The Markov-modulated Erlang loss system

M Mandjes; PG Taylor; K De Turck

Journal article

The Markov-modulated Erlang loss system

M Mandjes, PG Taylor, K De Turck

Performance Evaluation | Elsevier | Published : 2017

DOI: 10.1016/j.peva.2017.08.005

Abstract

This paper focuses on a loss system in which both the arrival rate and the per-customer service rate vary according to the state of an underlying finite-state, continuous-time Markov chain. Our first contribution consists of a closed-form expression for the stationary distribution of this Markov-modulated Erlang loss queue. This, in particular, provides us with an explicit formula for the probability that the queue is full, which can be regarded as the Markov-modulated counterpart of the well-known Erlang loss formula. It facilitates the computation of the probability that an arbitrary arriving customer is blocked. Furthermore, we consider a regime where, in a way that is common for this ty..

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University of Melbourne Researchers

Peter Taylor Author

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Grants

Awarded by NWO Gravitation project NETWORKS

Awarded by Australian Research Council (ARC)

Funding Acknowledgements

The authors thank S. Asmussen and the anonymous referees for useful comments. M. Mandjes' research is partly funded by the NWO Gravitation project NETWORKS, grant number 024.002.003. P.G. Taylor's research is supported by the Australian Research Council (ARC) Laureate Fellowship FL130100039 and the ARC Centre of Excellence for the Mathematical and Statistical Frontiers (ACEMS). This research was partly performed when K. De Turck was a Postdoctoral Fellow of Fonds Wetenschappelijk Onderzoek/Research Foundation - Flanders.