1. WCNC 2008
Markov Chain Model for Polling Delay and Throughput Analyses of Uplink Subframe in WiMAX Networks
Ben-Jye Chang
Department of Computer Science & Information Engineering
Chaoyang University of Technology
Chien-Ming Chou
Graduate Institute of Networking and Communication Engineering
Chaoyang University of Technology

2. Outline Introduction Network model Performance analysis for WiMAX
Numerical results
Conclusions

3. Introduction WiMAX provides some advantages middle-range access
high data rate
mobile access
convenient deployment

4. Introduction
The characteristics of PMP are summarized in three aspects
physical frame
wireless multiplexing technology
polling mode

5. Introduction physical frame … … Frame N DL subframe UL subframe
Preamble
FCH
DL-MAP UL-MAP DCD UCD …
Initial ranging
BW requests …

6. Introduction
polling mode
unicast
multicast
broadcast

7. Introduction
In unicast polling, two problems obviously impact on the performance of WiMAX
(1) not all the polled nodes have packets to be sent and thus waste bandwidth used for polling these nodes
(2) that the node has packets to be sent may not be polled immediately that increases the polling delay

8. Introduction Motivation
to analyze NPS based for increasing network throughput and utilization while decreasing average polling delay
NPS: number of polls

9. Network Model
W = (V, E)
V: node
E: link

10. Performance Analysis For WiMAX
Assume that each SS does not adopt the piggyback bandwidth request for continuous request after sending data on bursts.
Tup: Uplink subframe duration time
R : Data rate
Lup: Uplink subframe length
Tf : Frame duration time
Tdown: Downlink subframe duration time

11. Performance Analysis For WiMAX
Frame N
DL subframe
UL subframe …
Initial ranging
BW requests
control period
TTx period

12. Performance Analysis For WiMAX
TTx_Data : Data slots period of the uplink subframe
TTx : Transmission slots period of the uplink subframe
TP : Unicast polling period for SSs to send bandwidth request
Φ : The number of polls within a frame period
Therefore, a physical frame is decomposed as

13. Performance Analysis For WiMAX

14. Performance Analysis For WiMAX
The state of the model is the number of served SSs within the network
λn : birth rate
μn : death rate

15. Performance Analysis For WiMAX
Let π(n), n=0,...,N, be the equilibrium probability of being in state n , satisfies
and

16. Performance Analysis For WiMAX
Thus, the expected number of SSs in the network is
where

17. Performance Analysis For WiMAX
Assume that all the arrival rate are the same and denoted as λ ,
and all the service rate are the same and denoted as μ

18. Performance Analysis For WiMAX
: The average polling delay

19. Performance Analysis For WiMAX
η: The total number of packets that want to be sent in the network
Pt : The probability that packets are ready for transmission at every SS
Ppoll : The polled probability of an SS
Φ : NPS (The number of polls within a frame period)
N : The total number of SSs

20. Performance Analysis For WiMAX
Thus, the network throughput can be formulated by
U : the average length that an uplink subframe are used by SSs
I : the average length in time of idle period
B :the average length in time of busy period

21. Performance Analysis For WiMAX

22. Performance Analysis For WiMAX

23. Performance Analysis For WiMAX
Finally, the waste rate of polled but not request is determined as

24. Numerical Results

25. Numerical Results

26. Numerical Results

27. Numerical Results

28. Conclusions
The analysis model of NPS in unicast polling for minimizing polling delay while increasing throughput and utilization
The analytic results of average polling delay and throughput are very close to the simulation results

29. Thank you