Abstract
A single server queue with Poisson arrival and exponential service times subject to a policy of single working vacation with customer impatience is considered. The service times are different for an active phase and a working vacation phase. The customer is allowed to leave the system during the working vacation phase. Catastrophes, when they occur, wipe out the system which results in the system being inactive for a random period of time. Explicit expressions for the transient probabilities of the close-down period, maintenance state, active state, working vacation state and system size for active phase and working vacation phase have been obtained. The corresponding steady-state analysis and performance measures are also obtained. The effects of various parameters on the system performance measures are studied using numerical examples.
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Thilaka, B., Poorani, B., Udayabaskaran, S. (2021). Performance Analysis of an M/M/1 Queue with Single Working Vacation with Customer Impatience Subject to Catastrophe. In: Mohapatra, R.N., Yugesh, S., Kalpana, G., Kalaivani, C. (eds) Mathematical Analysis and Computing. ICMAC 2019. Springer Proceedings in Mathematics & Statistics, vol 344. Springer, Singapore. https://doi.org/10.1007/978-981-33-4646-8_24
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