Computation and optimization of a working breakdown queue with second optional service

Abstract

This paper considers an M/M/1 queue with second optional service, in which the server is subject to working breakdowns and repairs. All arriving customers require the first essential service, whereas only a portion of them require a second optional service. In case where the server may break down while providing the first (essential) or second (optional) service, the server continues operation at a reduced level rather than ceasing service entirely. The stability condition for this queue is derived in explicit form. The matrix-geometric method is used to compute the stationary probability distribution of the system size and various system performance measures. The genetic algorithm is applied to a cost optimization problem with the aim of optimizing service rates by minimizing the expected cost per unit time. Finally, a numerical example is presented for illustrative purposes.

Keywords:

• Genetic algorithm
• matrix-geometric method
• optimization
• second optional service

Acknowledgements

The authors thank the anonymous referee for valuable comments, which improved this manuscript.