Abstract
A semi-Markov model describing the performance of an ATM multiplexer with VBR video sources as inputs is presented. The considered system consists of the bit-streams generated by a collection of these sources. The streams which are first separately packetized into fixed size cells, and then, through a statistical multiplexer, join a common queue (assumed to be infinite) where they are served on a FIFO basis by a constant capacity channel. The model to be used is based on the assumption that the video sources operate in two bit-rate modes with unequal average holding times. Each video source is decomposed into an aggregate of two types of ON/OFF mini-sources. Multiplexing a number of such sources leads to a semi-Markov process, which is defined and solved using a phase process with as states the number of active mini-sources of each type. By relating an embedded Markov chain to this phase process, a solution to the resulting queueing system is presented, and the queue length distribution is derived using matrix-geometric techniques. Lastly, results are presented showing that the system performance depends not only on the ratio of the average holding times in the two modes, but also on their magnitudes.