Queues with interruption in random environment

Krishnamoorthy, A.; Jaya, S.; Lakshmy, B.

doi:10.1007/s10479-015-1931-4

Cited by 6 publications

(1 citation statement)

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“…Furthermore, the breakdown rate can also depend on the on-going phase (Wang, 2004;Choudhury and Tadj, 2009), or breakdowns can either trigger a preemptive resume or preemptive repeat interruption (Fiems et al, 2008). Some breakdown models include additional features such as multiple vacations when the server is idle (Tang et al, 2008), setup and closedown times (Ke, 2007), reneging (Martin and Mitrani, 2008), customer expulsions on arrivals (Atencia, 2014;2015), delayed detection of breakdowns (Krishnamoorthy et al, 2015), multiple types of interruptions (Wu et al, 2011), or working breakdowns (Jiang and Liu, 2017).…”

Section: 2mentioning

confidence: 99%

From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

Fiems

Vuyst

2018

International Journal of Applied Mathematics and Computer Science

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We consider the discrete-time G/GI/1 queueing system with multiple exhaustive vacations. By a transform approach, we obtain an expression for the probability generating function of the waiting time of customers in such a system. We then show that the results can be used to assess the performance of G/GI/1 queueing systems with server breakdowns as well as that of the low-priority queue of a preemptive M X +G/GI/1 priority queueing system. By calculating service completion times of low-priority customers, various preemptive breakdown/priority disciplines can be studied, including preemptive resume and preemptive repeat, as well as their combinations. We illustrate our approach with some numerical examples.

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