1. Dusit Niyato, Student Member, IEEE Ekram Hossain, Senior Member, IEEE
Queue-Aware Uplink Bandwidth Allocation and Rate Control for Polling Service in IEEE 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/ OPLab, IM, NTU

2. Outline Introduction System Model
Queuing Analytical Model for Polling Service (PS)
Queuing Model for Best-Effort (BE) Service
Performance Evaluation
Conclusions
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3. Introduction
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4. IEEE 802.16 TDM frame structure
Introduction (1/3)
There are two types of stationary stations in IEEE :
- Base station (BS) and Subscriber station (SS)
Use TDM for downlink transmission and TDMA for uplink transmission
IEEE 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 TDM frame structure
source: Packet scheduling for QoS support in IEEE Broadband wireless access systems
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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
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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
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7. System Model
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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
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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
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10. System Model (3/7) The bandwidth allocation function for PS
: the number of PDUs in the queue
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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
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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
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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 )
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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
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15. Queuing Analytical Model for Polling Service (PS)
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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
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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
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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
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19. PDU Arrival Process for PS Connections (3/4)
In the case of aggregated traffic from two users
for , where denotes Kronecker product
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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
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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)
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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)
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38. QoS Measures for Polling Service (6/7)
Average Allocated Bandwidth
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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
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40. Queuing Model for Best-Effort (BE) Service
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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:
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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:
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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
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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
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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
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46. Performance Evaluation
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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)
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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)
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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:
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50. Performance Evaluation
Fig. 2. (a) Queue-length distribution for the PS queue
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51. Performance Evaluation
Critical rate
Critical rate
Fig. 2. (b) average delay for the PS queue
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52. Performance Evaluation
Fig. 3. Average delay for the BE queue
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53. Performance Evaluation
Fig. 4. Probability mass function for allocated bandwidth
under different threshold settings
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54. Performance Evaluation
Fig. 5. (a) variations in average delay
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55. Performance Evaluation
Fig. 5. (b) Variations in bandwidth utilization under varying
traffic intensity
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56. Performance Evaluation
Set
Fig. 6. (a) Variations in controlled PDU arrival rate for a PS connection
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57. Performance Evaluation
Fig. 6. (b) Variations in average delay under different rate control threshold settings
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58. Fig. 7. (a) Queue-length and allocated bandwidth for PS queue
Fig. 7. (a) Queue-length and allocated bandwidth for PS queue
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59. Fig. 7. (b) controlled arrival rate and average delay obtained from
Fig. 7. (b) controlled arrival rate and average delay obtained from
transient analysis
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60. Conclusion
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61. Conclusions Key results
- When the PS queue is stable, the queue-aware uplink bandwidth allocation scheme can maintain the average delay at a constant level while maximizing the resource utilization.
- Since the setting of the rate-control thresholds (i.e., and ) affects the QoS performances, rate control can be used to prioritize different PS connections through different threshold settings.
- The impacts of bandwidth allocation and rate-control parameter settings (for PS connections) on the performance of BE service can be quantified by the approximate queuing analytical model for BE service presented in this paper.
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62. Conclusions
- The maximum allocated bandwidth affects the critical rate and the maximum delay when the queue is unstable.
- A larger interval between thresholds results in higher delay; however, the fluctuation in the allocated bandwidth becomes smaller.
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63. Conclusions Contributions
- proposed a queue-aware adaptive uplink bandwidth allocation and rate control mechanisms for polling service in IEEE
- A queuing analytical model is developed to investigate the performances of the queue-aware bandwidth allocation and the rate control mechanisms for polling service.
- An approximate queuing model is developed for analyzing the performance of best-effort traffic in presence of polling service.
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64. Thanks for your listening by Jason
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65. Source: Wikipedia
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