On the Queue Length Distribution in BMAP Systems

Bmap/g/1 Queue under D-policy: Queue Length Analysis

The Inhomogeneous Bmap/g/∞ Queue

In queueing theory, most models are based on time-homogeneous arrival processes and service time distributions. However, in communication networks arrival rates and/or the service capacity usually vary periodically in time. In order to reflect this property accurately, it is most natural to consider inhomogeneous arrival processes in queueing models. In the present paper, the inhomogeneous BMAP...

Transient queue length and busy period of the BMAP / PH / 1 queue

We derive in this paper the transient queue length and the busy period distributions in the single server queue with phase-type (PH) services times and a batch Markovian arrival process (BMAP). These distributions are obtained by the uniformization technique which gives simple recurrence relations. The main advantage of this technique is that it leads to stable algorithms for which the precisio...

The Transient Bmap / G /1 Queue

We derive the two-dimensional transforms of the transient workload and queue-length distributions in the single-server queue with general service times and a batch Markovian arrival process (BMAP). This arrival process includes the familiar phase-type renewal process and the Markov modulated Poisson process as special cases, and allows correlated interarrival times and batch sizes. Numerical re...

The BMAP/G/1 QUEUE: A Tutorial

We present an overview of recent results related to the single server queue with general independent and identically distributed service times and a batch Markovian arrival process (BMAP). The BMAP encompasses a wide range of arrival processes and yet, mathematically, the BMAP/G/I model is a relatively simple matrix generalization of the M/G/l queue. Stationary and transient distributions for t...