On the Shannon capacity of discrete time queues

Motivated by the analysis of high speed packet switched networks like ATM networks and the work on bits through queues, we analyze the information theoretic capacity of a discrete time queue. We assume that time is divided into slots and a random number of identical packets arrive during each slot. A server serves a random number of packets in a slot. We consider various cases of this channel, some of which are analogous to the continuous time case considered by Ananthram and Verdu (see IEEE Trans. Inform. Theory, vol.IT-42, p.4-18, 1996) and others which show some interesting new features.