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July  2009, 5(3): 525-540. doi: 10.3934/jimo.2009.5.525

Delay distribution and loss probability of bandwidth requests under truncated binary exponential backoff mechanism in IEEE 802.16e over Gilbert-Elliot error channel

1. 

Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, Seoul, South Korea, South Korea

2. 

Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, Seoul 136-701, South Korea

Received  August 2008 Revised  April 2009 Published  June 2009

This paper presents the mathematical analysis of the truncated binary exponential backoff (TBEB) mechanism as a contention resolution for bandwidth requests in the broadcast polling and the multicast polling in the IEEE 802.16e. We derive the delay distribution and the loss probability of request packets in the TBEB over Gilbert-Elliot error channel, by analytic methods on the assumption of Bernoulli arrival process and the unsaturated condition. The optimal contention period of transmission opportunities for transmitting bandwidth requests can be obtained while satisfying QoS on delay bound and loss bound. Furthermore, we find the utilization of transmission opportunity to see efficiency of the bandwidth. Numerical examples show that the analytical results are well-matched with simulations, and the performance evaluations in the broadcast polling and multicast polling are compared on the mean delay, the loss probability and the utilization of transmission opportunity. Numerical results address that the multicast polling with more groups has better performance than the broadcast polling in the sense of shorter delay, lower loss probability and higher utilization of transmission opportunity.
Citation: Eunju Hwang, Kyung Jae Kim, Bong Dae Choi. Delay distribution and loss probability of bandwidth requests under truncated binary exponential backoff mechanism in IEEE 802.16e over Gilbert-Elliot error channel. Journal of Industrial & Management Optimization, 2009, 5 (3) : 525-540. doi: 10.3934/jimo.2009.5.525
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