A delay model approach to analysing the performance of wireless communications

A novel Markov model, called the delay model, is proposed to find the packet loss probability of wireless real-time communication systems. Conventional queueing models, which track the number of packets in the queue buffer, have been used successfully for decades but are not suitable for the analysis since they usually lack the delay information of each packet to model the dropping process. The de-lay model tackles the problem by tracking the head-of-queue packet delay, which includes queueing and retransmission delays, instead of the number of queueing packets. Four problems in wireless real-time communications with progressive difficul-ties have been solved. The solutions are useful in designing wireless real-time communication systems to satisfy the quality of service (QoS) requirements, including delay constraints and packet loss probabilities for different users. The first delay model solves a problem which was described as difficult in a recent IEEE transactions paper. It is modeled by a two-dimensional Markov chain and a simple closed-form expression of packet loss probability has been obtained. In addition to correlated errors in the first problem, the second problem further allows correlated arrivals, which have significant impact on performance. Surprisingly, the Markov chain and the solution are nearly the same in structure as those of the first problem. Wireless effective bandwidth, which is the bandwidth required to satisfy the quality of service requirements, has been estimated in the third problem. It uses hybrid ARQ for error correction and allows batch arrivals. The last problem is the most general. The arrival and error processes are discrete batch Markovian arrival and discrete Markovian arrival processes respectively. The steady state probability of packet loss probability is obtained by matrix-analytic techniques