Asymptotics for steady-state tail probabilities in structured markov queueing models

Abstract

We apply Tauberian theorems with known transforms to establish asymptotics for the basic steady-state distributions in the BMAP/G/l queue. The batch Markovian arrival process (BMAP)is equivalent to the versatile Markovian point process or Neuts (N) process; it generalizes the Markovian arrival process (MAP) by allowing batch arrivals. We consider the waiting time, the workload (virtual waiting time) and the queue lengths at an arbitrary time, just before an arrival and just after a departure. We begin by establishing asymptotics for steady-state distributions of M/G/1-type Markov chains. Then we treat steady-state distributions in the BMAP/G/l and MAP/MSP/l queues. The MSPis a MAPindependent of the arrival process generating service completions during