Discrete NT-policy single server queue with Markovian arrival process and phase type service

Discrete NT-policy single server queue with Markovian arrival process and phase type service

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Article ID: iaor19982481
Country: Netherlands
Volume: 88
Issue: 3
Start Page Number: 599
End Page Number: 613
Publication Date: Feb 1996
Journal: European Journal of Operational Research
Authors: ,
Keywords: vacation models
Abstract:

We consider a discrete time single server queueing system in which arrivals are governed by the Markovian arrival process. During a service period, all customers are served exhaustively. The server goes on vacation as soon as he/she completes service and the system is empty. Termination of the vacation period is controlled by two threshold parameters N and T, i.e. the server terminates his/her vacation as soon as the number waiting reaches N or the waiting time of the leading customer reaches T units. The steady state probability vector is shown to be of matrix-geometric type. The average queue length and the probability that the server is on vacation (or idle) are obtained. We also derive the steady state distribution of the waiting time at arrivals and show that the vacation period distribution is of phase type.

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