The discrete-time MAP/PH/1 queue with multiple working vacations |
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Authors: | Cosmika Goswami N Selvaraju |
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Institution: | Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati 781 039, India |
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Abstract: | We consider a discrete-time single-server queueing model where arrivals are governed by a discrete Markovian arrival process (DMAP), which captures both burstiness and correlation in the interarrival times, and the service times and the vacation duration times are assumed to have a general phase-type distributions. The vacation policy is that of a working vacation policy where the server serves the customers at a lower rate during the vacation period as compared to the rate during the normal busy period. Various performance measures of this queueing system like the stationary queue length distribution, waiting time distribution and the distribution of regular busy period are derived. Through numerical experiments, certain insights are presented based on a comparison of the considered model with an equivalent model with independent arrivals, and the effect of the parameters on the performance measures of this model are analyzed. |
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Keywords: | Discrete-time queue Working vacation Markovian arrival process Phase-type distribution Matrix-geometric method |
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