Queue length and delay for statistical multiplexers with variable-length messages

Studies 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. The distribution of the message lengths is general. The system is analyzed by using an infinite-dimensional state description and a generating-functions approach. An explicit expression is obtained for the probability generating function (pgf) of the queue length and the packet delay. Also, closed-form expressions are derived for the mean and the tail distribution of the queue length and the packet delay. The mean message waiting time is obtained as well. The buffer behavior with train arrivals is compared to that with batch arrivals, where all the packets of a message enter the buffer during the same slot. By means of some numerical examples, the impact of the message-length distribution on the multiplexer performance is investigated.