WCNC 2008 Markov Chain Model for Polling Delay and Throughput Analyses of Uplink Subframe in WiMAX Networks Ben-Jye Chang Department of Computer Science.

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Presentation transcript:

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

Outline Introduction Network model Performance analysis for WiMAX Numerical results Conclusions

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

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

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

Introduction polling mode unicast multicast broadcast

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

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

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

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

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

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

Performance Analysis For WiMAX

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

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

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

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

Performance Analysis For WiMAX : The average polling delay

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

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

Performance Analysis For WiMAX

Performance Analysis For WiMAX

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

Numerical Results

Numerical Results

Numerical Results

Numerical Results

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

Thank you