Queueing Behavior over a Gilbert-Elliott Packet Erasure Channel

This thesis explores the queueing performance of a wireless communication system that transmits packets over a correlated erasure channel using the IEEE 802.11 protocol suit. The channel states and the queue length together form a Markov chain. Exploiting this mathematical structure, the probability of the queue exceeding a certain threshold can be obtained. Most previous contributions in this area treat code-rate selection, channel erasure probability and network congestion separately. In this thesis, a simple integrated approach, which jointly considers these factors, is introduced. This approach becomes especially valuable for capturing the performance of delay-sensitive communication systems over time-varying channels. This thesis starts with a review of related work about correlated bit-erasure wireless channel models. A numerical study is then conducted to demonstrate the importance of optimizing overall system performance, and how this process impacts error-control coding at the physical layer. Following this exercise, a packet-erasure channel model with a Poisson arrival process is analyzed. The Baum-Welch algorithm is subsequently presented as a means to estimate the parameters of wireless communication systems. Furthermore, a matrix geometric method for obtaining the stationary distribution of the ensuing Markov chain is discussed. This offers a new perspective on wireless communication in the context of delay-sensitive applications. To complement the analysis platform put forth in this work, illustrative numerical results are contained in the last section of the thesis. From these results, design guidelines for improving the performance of delay-sensitive wireless communication systems are established. Although these results are obtained under simplifying assumptions, the overall methodology applies to more general situations, especially for wide-band delay-sensitive wireless communication applications.