Abstract
We study a queueing system having a mixture of a special semi-Markov process (SSMP) and a Poisson process as the arrival process, where the Poisson arrival is regarded as interfering traffic. It is shown by numerical examples that the SSMP customers receive worse treatment than Poisson customers, i.e., the mean waiting time of SSMP customers is longer than that of Poisson customers. We also propose a model of Moving Picture Experts Group (MPEG) frame arrivals as an SSMP batch arrival process. This model captures two features of the MPEG coding scheme: (i) the frequency of appearance of the I-, B-, and P-frames in a Group of Pictures (GOP), and (ii) the distinct distributions for the size of the three types of frames. The mean and variance of waiting time of ATM cells generated from the MPEG frames are evaluated in the numerical examples drawn from some real video data.
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