BUFFER CONTENTS AND DELAY FOR STATISTICAL MULTIPLEXERS WITH FIXED-LENGTH PACKET-TRAIN ARRIVALS

A slotted statistical multiplexer is considered, to which messages containing a fixed number of fixed-length packets each, arrive at the rate of one packet per slot. The multiplexer buffer can therefore be studied using a discrete-time queueing model with correlated arrivals, referred to as ''train arrivals'' in the paper. This train arrival model is completely analyzed by means of a generating-functions approach. An explicit expression for the probability generating function (pgf) of the buffer contents is obtained. Furthermore, a simple relationship is derived between the pgf of the buffer contents and the pgf of the packet delay in a discrete-time G/D/1 queueing system, which is, of course. also valid for the train arrivals case. Finding this simple and general relationship is one of the contributions of this paper. The pgf of the message delay is obtained as well. Some numerical results are presented. A comparison is also made with the case of ''batch arrivals'' in which all packets of a message arrive simultaneously to the buffer.