Deriving delay characteristics from queue length statistics in discrete-time queues with multiple servers

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