an:02189022
Zbl 1069.60085
Xue, Jungong; Alfa, Attahiru Sule
Tail probability of low-priority queue length in a discrete-time priority BMAP/PH/1 queue
EN
Stoch. Models 21, No. 2-3, 799-820 (2005).
00117386
2005
j
60K25 90B22
asymptotic decay rate; batch Markovian arrival process; discrete-time queues; phase-type distribution
Summary: We investigate the tail probability of the queue length of low-priority class for a discrete-time priority BMAP/PH/1 queue that consists of two priority classes, with BMAP (batch Markovian arrival process) arrivals of high-priority class and MAP (Markovian arrival process) arrivals of low-priority class. A sufficient condition under which this tail probability has the asymptotically geometric property is derived. A method is designed to compute the asymptotic decay rate if the asymptotically geometric property holds. For the case when the BMAP for high-priority class is the superposition of a number of MAP's, though the parameter matrices representing the BMAP are huge in dimension, a sufficient condition is numerically easy to verify and the asymptotic decay rate can be computed efficiently.