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 i n statistical multiplexing systems with two classes of sources - one with h igh priority and the other with low priority. The priority discipline is as sumed to be nonpreemptive. Exact expressions for the transforms of these qu antities are derived assuming that packet or cell streams are generated by Markovian Arrival Processes (MAPs). Then a numerical investigation of the l arge-buffer asymptotic behavior of the the waiting-time distribution for lo w-priority sources shows that these asymptotics are often non-exponential.