Multiserver Queue with Semi-Markovian Batch Arrivals with Application to the MPEG Frame Sequence

We consider a queueing system consisting of multiple identical servers and a common queue. The service time follows an exponential distribution and the arrival process is governed by a semi-Markov process (SMP). The motivation to study the queueing system with SMP arrivals lies in that it can model the auto-correlated traffic on the high speed network generated by a real time communication, for example, the MPEG-encoded VBR video. Our analysis is based on the theory of piecewise Markov process. We first derive the distributions of the queue size and the waiting time. The stability condition of the system is also discussed. When the sojourn time of SMP follows an exponential distribution all the unknown constants contained in the generating function of queue size can be determined through the zeros of the denominator for this generating function. Based on the result of the analysis, we propose a model to evaluate the waiting time of MPEG video traffic on an ATM network with multiple channels. Here, the SMP corresponds to the exact MPEG sequence of frames. Finally, a numerical example using a real video data is shown.