth is required and b r ðtþ becomes negative in order not to waste bandwidth. The rate

5 PARK: EFFICIENT UPLINK BANDWIDTH REQUEST WITH DELAY REGULATION FOR REAL-TIME SERVICE IN MOBILE WIMAX NETWORKS 1239 feedback provides predictive information about queue length, and thus, the bandwidth request control based on the rate feedback shows anticipatory response to the queue length change, giving fast response to the variation of packet arrival rate. The total additional bandwidth request under the dual feedback architecture, BðtÞ, consisting of queue-based component b q ðtþ and rate-based component b r ðtþ, can be represented in a generalized form as BðtÞ ¼b q ðtþþb r ðtþ ð2þ ¼ fðe q ðtþþ þ gðe r ðtþþ; where fðþ and gðþ indicate appropriate nonnegative functions. 3.2 Algorithm We consider linear functions for fðþ and gðþ in (2) for the simplicity as þ BðtÞ ¼ K q e q ðtþþk r e r ðtþ ; ð3þ where K q and K r denote constant control gains that have nonnegative values. In (3), ½Š þ denotes a saturation function with upper/lower limit of B max =B min in order to take the implementation constraint into account. The rate mismatch e r ðtþ can be represented in terms of queue length mismatch, i.e., e r ðtþ ¼aðtÞ sðtþ ¼ d dt qðtþ ¼ d dt e qðtþ; for 0 <qðtþ <Q max : Here, Q max is the maximum queue size. To implement this algorithm, we need to transform the continuous-time function BðtÞ to a discrete-time function by sampling every bandwidth allocation interval, i.e., B½nŠ ¼Bðn Þ, where n is a nonnegative integer. We approximate the derivative term in (4) using a first-order Euler approximation, i.e., e r ðtþ ¼ d dt e qðtþ e q½nš e q ½n 1Š : ð5þ In order to avoid a sudden change of the bandwidth request and to make the system stable, we calculate the queue length error based on the moving average, instead of the instantaneous value. The moving average of queue length error, denoted as e q ½nŠ, can be obtained in a typical autoregressive manner as e q ½nŠ ¼ð1 wþe q ½n 1Šþwe q ½nŠ; where w denotes a weighting factor. As the value of w increases, the weighted average e q puts more weight on the recent samples so that it better reflects the current state. Otherwise, if the value of w decreases, e q changes slowly and steadily. There is a trade-off between responsiveness and stability in setting the value of w. From (3)-(6), we can calculate the bandwidth request B½nŠ only with the current and previous values of e q as B½nŠ ¼ K q þ K r e q ½nŠ K r e q ½n 1Š þ ð4þ ð6þ : ð7þ 3.3 Discussions Implementation It is important to note that B½nŠ in (7) is the increment or decrement of bandwidth request during the nth allocation interval. After calculating B½nŠ, an SS informs the BS of the bandwidth request by conveying it on the extended piggyback request (EPBR) field of grant management subheader [1]. According to IEEE e standard, the size of EPBR field is 11 bits and it has two operation modes, incremental mode and aggregate mode. If the first bit of EPBR field is set to zero, the remaining 10 bits represent the increment of bandwidth request (i.e., B max ¼ 1;023 bytes); otherwise, they represent the aggregate bandwidth request. Therefore, if B½nŠ > 0, it can be carried in both incremental and aggregate modes. Otherwise if B½nŠ < 0, the SS calculates the total bandwidth request B½nŠ as B½nŠ ¼maxðB½n 1ŠþB½nŠ;B min Þ; where B min denotes the minimum amount of bandwidth allocation required for transmitting bandwidth request message, i.e., the size of grant management subheader. Then, the SS requests B½nŠ in the aggregate mode. In order to cope with the transmission failure of EPBR field, we prefer the aggregate mode regardless of the value of B½nŠ Computation/Communication Overhead The computation overhead of the proposed algorithm is not significant. The number of operations is quite small and the operations consist of addition and multiplication. Moreover, the calculation of bandwidth request is performed by each SS in a distributed manner and only requires keeping track of the current and previous values of its own transmission queue length, as given in (7). The BS requires neither additional calculation nor modification to implement the proposed algorithm; it only allocates the required bandwidth via priority scheduling mechanism. Thus, the proposed algorithm does not degrade scalability of the BS. On the other hand, the communication overhead associated with piggybacking the bandwidth request is negligible. The size of the grant management subheader is just 2 bytes according to the standard of IEEE e [1]. This minimal overhead is mandatory for the real-time scheduling services of IEEE (e.g., UGS and rtps, as well as ertps) and, hence, the proposed algorithm does not result in any additional overhead in the packet header. Consequently, it can be a practical solution for dynamic bandwidth request mechanism for real-time services Optimization Problem and Proportional-Derivative Control The problem dealt in this paper can be formulated as an optimization problem that minimizes the wastage of bandwidth allocation under constraints of per-flow delay requirement and total network capacity, i.e., minimize X ja i ðtþ s i ðtþj i subject to d i ðtþ T ref;i and X i s i ðtþ CðtÞ; ð8þ ð9þ

6 1240 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 8, NO. 9, SEPTEMBER 2009 in the MAP. When transmitting packets, the SS requests bandwidth for the backlogged packets in a piggyback manner. Then, the bandwidth request is virtually buffered at the per-ss request queue 4 in BS. At every time, the scheduler in BS calculates the amount of bandwidth allocation from the request queue and generates/delivers UL MAP to SS. Note that the scheduler does not allocate bandwidth as soon as it receives request but it is done at the constant period of. Therefore, as illustrated in Fig. 3, SS transmits packets at the same period of ð¼ T pkt Þ. Fig. 3. Timing diagram for bandwidth request/allocation process. where CðtÞ is network capacity, a i ðtþ and s i ðtþ denote arrival and service rates of flow i, and d i ðtþ and T ref;i are its MAC-to-MAC delay and target delay, respectively. The bandwidth wastage can be minimized by preventing buffer underflow, and delay requirement can be satisfied by making queue length not exceed a certain threshold value. Also, the constraint of total network capacity can be relaxed by adopting an admission control that only allows a new service flow if its bandwidth requirement can be satisfied with the available network capacity. Under these rationales, the optimization problem given in (9) can be considered equivalent to the problem of queue regulation around the target value, i.e., the problem of minimizing queue length error. Moreover, in the literature of feedback control system, the proposed dual control can be formulated as proportional-derivative (PD) control [11] with respect to the queue length error. The proportional control determines the reaction to the current error, and the derivative control determines the reaction to the rate at which the error has been changing. Thus, the derivative control improves anticipatory response by adding an appropriate correction prior to the actual change of error. The queue length error can be minimized with the optimal values of control parameters, which can be obtained by deriving system model and applying various tuning techniques [12], e.g., Ziegler-Nichols method and Cohen-Coon method, to the derived model Timing Diagram for Bandwidth Request/Allocation Process Fig. 3 shows timing diagram for bandwidth request/ allocation process between SS and BS. As shown in Fig. 3, packets arrive at the period of T pkt and bandwidth is allocated at the period of. It is important to note that packet arrival process and bandwidth allocation process are independent of each other and that is set to be equal to T pkt, as already stated in the assumption (A5). Arriving packets are buffered in SS s transmission queue and they are served after receiving bandwidth allocation from BS. If an SS receives UL MAP containing bandwidth allocation message at frame k, the SS decodes the MAP and transmits the buffered packet at frame k þ 1 by the amount indicated Interaction with Scheduling To serve uplink traffic in WiMAX networks, BS performs scheduling (bandwidth allocation) and SS performs bandwidth request. 5 Once each SS requests bandwidth, the BS schedules these requests based on available resource, QoS requirement, and/or channel status. We can consider that both bandwidth request and scheduling algorithms have the same objective such as satisfying QoS requirement and/ or maximizing utilization. This paper deals with bandwidth request problem rather than bandwidth allocation problem. It is clear that the bandwidth request can be performed by SS independent of scheduling algorithm employed in BS and that the proposed bandwidth request algorithm can be incorporated with any well-known scheduling algorithms, e.g., weighted fair queuing (WFQ) (or its variant for wireless network), proportional fair (PF) scheduling [13], earliest deadline first (EDF) scheduling, and modified largest weighted delay first (M-LWDF) scheduling [14], as well as simple priority scheduling. 4 ANALYSIS OF THE PROPOSED ALGORITHM This section analyzes the behavior of the proposed algorithm. A system model is derived and the stability is analyzed from a control-theoretic viewpoint. Based on this analysis, a design guideline for control parameters is provided. 4.1 System Modeling The overall architecture of the proposed system is represented as a block diagram in Fig. 4. The system consists of transmission queue, low pass filter, queue length controller, rate controller, and uplink scheduler. In Fig. 4, the left part represents bandwidth request by SS while the right part represents bandwidth allocation by BS. 6 The SS calculates additional bandwidth request with queue length controller and rate controller. Then the service rate is determined by the uplink scheduler based on bandwidth request. Accordingly, the queue length is changed. The backward delay in Fig. 4 is used to represent previous bandwidth request while forward delay corresponds to the bandwidth allocation interval. It is worthwhile to note that 4. The request queue does not buffer actual data packets but buffers control messages containing the amount of bandwidth request for UL scheduling. 5. For downlink traffic, the process of bandwidth request is not required since BS maintains queue for downlink traffic and it is aware of queue status. 6. If aggregate mode is used as bandwidth request, the process of summing previous request (Bðt Þ) and current additional request (BðtÞ), which is indicated below uplink scheduler block in Fig. 4, is performed by SS. Otherwise if incremental mode is used, it is performed by BS.

7 PARK: EFFICIENT UPLINK BANDWIDTH REQUEST WITH DELAY REGULATION FOR REAL-TIME SERVICE IN MOBILE WIMAX NETWORKS 1241 _BðtÞ ¼BðtÞ ; ð13þ sðtþ ¼ Bðt Þ : ð14þ In (14), ð 1Þ denotes the ratio of bandwidth allocated by the BS to bandwidth requested by the SS. Under the assumptions of admission control and priority scheduling, 1 on average, i.e., almost all the required bandwidth is allocated to serve packets. The details about the derivations of (10)-(14) are given in Appendix A.1. We investigate the behavior and stability of the proposed bandwidth request-allocation mechanism using the transfer function. Taking Laplace Transform to the system model described in (10)-(14), we have the following transfer function: GðsÞ ¼ E qðsþ AðsÞ ¼ s 3 þ 1 s 2 þ w T 2 s a s 4 þ 1 s 3 þ w T s 2 þ w ðk a 2 r s þ K q Þ : T 4 a ð15þ Fig. 4. Block diagram of the proposed feedback system. these two delays have the same value of and that they are constant, as shown in Fig. 3. This feedback system can be modeled with several dynamic equations for queue length error and bandwidth request under the assumptions (A1)-(A5) made in Section 3. For the sake of tractability, we consider continuous-time model instead of discrete-time model. From (3)-(8), the overall system constitutes a fourth-order linear feedback system with time delay: _e q ðtþ ¼aðtÞ sðtþ; _e q ðtþ ¼ w ðe q ðtþ e q ðt ÞÞ; _BðtÞ ¼K q _e q ðtþþk r e q ðtþ; ð10þ ð11þ ð12þ The transfer function (15) is characterized by two control parameters K q and K r, bandwidth allocation interval, and weighting factors w and. Note that the transfer function is independent of the average packet size. Refer to Appendix A.2 for the details about the derivation of (15). 4.2 Effect of Control Parameters In this section, we investigate the behavior of the proposed algorithm using numerical analysis. For the simplicity of analysis, we ignore the limits on the queue length and bandwidth request, i.e., Q max ¼1 and B max =B min ¼ 1= 1. In the numerical analysis, we set and w to 0.05 sec and 0.9, respectively. Figs. 5a and 5b show impulse responses for several values of K q and K r, respectively. The impulse response shows how e q ðtþ decays and is stabilized for the impulse input of aðtþ. First, we investigate the effect of K q from Fig. 5a. Here, K r is fixed at If K q ¼ 0:01;e q ðtþ converges to zero with negligible fluctuation. However, the fluctuation of e q ðtþ increases as the value of K q increases. If K q exceeds a certain critical value (approximately in this numerical analysis), e q ðtþ oscillates continuously and diverges. Next, we observe the effect of K r on system stability from Fig. 5b. Here, we fixed K q at 0.15 and varied K r from 0.01 to In the case Fig. 5. Impulse response of the proposed system for various values of control parameters. (a) Effect of K q (K q ¼ 0:15). (K r ¼ 0:01) and (b) effect of K r

8 1242 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 8, NO. 9, SEPTEMBER 2009 Fig. 6. Stability region for control parameters. (If the values of two control parameters K q and K r are in the region below the curve, the system is stable.) of K r ¼ 0:01;e q ðtþ diverges, which implies that the amount of bandwidth request can increase infinitely. However, if K r exceeds this value, the error converges to zero. As the value of K r increases, the frequency of fluctuations increases. In the case of K r ¼ 0:04;e q ðtþ diverges. 4.3 Stability Analysis As confirmed in Fig. 5, the convergence of queue length depends on the value of control parameters. It is imperative to derive condition of control parameters that assures system stability. For this purpose, we provide the following stability criterion, which can be used as a design guideline for control parameters. Proposition. The proposed bandwidth request-allocation system employing the dual feedback is stable, i.e., the queue length converges to the desired target value in steady state, if and only if the control parameters satisfy the following condition: wk 2 r wk r þ T 2 a K q < 0: ð16þ Proof. Proof is given in Appendix A.3. tu Corollary. The bandwidth request-allocation system without rate-based control is unstable, regardless of the value of queuebased control parameter and system parameters. Proof. It is obvious that the stability condition (16) cannot be satisfied with K r ¼ 0. tu Fig. 6 shows the stability region for K q and K r, which is obtained based on the stability criterion described in (16). From this numerical analysis, we can make the following conclusions:. For a given K r, there exists an upper bound on K q to assure stability.. For a given K q, there exist both upper and lower bounds on K r.. As increases, the stability region expands. However, the upper bound on K q is not affected by. Fig. 7. Simple network configuration used in the simulations. performance of the proposed algorithm in several aspects and to compare it with other algorithms regarding bandwidth allocation efficiency and QoS assurance. 5.1 Simulation Setup We consider an IEEE network under PMP architecture consisting of multiple SSs and an BS, as shown in Fig. 7. The BS is connected to the server via a wired T3 link. The OFDMA physical (PHY) layer parameters and their values are listed in Table 1. The simulation considers an urban environment to model long-term characteristics of wireless channel. The empirical COST-231 HATA model [15] is used for path-loss model, and ITU channel model [16] is used for multipath fading effect. Also, the shadowing is modeled as a lognormal random variable with zero mean and standard deviation of 8.9 db, and the interference from the neighboring cells are taken into account in calculating packet error rate. In the OPNET simulator, we implemented adaptive modulation and coding scheme. The supported modulation and coding rate are as follows: QPSK (1/12, 1/8, 1/4, 1/2, 3/4), 16QAM (1/2), 64QAM (2/3, 3/4, 5/6) for downlink, and QPSK (1/12, 1/8, 1/4, 1/2, 3/4), 16QAM (1/2, 3/4) for uplink. The modulation and coding rate change dynamically depending on the signal-to-interference-noise ratio. The maximum transmission queue size of SS is set to 16 Kbytes. The simulator does not implement packet retransmission mechanisms, e.g., HARQ and ARQ, because they incur additional processing delay to degrade QoS for delaysensitive real-time service. Unless otherwise stated, the TABLE 1 IEEE e OFDMA PHY Parameters and Their Values Used in the Simulations 5 PERFORMANCE EVALUATION In this section, we conduct extensive simulations using OPNET simulator with WiMAX module [10] to evaluate the

9 PARK: EFFICIENT UPLINK BANDWIDTH REQUEST WITH DELAY REGULATION FOR REAL-TIME SERVICE IN MOBILE WIMAX NETWORKS 1243 simulation configuration is identical to that recommended by WiMAX forum [17]. The performance will be evaluated in terms of efficiency, delay, and jitter:. MAC efficiency: It is defined as B sent Brcvd, where B sent and B rcvd are total bytes of MSDU sent and total bytes of bandwidth allocation received during the whole simulation time, respectively. Note that MAC-layer overhead is not included in the allocated bandwidth.. MAC-to-MAC delay: It is defined for every packet as the time difference between the generation of MSDU at SS and its reception at BS. This delay includes queuing delay, processing delay, and transmission delay over wireless link, but it does not include packetization delay and codec delay.. jitter: It is defined as standard deviation (STD) of MAC-to-MAC delay. 7 Note that packet loss rate is not considered as a performance index because the transmission queue size is large enough to prevent packet loss due to buffer overflow. We compare these performance indexes for the following four bandwidth request mechanisms implemented over the ertps connection:. conv: This algorithm is a conventional approach. The bandwidth is periodically allocated without request from SS at the amount of average MSDU arrival rate. If there still remains MSDUs in the transmission queue after serving them with the allocated bandwidth, the SS requests additional bandwidth at the amount of traffic remaining in the transmission queue. This algorithm is considered to have target delay of zero to minimize delay.. single-q: This algorithm employs queue-lengthbased control with nonzero target delay, but disables rate-based control, i.e., K q ¼ 1, K r ¼ 0, and Q ref > 0. Then, B½nŠ ¼e q ½nŠ from (7).. single-r: This algorithm employs only rate-based control without queue-length-based control, i.e., K q ¼ 0;K r ¼, so that B½nŠ ¼e q ½nŠ e q ½n 1Š from (7).. dual: This employs dual feedback control with target delay. The control parameters are set as K q ¼ 0:1 and K r ¼ 0:01, based on the stability criterion (16). By comparing performance of conv and single-q, we can evaluate the effect of target delay on the queue-lengthbased control. In a similar way, we can observe the effect of dual feedback by comparing performance of dual with those of single-q and single-r. The weight w used in calculating average value of queue length is set to 0.9. A real-time video traffic is considered in the simulations. Its packet size is randomly distributed (e.g., along with exponential, normal, or Pareto distributions) while the packetization interval is fixed. At the same time, we consider the background traffic with greedy FTP traffic. 7. Alternatively, the jitter may be defined as the time difference between two consecutive packets arrived at the receiver. In this study, however, the jitter is defined as the standard deviation of delay in order to evaluate the queue regulation performance. The real-time traffic is transferred using RTP/UDP/IP protocol suite, while background traffic uses TCP/IP protocol suite. In Fig. 7, the left four SSs are considered to send uplink real-time traffic, each of which has conv, single-q, single-r, and dual algorithms, and the remaining five SSs are considered to send and receive background traffic over BE connections. Note that the simulation results shown with respect to time (e.g., in Fig. 8) are obtained from a single instance of simulation; on the other hand, the results shown with respect to parameters (e.g., in Fig. 10) are averaged over 10 instances of simulation with different random seeds. 5.2 Queue Regulation and Rate Adaptation In the first simulation, we evaluate the performance focusing on queue regulation and rate adaptation. Here, the application-layer payload size is randomly determined from an exponential distribution with mean of 500 bytes, and both the packetization interval and bandwidth allocation interval are set to 20 ms. 8 Also, the target values of delay and queue length are set to 100 ms and 2 KB, respectively. Fig. 8 shows the queue length and MAC-to-MAC delay for the conv, single-q, single-r, and dual algorithms. As shown in Fig. 8a, both queue length and delay of conv are minimized because its target value corresponds to zero. Thus, conv suffers from a significant bandwidth wastage, which will be shown in Fig. 9. In the case of single-q (Fig. 8b), the introduction of target delay makes the average values of queue length and delay close to their target values (i.e., 2 KB and 100 ms). However, due to the lack of rate control, they are not regulated tightly and fluctuate severely causing large delay jitter. 9 As shown in Fig. 8c, single-r fails to regulate queue length and delay around the target values. It is because the additional bandwidth request of single-r is independent of the target delay, i.e., B½nŠ ¼e q ½nŠ e q ½n 1Š ¼q½nŠ q½n 1Š from (6) and (7). However, Fig. 8d shows that dual outperforms the other algorithms in terms of queue length and delay regulation. Moreover, we can observe that the delay is directly related to the queue length, which validates the relationship between target queue length and target delay described in (1). Fig. 9 shows the rate mismatch between the packet arrival rate (aðtþ) and bandwidth grant rate (bðtþ). Note that the bandwidth grant rate is identical to the packet service rate as long as there are sufficiently many packets to serve. However, the allocated bandwidth may be wasted if the bandwidth grant rate is excessive so that there remains no packet to serve. In the case of conv (Fig. 9a), bðtþ is much higher than aðtþ, which confirms that conv achieves minimizing delay at the cost of significant bandwidth wastage. The difference between aðtþ and bðtþ is reduced in the cases of single-q (Fig. 9b) and single-r (Fig. 9c). 8. Since the header sizes of RTP/UDP/IP are 12/8/20 bytes, respectively, the average arrival rate of MSDU becomes ð500 þ 40Þ 8 bits= 20 ms ¼ 216 Kb=s. 9. According to the stability analysis stated in Corollary of Section 4.3, the single-q algorithm is unstable. However, its queue length and delay do not diverge in the simulation. It is because the analysis did not take the limits on the queue length and bandwidth request into account, which are set as Q max ¼ 16 KB and B max =B min ¼þ= 1;024 B in this simulation.

10 1244 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 8, NO. 9, SEPTEMBER 2009 Fig. 8. Comparison of queue length and MAC-to-MAC delay for conv, single-q, single-r, and dual algorithms. (a) conv, (b) single-q, (c) single-r, and (d) dual. The bandwidth grant rate of single-q fluctuates severely due to the lack of rate control, thus the queue length and delay oscillate severely (see Fig. 8b). As shown in Fig. 9c, bðtþ of single-r keeps track of aðtþ, but there exists some discrepancy between them. On the other hand, in the case of dual (Fig. 9d), bðtþ agrees quite well with aðtþ, because dual employs rate control as well as queue length control. The outstanding rate adaptation performance of dual results in the tight regulation of delay. Table 2 lists the average and standard deviation (STD) of qðtþ, and rate mismatch (i.e., jaðtþ bðtþj) for the four algorithms. Since both single-q and dual make use of the target queue length, their average queue lengths are close to the target value of 2 KB while those of conv and single-r are less than 1 KB. In the case of dual, the STD of queue length is smaller than those of single-q and single-r by 3.0 and 1.9 times, respectively. Also, dual decreases the average and STD of rate mismatch compared to the other algorithms up to 7.3 and 3.6 times, respectively. The queue regulation and rate adaptation of dual are key features to provide optimal bandwidth allocation and delay control. 5.3 Optimal Bandwidth Allocation This simulation focuses on the performance from the perspective of optimal bandwidth allocation. It is clear that there is a trade-off between efficiency and performance in allocating bandwidth. As the allocated bandwidth increases, the performance (e.g., delay and jitter) is improved at the cost of decreased efficiency. In order to evaluate this trade-off for the various conditions of bandwidth allocation, we introduce provisioning level,, defined as the ratio of the minimum reserved bandwidth to the average packet arrival rate. In this simulation, we observe performance indexes for ranging from 0.8 to Unless otherwise stated, the simulation configuration is same as that in the previous simulation. As shown in Fig. 10a, the efficiency of conv is much lower than the other algorithms and it decreases almost linearly according to the increase of ; its maximum value is only 70 percent and it falls below 59 percent. The conv algorithm wastes bandwidth by about percent. The reason is that conv requests additional bandwidth at the amount of remaining packets in the transmission queue, but it does not adapt bandwidth request as long as the transmission queue becomes empty after serving packets. However, the efficiency of single-q increases remarkably due to the introduction of (nonzero) target delay. Unlike conv, single-q sets a nonzero target delay and the corresponding target queue length, so it requests increasing/decreasing bandwidth allocation as long as the transmission queue length becomes larger/smaller than the target value. Thus, the efficiency of single-q is much 10. The corresponding minimum reserved bandwidth is set to range from 0:8 216 Kb=s 175 Kb=s to 1:2 216 Kb=s 260 Kb=s.

11 PARK: EFFICIENT UPLINK BANDWIDTH REQUEST WITH DELAY REGULATION FOR REAL-TIME SERVICE IN MOBILE WIMAX NETWORKS 1245 Fig. 9. Comparison of arrival rate and bandwidth grant rate for conv, single-q, single-r, and dual algorithms. (a) conv, (b) single-q, (c) single-r, and (d) dual. higher than that of conv and it is almost immune to the provisioning level. In the case of single-r, the adaptation process of bandwidth request is performed based on the difference of queue length B½nŠ ¼ðq½nŠ q½n 1ŠÞ. If the queue length tends to increase/decrease, it requests increasing/decreasing bandwidth allocation accordingly. Since single-r does not have the notion of target queue length, its efficiency is smaller than that of single-q by about 4-5 percent, as shown in Fig. 10. However, dual maintains high level of efficiency close to 100 percent regardless the value of. The efficiency of dual lies between 98.3 percent and 98.5 percent and is higher than those of conv, single-q, and single-r by about percent, percent, and percent, respectively. By comparing the efficiency of dual with those of TABLE 2 Performance Comparison with Respect to Queue Regulation and Rate Adaptation single-q and single-r, we can confirm the importance of dual feedback control. Next, we investigate the effect of on delay from Fig. 10b. For all the four algorithms, the delays are not sensitive to. Regardless the value of, conv maintains the minimized delay and it is not greater than 26 ms. By comparing Fig. 10a and Fig. 10b, we observe that conv has a clear trade-off between efficiency and delay with respect to the provisioning level. On the other hand, single-q and dual regulate delay around the target value of 100 ms, their average delays are ms and ms, respectively. Also, they are robust to the provisioning level. It is because they adaptively change bandwidth request, regardless of the predefined bandwidth reservation, so as to satisfy the desired target delay. On the other hand, the delay of single-r is smaller than those of single-q and dual but larger than that of conv, it lies between 52 ms and 63 ms. We compare the jitter from Fig. 10c. For the entire range of, the jitter of conv is smallest among the four algorithms and it decreases slightly as increases. On the other hand, the jitter of single-r is largest. However, dual has almost constant delay jitter, regardless of the provisioning level, since it tightly regulates the queue length, as already confirmed in Fig. 8. The jitter of dual is about 20 ms and is smaller than those of single-q and single-r by up to about 1.5 and 2.4 times, respectively.

12 1246 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 8, NO. 9, SEPTEMBER 2009 Fig. 10. Comparison of several performance indexes with respect to the provisioning level. (a) Efficiency, (b) delay, and (c) jitter. Fig. 10 confirms that dual adjusts the amount of bandwidth request to satisfy delay requirement, while minimizing bandwidth wastage and reducing delay jitter, regardless of the bandwidth provisioning level. Once the desired target delay is given, dual allocates bandwidth optimally due to the dual feedback mechanism. 5.4 Delay Control According to Target Value This simulation is performed to evaluate how the proposed dual scheme can control delay according to the target value. For this purpose, we repeat simulations with different values of T ref, 50, 100, 150, 200, and 300 ms. Fig. 11 shows cumulative distribution of MAC-to-MAC delay. Remind that the granularity of MAC-layer scheduling delay is 5 ms, TDD/OFDMA frame duration. From Fig. 11, we can observe that the delay is tightly distributed around its target value. The median delay is almost equal to the given target value, while its 90-percentile value is deviated from T ref no more than about 20 ms. Table 3 summarizes delay statistics and efficiency. The difference between average delay and target delay is not larger than 15 ms, and the standard deviation is not much affected by the target delay; it ranges from 20 ms to 37 ms for the entire range of the target delay. Also, we observe that the efficiency of dual is little affected by the value of target delay; it lies between 96.3 percent and 98.6 percent. These results show the unique competence of the proposed dual algorithm in terms of fine controllability of delay, which cannot be achieved with other algorithms. 5.5 Robustness to Traffic Pattern In this simulation, we investigate the effect of payload size and its distribution on the performance of the dual algorithm. We change the average payload size from 100 bytes to 1,500 bytes and consider the following three random distributions for the payload size:. Normal distribution: mean ¼, variance ¼,. Exponential distribution: mean ¼, and. Pareto distribution: shape ¼ 2; location ¼ =2. Note that the degree of randomness is weakest for the normal distribution and is strongest for the Pareto distribution. With the packetization interval of 20 ms, the application-layer bit rate changes from 40 kb/s to 400 kb/s. Figs. 12a, 12b, and 12c show efficiency, delay, and jitter, respectively. As shown in Fig. 12a, the efficiency of dual is best for the normal distribution, it is about 99 percent, regardless the value of. In the cases of exponential and Pareto distributions, however, the efficiency decreases especially when <500 bytes. Even for the worst case, the efficiency is larger than 95 percent. As decreases, Q ref decreases and the allowable amount of traffic in the transmission queue decreases accordingly. Thus, the probability that the transmission queue becomes empty increases, resulting in the decrease of efficiency. As was expected, the efficiency is positively related to the degree of randomness; i.e., it is highest for the normal distribution and lowest for the Pareto distribution. Next, we observe the delay and jitter from Figs. 12b and 12c, respectively. The delay and jitter are not significantly affected by the packet size and its distribution. We observe that both average delay and jitter slightly increase as increases. The actual average delay is around its target value of 100 ms; it ranges between 88 ms and 109 ms, for the entire range of and its TABLE 3 Performance Indexes of the dual Algorithm with Respect to the Several Target Delays Fig. 11. Delay distribution of the dual algorithm with respect to the several target delays.

13 PARK: EFFICIENT UPLINK BANDWIDTH REQUEST WITH DELAY REGULATION FOR REAL-TIME SERVICE IN MOBILE WIMAX NETWORKS 1247 Fig. 12. Robust performance of the dual algorithm to the packet size and its distribution. (a) Efficiency, (b) delay, and (c) jitter. distributions. On the other hand, the jitter lies between 11 ms and 14 ms (normal distribution), 17 ms and 25 ms (exponential distribution), and 29 ms and 43 ms (Pareto distribution). The simulation results in Fig. 12 confirm the robust performance of the dual algorithm with respect to the payload size and its distribution. 6 RELATED WORK In the literature, there have been proposed several QoS scheduling frameworks and algorithms for IEEE networks. To provide differentiated levels of QoS to various applications, a QoS framework was proposed for uplink scheduling and admission control [4]. In this framework, different scheduling algorithms are combined: strict priority scheduling for UGS, earliest deadline first for rtps, and weighted fair queuing for nrtps. The performance of different scheduling service was evaluated in [5], where weighted round-robin scheduler and deficit round-robin scheduler are used for uplink bandwidth allocation in the BS and SS, respectively. In [18], a hierarchical and distributed scheduling architecture was proposed; it implements two layers of schedulers at BS and SS. The BS scheduler allocates bandwidth to SSs in order that the minimum reserved bandwidth is assured and the excess bandwidth is distributed fairly, while the SS scheduler redistributes the received transmission opportunity to satisfy QoS requirements. The approach in [7] is based conceptually on a single-level roundrobin scheduler such that the BS performs polling and allocates bandwidth based on QoS requirements and bandwidth request sizes. Besides approaches to assure diverse QoS requirements through scheduling, other approaches consider fairness and efficiency issues in dealing with QoS enhancement [6], [8], [19]. The scheduling algorithm in [6] introduces a utility function based on the waiting time in the queue and makes use of queue state information, as well as wireless channel information, to provide QoS in terms of delay while maintaining fairness among users. Also, a dynamic bandwidth allocation algorithm was proposed in [19], aiming to minimize delay for high-priority traffic and to maintain acceptable throughput for low-priority traffic. The BS employs a priority scheduling for high-priority traffic and controls back off window size used in the contention of transmission opportunity for low-priority traffic. The scheduler proposed in [8] dynamically calculates service priority based on both channel quality and service requirement, to improve wireless channel efficiency and to satisfy diverse QoS requirements. Recently, a queue-aware uplink bandwidth allocation mechanism along with a rate control mechanism has been proposed for polling service [9]. Based on the queue length, this scheme adjusts the amount of bandwidth allocation dynamically and limits packet generation rate so that delay and packet dropping probability can be controlled. Our approach is different from the previous work in the following aspects. The previous QoS scheduling algorithms in [4], [5], [7], [18] mainly focus on the bandwidth allocation problem to satisfy diverse QoS requirements, and they apply priority scheduling and/or fair scheduling algorithms to the queue of each service class. Thus, the scheduling algorithm is implemented in the BS. However, our approach focuses on the bandwidth request problem for dynamic bandwidth allocation such that the delay is regulated around the target value while maintaining high efficiency. Also, our mechanism is implemented in the SS, not in the BS, and works in a distributed manner. In striking a balance between QoS and efficiency, the proposed approach is different from the previous scheduling algorithms [6], [8], [19], in that our approach introduces the notion of target delay, which is controllable via a design parameter. Our approach tends to minimize bandwidth wastage without violating delay requirement. Moreover, the rate control in [9] is used to limit packet arrival rate, while the rate feedback in our approach is used to control bandwidth request by predicting queue length change. 7 CONCLUSION We have proposed the dynamic bandwidth request mechanism for VBR real-time traffic in IEEE broadband wireless access networks. By introducing the notion of target delay, a tolerable delay for real-time service, we can calculate an appropriate amount of bandwidth request that improves efficiency of wireless channel without degrading QoS. Moreover, to make the response to the change of traffic load fast, we have introduced the dual feedback architecture, where the feedback information consists of the difference between the actual queue length and the desired target length and the rate mismatch between packet arrival rate and service rate. Due to the target delay and the dual feedback, the proposed algorithm tightly regulates the

14 1248 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 8, NO. 9, SEPTEMBER 2009 queue length around the desired level, thus it can control delay to the target level while minimizing delay jitter. Also, the efficiency of bandwidth allocation is improved by controlling the service rate depending on the packet arrival rate. We have analyzed the proposed bandwidth requestallocation system based on a systematic approach. Using this analysis, we have derived a design guideline for the proposed algorithm to assure stability. By implementing the proposed algorithm in the OPNET simulator, we have evaluated its performance in terms of optimality of bandwidth allocation and capability of delay control. The simulation results confirm that the proposed algorithm can control delay to the desired level while reducing jitter and bandwidth wastage significantly, and its performance is robust to various traffic patterns. APPENDIX A A.1 Derivation of System Model We derive system model described in (10)-(14). The dynamic equation of e q ðtþ in (10) rephrases (4), and (11) can be obtained from (6) as _e q ðtþ e q½nš e q ½n 1Š ¼ w e q ½nŠ e q ½n 1Š ¼ w ðe q ðtþ e q ðt ÞÞ: We can straightforwardly derive (12) from (3) and (4) in which e q is replaced with e q. Here, we ignore the saturation function for the sake of tractability. To derive (13), we simplify (8) such that B½nŠ ¼B½n 1ŠþB½nŠ by assuming B½nŠ B min for 8n. Then, we can rewrite (8) as B½nŠ B½n 1Š ¼ B½nŠ : ða-1þ The left side of (A-1) can be approximated as _BðtÞ from a first-order Euler approximation. Finally, (14) represents that the service rate in the SS is given as the total bandwidth requested to the BS in the previous bandwidth allocation instant divided by the bandwidth allocation interval. A.2 Derivation of Transfer Function We can represent the system model described in (10)-(14) in s domain by taking Laplace Transform: E q ðsþ ¼ se q ðsþ ¼AðsÞ SðsÞ; w s þ w e sta E qðsþ w s þ w T 2 a s 2 þ 1 s þ w T 2 a BðsÞ ¼K q E q ðsþþk r s E q ðsþ; sbðsþ ¼BðsÞ ; E q ðsþ; ða-2þ ða-3þ ða-4þ ða-5þ SðsÞ ¼ BðsÞe Tas 1 BðsÞ: ða-6þ 1 þ s In deriving (A-3) and (A-6), we approximate the time delay as a first-order lag, i.e., e s 1 ð1 þ sþ [11]. This approximation of delay is widely used in the literature of feedback system and is valid in a typical WiMAX configuration. From (A-3)-(A-5), we can rewrite (A-6) as SðsÞ ¼! w K r s þ K q s þ w Ta 2 Ta 2s 1 þ s s 2 þ 1 s þ w E q ðsþ Ta 2 ða-7þ E q ðsþ: ¼ w T 2 a s K r s þ K q T 2 a s2 þ s þ w We replace SðsÞ in (A-7) with AðsÞ se q ðsþ from (A-2), then we can get the transfer function GðsÞ ¼E q ðsþ=aðsþ, as stated in (15). A.3 Proof of Proposition From (15), the characteristic equation is given as s 4 þ 1 s 3 þ w Ta 2 s 2 þ w Ta 4 K r s þ K q ¼ 0: ða-8þ Let us define the coefficient of nth-order term in (A-8) as a n (n ¼ 0; 1;...; 3), e.g., a 2 ¼ w Ta 2. Since the given system is a linear time-invariant system, the stability condition can be derived by applying the Routh-Hurwitz criterion [11] to (A-8). The necessary and sufficient conditions for stability are represented as a 3 a 2 a 1 > 0; a 1 ða 3 a 2 a 1 Þ a 2 3 a 0 > 0: ða-9þ ða-10þ Note that all the coefficients a n s are positive. If (A-10) is satisfied, (A-9) is also satisfied, i.e., a 3 a 2 a 1 >a 2 3 a 0=a 1 > 0. Therefore, the condition (A-9) is redundant and only the condition (A-10) is required for stability. The stability condition in (16) is directly derived from (A-10). ACKNOWLEDGMENTS This work was supported in part by the Dongguk University Research Fund of The author would like to thank Hwangnam Kim, Jae-Young Kim, Han-Seok Kim, and the anonymous reviewers for their valuable comments and suggestions. A preliminary version of this paper was presented at IEEE INFOCOM REFERENCES [1] IEEE WG, IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems, Amendment 2, IEEE, Dec [2] WiMAX Forum, WiMAX Technology Forecast ( ), June [3] IEEE WG, IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed Broadband Wireless Access Systems, IEEE, June [4] K. Wongthavarawat and A. Ganz, Packet Scheduling for QoS Support in IEEE Broadband Wireless Access Systems, Int l J. Comm. Systems, vol. 16, pp , Feb [5] C. Cicconetti, L. Lenzini, E. Mingozzi, and C. Eklund, Quality of Service Support in IEEE Networks, IEEE Network, vol. 20, no. 2, pp , Mar./Apr [6] G. Song, Y. Li, J.L.J. Cimini, and H. Zheng, Joint Channel-Aware and Queue-Aware Data Scheduling in Multiple Shared Wireless Channels, Proc. IEEE Wireless Comm. and Networking Conf. (WCNC 04), vol. 3, pp , Mar

15 PARK: EFFICIENT UPLINK BANDWIDTH REQUEST WITH DELAY REGULATION FOR REAL-TIME SERVICE IN MOBILE WIMAX NETWORKS 1249 [7] A. Sayenko, O. Alanen, J. Karhula, and T. Hämäläinen, Ensuring the QoS Requirements in Scheduling, Proc. Ninth ACM Int l Symp. Modeling Analysis and Simulation of Wireless and Mobile Systems (MSWiM 06), pp , [8] Q. Liu, X. Wang, and G.B. Giannakis, A Cross-Layer Scheduling Algorithm with QoS Support in Wireless Networks, IEEE Trans. Vehicular Technology, vol. 55, no. 3, pp , May [9] D. Niyato and E. Hossain, Queue-Aware Uplink Bandwidth Allocation and Rate Control for Polling Service in IEEE Broadband Wireless Access Networks, IEEE Trans. Mobile Computing, vol. 5, no. 6, pp , June [10] OPNET WiMAX Model Development Consortium, OPNET Network Simulator with WiMAX Model, WiMax, [11] G.F. Franklin, J.D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, third ed. Addsion-Wesley, [12] A.O. Dwyer, Handbook of PI and PID Controller Tuning Rules. Imperial College Press, [13] A. Jalali, R. Padovani, and R. Pankaj, Data Througput of CDMA- HDR: A High Efficiency-High Data Rate Personal Communication Wireless System, Proc. IEEE Vehicular Technology Conf. (VTC- Spring), pp , May [14] M. Andrews, K. Kumaran, K. Ramanan, A. Stolyar, and P. Whiting, Providing Quality of Service over a Shared Wireless Link, IEEE Comm. Magazine, vol. 39, no. 2, pp , Feb [15] N. Blaunstein, Radio Propagation in Cellular Networks. Artech House, [16] ITU-R Task Group 8/1 Guidelines for Evaluation of Radio Transmission Technologies for IMT-2000, Recommendation ITU- R M.1225, [17] WiMAX Forum Mobile WiMAX Part I: A Technical Overview and Performance Evaluation, white paper, Aug [18] J. Son, Y. Yao, and H. Zhu, Quality of Service Scheduling for Broadband Wireless Access Systems, Proc. IEEE Vehicular Technology Conf. (VTC 2006-Spring), vol. 3, pp , [19] D.-H. Cho, J.-H. Song, M.-S. Kim, and K.-J. Han, Performance Analysis of the IEEE Wireless Metropolitan Area Network, Proc. First Int l Conf. Distributed Frameworks for Multimedia Applications (DFMA 05), pp , Feb Eun-Chan Park received the BS, MS, and PhD degrees from the School of Electrical Engineering and Computer Science, Seoul National University, Korea, in 1999, 2001, and 2006, respectively. He worked for Samsung Electronics, Suwon, Korea, as a senior engineer from 2006 to 2008, developing broadband wireless access systems based on IEEE He is currently an assistant professor in the Department of Information and Communication Engineering, Dongguk University. His research interests include performance analysis, resource allocation, quality of service, congestion control, and cross-layer optimization in wired and wireless networks. He is a member of the IEEE.. For more information on this or any other computing topic, please visit our Digital Library at