| Abstract: | ABSTRACT 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 is huge in dimension, the sufficient condition is numerically easy to verify and the asymptotic decay rate can be computed efficiently. |
