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Queue-Aware Uplink Bandwidth Allocation and Rate Control for Polling Service in IEEE 802.16 Networks

This paper presents a system model and queuing analytical model for polling service in IEEE 802.16 networks. It proposes a queue-aware bandwidth allocation and rate control mechanism to improve the performance of the polling service. Performance evaluation results are provided, and conclusions are drawn from the analysis.

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Queue-Aware Uplink Bandwidth Allocation and Rate Control for Polling Service in IEEE 802.16 Networks

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  1. Queue-Aware Uplink Bandwidth Allocation and Rate Control for Polling Service in IEEE 802.16 Broadband Wireless Networks Dusit Niyato, Student Member, IEEE Ekram Hossain, Senior Member, IEEE IEEE TRANSACTIONS on MOBILE COMPUTING VOL. 5, NO. 6, June 2006 Presented by Jason L.Y. Lin 2006/6/12 OPLab, IM, NTU 1

  2. Outline • Introduction • System Model • Queuing Analytical Model for Polling Service (PS) • Queuing Model for Best-Effort (BE) Service • Performance Evaluation • Conclusions OPLab, IM, NTU

  3. Introduction OPLab, IM, NTU

  4. Introduction (1/3) • There are two types of stationary stations in IEEE 802.16: - Base station (BS) and Subscriber station (SS) • Use TDMfor downlink transmission and TDMA for uplink transmission • IEEE 802.16 MAC supports two classes of SS: - grant per connection (GPC) and grant per SS (GPSS) • The lengths of uplink and downlink subframes are determined dynamically by the BS and are broadcast to the SSs through downlink and uplink map messages (UL-MAP and DL-MAP) at the beginning of each frame. IEEE 802.16 TDM frame structure source: Packet scheduling for QoS support in IEEE 802.16 Broadband wireless access systems OPLab, IM, NTU

  5. Introduction (2/3) • Each SS can request bandwidth to BS by using BW-request PDU • There are two modes to transmit BW-request PDU: - contention mode and contention-free (polling) mode • Due to predictable delay, the contention-free mode is suitable for QoS sensitive applications OPLab, IM, NTU

  6. Introduction (3/3) • Three major type of services with different QoS requirements - Unsolicited Grant Service (UGS) - BS generally allocates a fixed amount of bandwidth to each of the connections in a static manner - Polling Service (PS) - real-time and non-real-time - the amount of bandwidth required is determined dynamically based on the required QoS performances and the traffic arrival rates for the corresponding connections - Best-Effort Service (BE) - no QoS guarantee OPLab, IM, NTU

  7. System Model OPLab, IM, NTU

  8. System Model (1/7) • System Description - consider an SS of type GPSS for which certain amount of bandwidth is reserved by the BS - the allocated bandwidth is shared among the different service types in the same SS, with UGS having the highest priority and the BE service having the lowest priority - the PDUs from all the PS connections are aggregated into a single queue of size X PDUs - the queue size for the BE traffic is assumed to be infinity OPLab, IM, NTU

  9. System Model (2/7) • Queue-Aware Bandwidth Allocation - : the maximum number of MAC PDUs that an SS can transmit per uplink transmission subframe ( ) - : the bandwidth allocated for UGS of an SS - two modes of bandwidth allocation for PS: => complete Partitioning (CP) and complete sharing (CS) - use the set of thresholds for bandwidth allocation where OPLab, IM, NTU

  10. System Model (3/7) • The bandwidth allocation function for PS : the number of PDUs in the queue OPLab, IM, NTU

  11. System Model (4/7) • Queue-Aware Rate Control (for PS connection) - the PDU arrival rate is controlled according to the number of PDUs in the queue - the rate control can be implemented either at the traffic source => the SS informs the traffic sources of the queue status or at the PS queue =>similar to the random early detection (RED) mechanism OPLab, IM, NTU

  12. System Model (5/7) • Rate control function - let denote the rate control thresholds for the number of PDUs in the queue - denotes the minimum guaranteed arrival rate denotes the PDU arrival rate where and is a nonincreasing function of OPLab, IM, NTU

  13. System Model (6/7) - the rate control mechanism can be applied either on aggregate => PDU arrival rates for all connections under PS are controlled unsing the same values of and or on per-flow basis => different parameter settings for rate control are used for each connection (i.e., and for connection ) OPLab, IM, NTU

  14. System Model (7/7) • Error Control - use an infinite persistent ARQ-based error recovery - let θ denote the PDU error rate (PER) - assuming an independent error process - the probability that n PDUs out of m transmitted PDUs are successfully received can be obtained as follows: - assume that the transmission status for the PDUs transmitted in the previous frame time is made available to the transmitter before transmissions in the current frame time start OPLab, IM, NTU

  15. Queuing Analytical Model for Polling Service (PS) OPLab, IM, NTU

  16. Queuing Analytical Model for Polling Service (PS) • PDU Arrival Process for PS connections • PDU Arrival Process for UGS connections • Formulation of the Queuing Model for Polling Service • QoS measures for Polling Service OPLab, IM, NTU

  17. PDU Arrival Process for PS Connections (1/4) • assume that the PDU arrival process for each PS connection follows an MMPP model • the PDU arrival rate is determined by the state s of the Markov chain and the total number of states is S (i.e., s=1,2,…..,S ) • is the transition probability matrix is the matrix of Poisson arrival rate OPLab, IM, NTU

  18. PDU Arrival Process for PS Connections (2/4) • the rate matrix is represented by diagonal probability matrix when the number of PDUs arriving in one frame is , • each diagonal element of can be obtained from where is the probability that Poisson events occur during time interval (i.e., frame length) with mean rate OPLab, IM, NTU

  19. PDU Arrival Process for PS Connections (3/4) • In the case of aggregated traffic from two users for , where denotes Kronecker product OPLab, IM, NTU

  20. PDU Arrival Process for PS Connections (4/4) • The average PDU arrival rate for connection is obtained as follows where and • With a total of N connections, the total average PDU arrival rate at the PS queue can be obtained as follows where and 1=1 1=1 OPLab, IM, NTU

  21. PDU arrival Process for UGS Connections (1/2) • consider a multistate on-off model • the transition matrix is similar to that of PS • The maximum number of states for each connection is C • The number of PDU arrivals when the source is in state c is c • the batch size is C(i.e.,A=C) OPLab, IM, NTU

  22. PDU arrival Process for UGS Connections (2/2) • the diagonal elements of the PDU arrival probability matrices, , are denoted as follows: where the first row corresponds to the case of no PDU arrival • denotes the maximum total bandwidth for UGS, where for a total of M multistate on-off sources OPLab, IM, NTU

  23. Formulation of the Queuing Model for Polling Service(1/10) • the state of the PS queue is observed at the beginning of each frame time • A PDU arriving during frame time f will not be transmitted until the next frame time f+1 at the earliest • the state space of the queue can be defined as follows: where S denotes the state of dMMPP traffic sources, denotes the state of multistate on-off sources, is the number of PDUs in the PS queue (12) OPLab, IM, NTU

  24. Formulation of the Queuing Model for Polling Service (2/10) • in case of complete partitioning, the model does not need to maintain the state of any multistate on-off source, and therefore, • The transition matrix P of the queue can be expressed as follows OPLab, IM, NTU

  25. Formulation of the Queuing Model for Polling Service (3/10) • Arrival Process under Rate Control - the matrix for the Poisson arrival process depends on the number of PDUs in the PS queue - the matrix is obtained by using OPLab, IM, NTU

  26. Formulation of the Queuing Model for Polling Service (4/10) • Transition Matrix for the Complete Partitioning (CP) Model - the probability of departure of PDUs ( ) when there are PDUs ( ) in the queue is obtained as follows: where OPLab, IM, NTU

  27. Formulation of the Queuing Model for Polling Service (5/10) - the element of matrix P in case of complete partitioning for and where represents the number of departed PDUs and represents the number of PDU arrivals and OPLab, IM, NTU

  28. Formulation of the Queuing Model for Polling Service (6/10) • Transition Matrix for the Complete Sharing (CS) Model - the departure probability matrix for the multistate on-off sources can be established as follows where OPLab, IM, NTU

  29. Formulation of the Queuing Model for Polling Service (7/10) - for the CS case, each element of matrix P is obtained as follows: where , and OPLab, IM, NTU

  30. Formulation of the Queuing Model for Polling Service (8/10) • PDU Blocking Process - the bottom part (i.e., the rows corresponding to the condition ) of matrix P has to capture the PDU blocking effect - therefore, (17) and (21) become for , (18) and (22) become where is obtained for the case without PDU dropping OPLab, IM, NTU

  31. Formulation of the Queuing Model for Polling Service (9/10) • Steady State Probability - the steady state probability is obtained by solving the equations where 1 is a column matrix of ones - this matrix can be decomposed into and OPLab, IM, NTU

  32. Formulation of the Queuing Model for Polling Service (10/10) • Transient State Probabilities - the probability matrix of system states during frame time f can be obtained from where P(f) is the transition matrix during frame time f - the transient state probabilities and can be obtained in the same way as that for the steady state probabilities OPLab, IM, NTU

  33. QoS Measures for Polling Service (1/7) • use and to represent the general probability that the dMMPP is in state s, the on-off source is in state c, and there are x PDUs in the PS queue • The average queue length for the CP and the CS cases OPLab, IM, NTU

  34. QoS Measures for Polling Service (2/7) • Average PDU Arrival Rate - this can be calculated for connection i as follows: - the total average PDU arrival rate at the PS queue OPLab, IM, NTU

  35. QoS Measures for Polling Service (3/7) • PDU Blocking Probability - first calculated the average number of blocked PDUs per frame time - given that there are x PDUs in the PS queue and the queue size increases by h, - if h + x>X, the number of blocked PDUs during one frame time is h – (X-x) - and zero otherwise OPLab, IM, NTU

  36. QoS Measures for Polling Service (4/7) - The average number of blocked PDUs per frame time for the CP and the CS cases are obtained as follows OPLab, IM, NTU

  37. QoS Measures for Polling Service (5/7) - the probability that an incoming PDU is blocking for the CP and the CS cases are • Queue Throughput - the queue throughput (number of PDUs/frame interval) OPLab, IM, NTU

  38. QoS Measures for Polling Service (6/7) • Average Allocated Bandwidth OPLab, IM, NTU

  39. QoS Measures for Polling Service (7/7) • Bandwidth Utilization - queue throughput / average allocated bandwidth • Delay Statistics - the time interval (in terms of frames) since the PDU arrived at the queue and the time that it has been successfully transmitted OPLab, IM, NTU

  40. Queuing Model for Best-Effort (BE) Service OPLab, IM, NTU

  41. Queuing Model for Best-Effort (BE) Service (1/5) • The state space for the BE queue can be expressed as follows: where y is the number of PDUs in the BE queue with infinite buffer size • simplified state space for the BE queue is shown as follows: OPLab, IM, NTU

  42. Queuing Model for Best-Effort (BE) Service (2/5) • Assume that the PDU arrival process is Poisson with average rate • The maximum bandwidth that can be allocated to the BE queue is denoted by • The transition matrix Q for this model can be obtained as follows: OPLab, IM, NTU

  43. Queuing Model for Best-Effort (BE) Service (3/5) • The probability of departure of n PDU from the BE queue based on the number of PDUs in the PS queue is calculate as follows: for and zero otherwise OPLab, IM, NTU

  44. Queuing Model for Best-Effort (BE) Service (4/5) • each element of Q is obtained as follows: for g=1,2,…,G and h=1,2,…,A, where OPLab, IM, NTU

  45. Queuing Model for Best-Effort (BE) Service (5/5) • Since the size of matrix Q is infinite, we apply the matrix-geometric method to obtain the steady state probabilities • The average number of PDUs in the BE queue and the average delay for a PDU in the BE queue can be obtained from where is the steady state probability of y PDUs in the BE queue obtained by the Matrix-geometric method OPLab, IM, NTU

  46. Performance Evaluation OPLab, IM, NTU

  47. Performance Evaluation • Parameter Setting - The SS under consideration is stationary and works in GPSS mode - The PDU arrival process for each PS connection is assumed to be identical and it follows a two-state MMPP model (i.e., S=2) with the following parameters: where α indicates the traffic intensity, and α=1.5 - the number of connections under PS is 2 (i.e., N=2) - the maximum batch size of PDU arrival is 20 (i.e., A=20) OPLab, IM, NTU

  48. Performance Evaluation - the PDUs from all PS connections are aggregated into the PS queue - the size of this queue is assumed to be 100 PDUs (i.e., X=100) - in a FIFO fashion - - the probability of successful transmission of a PDU is 0.995 (i.e., θ=0.005) - - OPLab, IM, NTU

  49. Performance Evaluation - for UGS traffic, we use a three-state on-off source with the transition matrix defined as follows: - is set to 2 - use the notation for the set of thresholds Ex: OPLab, IM, NTU

  50. Performance Evaluation Fig. 2. (a) Queue-length distribution for the PS queue OPLab, IM, NTU

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