A general relationship between buffer occupancy and delay in discrete-time multiserver queueing models, applicable in ATM networks

A multiserver discrete-time buffer system is studied. Packets arrive in the system according to a general correlated process, which is not further specified. The service times of the packets are of constant length. Explicit expressions are derived for the distribution, the probability generating function, and the mean and variance of the packet delay, in terms of the distribution, the probability generating function, and the mean and variance of the buffer contents. It is observed that knowledge of the exact nature of the arrival process is not required to be able to derive these relationships between the statistics of the delay and the occupancy