Tail probabilities of low-priority waiting times and queue lengths in MAP/GI/1 queues

We consider the problem of estimating tail probabilities of waiting times 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 transiforms of these quantities are derived assuming that packet or cell streams are generated by Markovian Arrival Processes (MAPs). Then a numerical investigation of the large-buffer asymptotic behavior of the the waiting-time distribution for low-priority sources shows that these asymptotics are often non-exponential.