Delay Analysis of IEEE Wireless Metropolitan Area Network

Delay Analysis of IEEE 802.16 Wireless Metropolitan Area Network Zsolt Saffer Technical University of Budapest 1521 Budapest Hungary safferzs@hit.bme.hu Sergey Andreev State University of Aerospace Instrumentation (SUAI), RUSSIA serge.andreev@gmail.com Abstract In this paper we present the delay analysis of IEEE 802.16 broadband wireless access network. We assume that the system operates in point-to-multipoint mode with TDD/TDMA scheme. The developed analytical model is used to evaluate the delay-load characteristic. It considers the overall delay including both the contention-free reservation and the scheduling delay and establishes a precise upper bound on it. In order to get first insight into the effect of modeling both kind of delays together, we choose to study a simplified model (Poisson arrivals, bandwidth request message for each data packet and one packet per frame). The analysis applies to the unicast polling bandwidth reservation mechanism. The proposed grouping model uses round-robin scheduling and enables symmetrical load situation. The analytical model is verified by means of simulation. Keywords: IEEE 802.16, WMAN, performance evaluation, bandwidth reservation, polling, queuing model, overall delay. Data Traffic Subscriber Station (SS) Applications /SFID Classification UGS rtps ertps nrtps BE Packet Scheduler UL-MAP Connection Request Connection Response BW-Request Data Packet Fig. 1. QoS Architecture of IEEE 802.16. Base Station (BS) Admission Control undefined by IEEE 802.16 Uplink packet scheduling algorithm undefined by IEEE 802.16 I. INTRODUCTION IEEE 802.16 is a recent standard specifying an air interface for Broadband Wireless Access (BWA) [1]. This specification is recommended for Wireless Metropolitan Area Networks (WMANs). It proposes a high-speed access system supporting multimedia services. In IEEE 802.16 protocol stack, the Medium Access Control (MAC) layer supports multiple Physical (PHY) layer specifications, each of them covering different operational environments. IEEE 802.16 is likely to emerge as an outstanding cost-competitive technology suited to fixed, nomadic, portable and fully mobile operations. The MAC layer supports a variety of bandwidth reservation mechanisms, each of them assigned to a particular service flow. The mechanisms are based upon unicast, multicast or broadcast polling technique. The standard also defines distinct service flow classes and assigns different Quality-of-Service (QoS) requirements to them. However, the standard specifies neither scheduling algorithm nor admission control mechanism (see Fig.1). Hence, it leaves open the question of ensuring the QoS requirements assigned to the defined service flow classes. Due to the uncompleteness of the standard many research papers address the question of ensuring the QoS requirements through different scheduling mechanisms. Cho, Song, Kim and Han [2] proposed an efficient QoS architecture, based on priority scheduling and dynamic bandwidth allocation. They analytically evaluated the channel utilization and verified it by simulation. Moraes and Maciel [3] proposed a bandwidth reservation protocol with a traffic scheduling mechanism based upon priority rules. They also set up an analytical model for 978-1-4244-2036-0/08/$25.00 c 2008 IEEE evaluating the packet delay in the system. Their scheduling assumes that all the arriving packets are transmitted as soon as the reserved bandwidth is available, that is no scheduling delay is considered. The implemented bandwidth reservation protocol can be crucial for the efficient media access. Kobliakov, Turlikov and Vinel [4] investigated the design of an efficient contentionbased random multiple access mechanism. They compared their multiple access mechanism with the standard collision resolution algorithm of IEEE 802.16. Lin, Jia and Lu [5] studied the utilization of another bandwidth reservation mechanism, the centralized polling of bandwidth requests. Their model considers multicast and broadcast polling mechanisms. In [6] Vinel, Zhang, Ni and Lyakhov also consider various polling schemes with the primary focus on multicast and broadcast polling. Moreover, the comparison with the simplest unicast polling is given. In fact, the performance of the system significantly depends on both the applied bandwidth reservation mechanism and the used scheduling algorithm. The fundamental paper of Rubin [7] presents a detailed description of the access-control disciplines and sets a general framework for their analysis. This framework accounts for both bandwidth reservation and packets serving. The analysis in [7] is general with no particular bandwidth reservation protocol or scheduling considered. Iyengar, Iyer and Sikdar [8] proposed an analytical approach for the overall system delay estimation. However they approximated the number of packets seen at packet arrival by the long term average of the number of packets. Although

it makes the analysis independent from the applied scheduling algorithm, this results in a rough approximation of the overall delay. For a recent summary on QoS in the context of IEEE 802.16 we refer to the on-line paper of Wood [9]. In this paper we investigate the overall delay of the system, but in contrast to the above references, we consider the reservation and the scheduling delay together with the particular classes of bandwidth reservation mechanism and scheduling. This results in better modeling capability of the overall delay. We provide a grouping model and a simple analytical approach, which utilizes the M/D/1 queuing models with and without vacation. The considered analysis is applied to the unicast polling as bandwidth reservation mechanism and the Round-Robin (RR) scheduler. The rest of the paper is structured as follows. Section II gives a brief overview of IEEE 802.16 MAC layer. In Section III we provide the description of the system model and the notations. We conduct the delay analysis in Section IV. The verification of the analytical results by means of simulation follows in Section V. Finally, we give concluding remarks in Section VI. A. MAC layer II. OVERVIEW OF IEEE 802.16 IEEE 802.16 standard supports two operational modes: the mandatory Point-to-MultiPoint (PMP) and the optional mesh mode. In the centralized PMP architecture the Base Station (BS) is the main node. It is responsible for coordinating the communication process among the other nodes - Subscriber Stations (SSs). All communication among the SSs is directed through the BS and takes place on the independent transmission channels of two types. In the Downlink Channel () only the BS transmits data to the SSs, while in the Uplink Channel (UL) the data is sent by the SSs to the BS. Hence, there is no multiple access on the channel, while the UL channel must be shared among the SSs. The standard provides two channel allocation schemes: Frequency Division Duplexing (FDD) and Time Division Duplexing (TDD). In FDD the the and the UL channels are assigned to the different frequencies, while in TDD both channels are assigned to the same frequency, and are differentiated by assigning different time intervals to them. In this case the time is divided into fixed-length frames composed of the and the UL sub-frames corresponding to the and the UL channels, respectively. The length of the sub-frames can be varied dynamically. The SSs access the UL channel by means of Time-Division Multiple Access (TDMA). The MAC frame structure can be seen in Fig.2. In the sub-frame the BS broadcasts data to all the SSs, and each of them captures only those addressed to it. Besides the scheduling, the BS is also responsible for the UL scheduling. The BS determines the number of slots to be allocated for each SS in the next UL sub-frame. This information is broadcasted in the UL-MAP message in the beginning of each frame. After receiving the UL-MAP message, the SS transmits data in the DownLink () sub-frame Fig. 2. Frame Polling Interval (PI) UpLink (UL) sub-frame UL-MAP indicates the starting time slot of each uplink burst UL-MAP -MAP Preamble SS1 Transmission Interval SS2 Transmission Interval IEEE 802.16 MAC frame structure in TDD/TDMA mode. next UL sub-frame using the time slots which are granted to it. The SS can initiate bandwidth reservation by sending a bandwidth request (BW-Req) message in the Polling Interval (PI) in the beginning of each UL sub-frame. The standard defines contention-free polling mechanism (unicast) and contention-based (random access) polling mechanisms (multicast or broadcast) to send BW-Req messages. The duration of the PI is not specified by the standard explicitly. In case of contention-based random access, the defined collision resolution mechanism is the truncated binary exponential backoff (BEB) algorithm. Additionally, IEEE 802.16 enables piggybacking for sending BW-Reqs attached to data packets. B. Service flow types In order to support a variety of traffic types (e.g. data, voice, video) the standard defines five service flow types with the corresponding QoS requirements. The service flow type also determines the kind of bandwidth reservation mechanism, which is necessary or enabled. ST.1 Unsolicited Grant Service (UGS), where the BS provides fixed-size bandwidth at periodic intervals. It supports real-time service flows that generate fixed-size data packets on a periodic basis, such as T1/E1 and Voice over IP (VoIP). The type assumes fixed time slots assignment, and thus no bandwidth reservation mechanism is used. ST.2 Real-Time Polling Service (rtps), which supports realtime service flows that generate variable-size data packets on a periodic basis, such as MPEG video. The bandwidth reservation mechanism is unicast polling. ST.3 Extended Real-Time Variable Rate Service (ERT-VR), which is designed to support real-time applications with variable data rate but requiring guaranteed throughput and strict delay constraints (VoIP with silence suppression). This class is defined only in the recent IEEE 802.16e standard and is often referred to as Extended Real-Time Polling Service (ertps). It supports both contention-free polling and contention-based random access reservation mechanisms. ST.4 Non-Real-Time Polling Service (nrtps), which supports non real-time service flows that generate variable-size data packets on a regular basis, such as high bandwidth FTP. The allowed bandwidth reservation mechanisms are unicast polling and contention-based random access (multicast and broadcast). ST.5 Best Effort Service (BE), which utilizes the remaining bandwidth after the allocation of the previous types of service. The reservation mechanism is contention-based random

access. III. SYSTEM MODEL AND NOTATIONS A. Limitations of the model Our model of IEEE 802.16 system has the following restrictions: R.1 The system operates in the more important PMP mode. R.2 TDD/TDMA channel allocation scheme is applied. R.3 One connection per SS is allowed. R.4 Unicast polling is used as the the bandwidth reservation mechanism. Our analysis concentrates on the nrtps service flow type. R.5 The uplink scheduler applies the round-robin scheduling. B. Analytical model There are N SSs and 1 BS in the system, which together comprise N+1 stations. We assume, that every station has infinite buffer capacity. Packets arrive to each SS according to Poisson arrival process. The arrival processes at the different SSs are mutually independent. We denote the overall packet arrival rate by λ. Hence, the arrival rate of a SS i is λ i = λ N. The fixed packet length is η 1 bit, including both header with packing/fragmentation overhead and data information. The transmission rate of each channel is β bps. Therefore, the packet transmission time (packet duration) is: µ = (ηβ) 1. All time durations are measured in seconds, i.e., our model does not use the time slot of the system. Denote the duration of each frame by T f, and the duration of the and UL sub-frames by T d and T u, respectively. T pi stands for the duration of the polling interval and T ud is the maximum available duration of the uplink data transmission in a frame. Hence, it holds: C. Grouping model T u = T pi + T ud. The BS never tries to poll all the SSs in one frame. Alternatively, even for the delay-sensitive connections it is enough to poll the corresponding SS once per some integer number of frames. Therefore, the BS is expected to split all the SSs into smaller groups in order to to poll each group in the corresponding frame. Therefore, N SSs are split into an integer number of groups with P N SSs in each of them (see example in Fig.3). Clearly, the number of groups is: L = N/P. (1) The duration of the polling slot is α. Hence, T pi = P α and we get: T ud = T u P α. (2) Clearly, L consecutive frames constitute a cycle, which lasts for: C = LT f. (3) 1 3 6 Outgoing BS grants shared buffer Tagged packet arrival sub-frame SS1 SS2 SS3 Packet arrivals No 1 2 3 transmission PI Outgoing SS packets buffers UL-MAP forming Bandwidth requests Tagged packet overall delay SS4 SS5 SS6 4 5 6 SS1 transmission Fig. 3. Grouping model example: 6 SSs are split into 2 equal groups, which are polled individually in a round-robin fashion. D. RR Scheduling We assume that for each data packet a separate BW-Req message is generated, which could mean that each packet belongs to a dedicated connection. This is the case, for example, when an SS serves as a gateway to a local area network and there are multiple connections, each of which has specific QoS requirements and, therefore, cannot be aggregated with others. The arrival rate for each connection is, practically, rather low and the piggybacking cannot be used. After receiving BW-Req messages from the stations, later on the uplink RR scheduler grants a slot for those SSs, which have requested bandwidth. The scheduler grants slots in the order of those SSs, from which BW-Req messages were received by using a shared buffer for the bandwidth grants to all N SSs (see Fig.3 for details). This way the BS realizes RR scheduling via the shared buffering and via polling the different SS groups, since the SSs of different groups send BW-Req message in consecutive frames. Hence during N consecutive frames each SS gets at least one uplink data transmission opportunity. E. Model assumptions We denote the utilization of SS i by ρ i. Since each SS gets a chance to transmit on UL at most once in each N consecutive frames, we get for the utilization of SS i: ρ i = λ i NT f. (4) Additionally, we formulate the following assumptions about our model: A.1 The following relation holds for the arrival rate: ρ i = λ i NT f < 1. (5) This ensures the stability of the model. A.2 For the simplicity of the further analysis we restrict our explorations to the case when at most 1 data packet can be transmitted per frame, i.e., the packet transmission time is µ = T ud. A.3 The channel propagation time is negligible. A.4 The transmission channels are error-free.

IV. DELAY ANALYSIS According to the unicast polling reservation mechanism and the RR scheduling, two kinds of queuing are assigned to each packet arriving to station i before its transmission: queuing of packet in the SS buffer, before the corresponding BW-Req message is sent (waiting for reservation), queuing of the corresponding bandwidth grant in the BS shared buffer after receiving the BW-Req message from station i (waiting for scheduling). A. Overall delay definition We define the overall delay (W ) of the tagged packet as the time interval spent from its arrival into SS s outgoing buffer up to the end of its successful transmission in the UL. It is composed of several parts: W = W r + α + W s + W t + µ, (6) where W r is the reservation delay, which is defined as the time interval from the packet arrival at the SS to the start of sending a corresponding BW-Req message to the BS. α is the transmission time of a BW-Req message. W s is the scheduling delay, which is defined as the time interval from the end of sending a BW-Req message to the time when the corresponding BS grant becomes the first one in the BS grants shared buffer. W t is the transmission delay, which is defined as the time interval from the time when a BS grant becomes the first one in the BS grants shared buffer to the start of the successful transmission of the corresponding packet in the UL sub-frame. µ is the transmission time of a data packet. B. Reservation delay The operation of our model can be analyzed as a TDMA system. Since the frame length, and hence the cycle length is fixed, the statistical behavior of a particular SS is independent of the behavior of the other SSs. As a consequence, the TDMA system can be modeled as the composition of the independent queuing systems, each of which represents the statistical behavior of one SS. The tagged packet arriving into the outgoing packets buffer of the particular SS waits until the start of sending a corresponding BW-Req message to the BS. Afterwards, the service starts with a length of C, since a SS gets access to the data transmission only once in a cycle. From the point of view of a particular SS a cycle starts at the start of sending a BW-Req message to the BS. Each cycle offers either service or vacation. Hence, the queuing system to describe the behavior of this SS is an M/D/1 queue with vacation, in which both the service time and the vacation time are deterministic and equal to C = LT f (see [10] for details). The reservation delay thus equals to the waiting time in this queuing system. Therefore, applying the mean waiting time formula (( [10]) eq. (3.58)) with the corresponding parameters and using (3) and (1), we obtain the mean reservation delay of the tagged packet: E [W r ] = C. Scheduling delay C 2(1 λ i C) = C 2(1 λt f P ). (7) The scheduling delay is caused by queuing in the outgoing BS grants shared buffer. We firstly remind that at most one data packet can be transmitted per frame. The overall performance of the system may thus be regarded as a queuing system with some arrival flow from SSs and a deterministic service time of T f. The arrival flow to the considered system is formed by the BW-Req messages that turn into bandwidth grants at the BS. Notice that the consecutive intervals between the arrivals of the bandwidth grants are statistically dependent, which makes the system indescribable by any basic queuing system type. However, as the processing of BW-Req messages given by (7) introduces more regularity to the structure of the bandwidth grants arrival flow, the service time in the system is bounded from above by M/D/1 waiting time. Therefore, we may use the mean waiting time of M/D/1 queuing system (see [10] or [11]) as the upper bound on the mean service time at the BS. Putting the appropriate values into M/D/1 mean waiting time formula, we establish: D. Transmission delay E [W s ] λt 2 f 2(1 λt f ). (8) The transmission delay is the interval from the BS grant arrival at the head of the BS grants shared buffer to the start of transmission of the corresponding packet in the UL sub-frame. To continue building an upper bound on the overall delay we approximate the transmission delay by a worst-case delay, which is the delay of a grant arriving into the empty BS grants buffer. Therefore, we can obtain the worst-case transmission delay of the i-th SS as: W t (i) T f αi T d + P α + T d. By averaging the above expression over the number of SSs in a group (P ) and simplifying we establish: E [ W t] T f + E. Upper bound on overall delay (P 1)α. (9) 2 Accounting for (6), the mean overall delay is given by: E [W ] = E [W r ] + α + E [W s ] + E [ W t] + µ. Substituting the expressions (7), (8) and (9) and simplifying we finally obtain the upper bound on the mean overall delay as follows: C E [W ] 2(1 λt f P ) + P + 1 α + 2 λtf 2 +T f + 2(1 λt f ) + µ.

V. EXPERIMENTAL EVALUATION In this section we verify our analytical model by means of simulation. Below we refer to the mean overall delay (E [W ]) simply as overall delay. A. Simulation summary In order to validate the accuracy of the considered analytical model a simulation program for IEEE 802.16 was developed. The program is a time-driven simulator that accounts for the discussed restrictions on the considered system model (see Section III.A). Overall delay, ms 26 24 22 20 18 16 14 12 Analysis, P = 4 Simulation, P = 4 Analysis, P = 5 Simulation, P = 5 Basic IEEE 802.16 simulation parameters: Parameter Value Frame duration (T f ) 2.5 ms /UL ratio 60:40 BW-Req duration (α) 114.58 µs Channel bandwidth 20 MHz MCS 16 QAM 1 / 2 10 8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arrival rate, packets per frame Fig. 4. Overall delay vs. arrival rate (packets per frame): N = 20, 10 6 cycles per point. B. Observations Fig.4 plots the overall delay against the overall arrival rate for two system configurations. According to restriction R.4 we consider the nrtps service flow type as it does not offer any guarantee on the packet delay. For convenience, we give the arrival rate in packets per frame and it follows from (5) that the value of 1 presents the saturation threshold for the considered model. The simulation uses the realistic IEEE 802.16 timings as given above and runs 10 6 cycles per point to ensure the stability of the obtained results. The figure shows that the analytical upper bound describes the behavior of the system closely for the broad range of arrival rates. However, some disagreement could be noticed when arrival rate is too high due to near-saturation conditions. Additionally, we compare the behavior of two different groupings: one with 4 SSs per frame and another one with 5 SSs. It is clear, that as the frame duration is fixed and the cycle is longer for the first grouping, we can see the higher overall delay in the first case. However, with longer PI (5 BW-Req messages per frame), as (2) shows, the second grouping has lower throughput (smaller value of µ). To be more specific, the first grouping allows transmitting 2000- bytes packets (6.4 M bps), whereas the second one permits to transmit only 1500-bytes packets (4.8 M bps). Different groupings thus demonstrate a throughput-delay trade-off which can be easily calculated with our analytical approach. VI. FINAL REMARKS We established an upper bound on the overall delay of packets in IEEE 802.16 system under defined restrictions. The proposed analysis applies to the unicast polling bandwidth reservation mechanism. Our grouping model uses round-robin scheduling under symmetrical load situation. The validation of the considered analytical approach shows very good accordance with the simulation results even for very high arrival rates. The round-robin scheduling provides a guaranteed minimum bandwidth in a simple way, which is one of the important requirements. The model can be extended to Weighted Round-Robin (WRR) scheduling and for asymmetrical load situation, as well as for enabling several packet transmissions per frame. Additionally, we believe, that our model can be extended to multicast and broadcast polling as well. REFERENCES [1] C. Eklund, R. B. Marks, K. L. Stanwood, and S. Wang, IEEE standard 802.16a: A technical overview of the W irelessman T M airinterface for broadband wireless access, IEEE Communications Magazine, vol. 40, no. 6, pp. 98 107, Jun. 2002. [2] D.-H. Cho, J.-H. Song, M.-S. Kim, and K.-J. 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