Elucidating the Short Term Loss Behavior of Markovian-Modulated Batch-Service Queueing Model with Discrete-Time Batch Markovian Arrival Process

This paper applies a matrix-analytical approach to analyze the temporal behavior of Markovian-modulated batch-service queue with discrete-time batch Markovian arrival process (DBMAP). The service process is correlated and its structure is presented through discrete-time batch Markovian service process (DBMSP). We examine the temporal behavior of packet loss by means of conditional statistics with respect to congested and noncongested periods that occur in an alternating manner. The congested period corresponds to having more than a certain number of packets in the buffer; noncongested period corresponds to the opposite. All of the four related performance measures are derived, including probability distributions of a congested and noncongested periods, the probability that the system stays in a congested period, the packet loss probability during congested period, and the long term packet loss probability. Queueing systems of this type arise in the domain of wireless communications.