Tail probabilities of low-priority waiting times and queue lengths in MAP/GI/1 queues. (English) Zbl 0942.90019

Subramanian, Vijay; Srikant, R.

Queueing Syst. 34, No. 1-4, 215-236 (2000).

Summary: 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 transforms of these quantities are derived assuming that packet or cell streams are generated by Markovian arrival processes. 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.

MSC:

90B22	Queues and service in operations research
90C40	Markov and semi-Markov decision processes
60K25	Queueing theory (aspects of probability theory)

Keywords:

priority queues; tail probabilities; waiting times; Markovian arrival processes