Queue Size and Delay Analysis for a Communication System Subject to Traffic Activity Mode Changes

We consider a discrete single-server queueing/communication system, in which the arrival distribution is changing stochastically with time. The distribution of the number of messages to arrive within a time slot depends on a traffic activity process of modes. This process of modes is a two-state Markov chain: mode 0 and mode 1, which represent light and heavy traffic conditions, respectively. The transition probabilities of this Markov chain [herein called mode duration parameters (MDP's)] determine the distribution of the duration of time the process stays in each mode. Expressions for the
z
-transform, expectation, and variance are obtained for the steady-state queue size and delay. A special consideration is given to the effect of the MDP's on the system performance, and the limiting cases (where the MDP's approach zero) are studied.