Statistical multiplexing with priorities: tail probabilities of queue lengths and waiting times

We consider the problem of estimating tail probabilities of waiting times and queue lengths in statistical multiplexing systems with two classes of sources-one with high priority and the other with low priority. The priority discipline is assumed to be nonpreemptive. Exact expressions for the transforms of these quantities are derived assuming that packet or cell streams are generated by Markovian arrival processes (MAPs). Then we numerically investigate the large-buffer asymptotic behavior of the waiting-time distribution for low-priority sources and show that these asymptotics may be non-exponential