Correlation effects in ATM queues due to data format conversions

We study the performance of a statistical multiplexer to which messages composed of a variable number of fixed-length packets arrive at the rate of one packet per slot (“train arrivals”), resulting in a correlated packet arrival stream. In this paper, unlike in previous related studies, the distribution of the message lengths is general. We introduce a technique for the exact analysis of the system, which is essentially a generating-functions approach that uses an infinite-dimensional state description. Explicit expressions are obtained for the probability generating functions of the queue length and the packet delay. Also, closed-form results are found for the mean, variance and tail distribution of the queue length and the packet delay. The mean message waiting time and the mean message delay are derived as well. A comparison is made between the buffer behavior with train arrivals and that with batch arrivals, where all the packets of a message enter the buffer during the same slot, and also it is shown that the correlation has a strong effect on the performance of the system. By means of some numerical examples, we also show that the exact nature of the message-length distribution has a significant impact on the multiplexer performance.