On modeling the packet error statistics in bursty channels

Wireless channels usually face bursty errors, i.e., errors are prone to occur in clusters. These bit errors can be modeled using the Gilbert-Elliott model. When data packets are transferred over channels with bursty errors, packet error statistics are more important than bit error statistics to analyze the communication performance. This has been modeled as a discrete time Markov chain (DTMC) in previous work. However, whether this Markov chain is time-homogeneous has never been addressed. In this paper, we prove that the packet errors can be modeled only as a Markov chain without constant transition probabilities. Thus finding a constant transition matrix and then discussing performance is not accurate. Instead, a gap model is adopted and the packet error/error-free length distributions are thus analyzed.