Performance of Statistical Multiplexers with Finite Number of Inputs and Train Arrivals

The subject of this paper is the analysis of a discrete-time queueing model with infinite capacity, a single server serving exactly one packet per slot and with N input lines. On each of these input lines, there are messages arriving to the system that consist of exactly m packets. The important feature of this model however, is the fact that the packets of a message do not all enter the system in the same slot. Instead, the case of train-arrivals is considered here, meaning that the m packets arrive in the system at the rate of exactly one packet per slot. In other words, the messages are ‘multiplexed’ into one output stream which has the same rate as each of the input lines. Once the first packet of a message has arrived, it is sure that in each of the m−1 following slots another packet of that message will arrive. Therefore, this situation accounts for a certain amount of slot-to-slot correlation in the packet arrival process of this system. Also, whenever there is no activity on an input line during a certain slot, i.e. no message is currently transmitting one of its packets, then it is assumed that a new message starts with probability q (06q61). Obviously, the start of a new message is marked by the arrival of its first ‘leading’ packet during that slot.