The BMAP/G/1 QUEUE: A Tutorial

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...

Logarithmic Asymptotics for the GI/G/1-type Markov Chains and their Applications to the BMAP/G/1 Queue with Vacations

We study tail asymptotics of the stationary distribution for the GI=G=1-type Markov chain with finitely many background states. Decay rate in the logarithmic sense is identified under a number of conditions on the transition probabilities. The results are applied to the BMAP=G=1 queuewith vacations. The relationship between vacation time and the decay rate of the queue length distribution is in...

Further Transient Analysis of the BMAP/G/1 Queue

Previously, we derived the two-dimensional transforms of the emptiness function, 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, as well as superpositions of thes...

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

The BMAP/G/1 queue with level dependent arrivals: An extended queueing model for stations with nonrenewal and state dependent input traffic

Parallel zu diesen Entwicklungen stiegen die Anforderungen an die Methoden zur Leistungsanalyse derartiger Systeme. Die Warteschlangentheorie stellt klassische Modelle zur Analyse von Kommunikationsnetzen bereit. Ein Bereich in der modernen Warteschlangentheorie sind die Matrix analytischen Methoden. Hier konzentriert sich die Forschung auf den Batch Markovian Arrival Process (BMAP), welcher äq...