Abstract
A single-server queueing system with a Poisson input and an unreliable server is studied. The breakdowns of the server are connected to a certain external factor, defined by a regenerative stochastic process. In this paper one assumes that the arrival process, customers’s service times, and an external environment are mutually independent. The service was interrupted by the breakdown of the server is continued after its reconstruction from the point at which it was interrupted. The Laplace–Stiltjese transform of the stationary distribution of virtual waiting time as well as ergodicity condition is given. The limit theorem in heavy traffic situation is established. Two examples of the applications are considered.
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The research was partially supported by RFBR grant 13-01-00653.
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Afanasyeva, L., Bashtova, E. (2014). Queueing Systems with Unreliable Servers in a Random Environment. In: Melas, V., Mignani, S., Monari, P., Salmaso, L. (eds) Topics in Statistical Simulation. Springer Proceedings in Mathematics & Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2104-1_1
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DOI: https://doi.org/10.1007/978-1-4939-2104-1_1
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