The MX/G/1 queue with queue length dependent service times

We deal with the MX/G/1 queue where service times depend on the queue length at the service initiation. By using Markov renewal theory, we derive the queue length distribution at departure epochs. We also obtain the transient queue length distribution at time t and its limiting distribution and the...

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Published in:Journal of applied mathematics and stochastic analysis 2001-01, Vol.14 (4), p.399-419
Main Authors: Choi, Bong Dae, Kim, Yeong Cheol, Shin, Yang Woo, Pearce, Charles E M
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container_title Journal of applied mathematics and stochastic analysis
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creator Choi, Bong Dae
Kim, Yeong Cheol
Shin, Yang Woo
Pearce, Charles E M
description We deal with the MX/G/1 queue where service times depend on the queue length at the service initiation. By using Markov renewal theory, we derive the queue length distribution at departure epochs. We also obtain the transient queue length distribution at time t and its limiting distribution and the virtual waiting time distribution. The numerical results for transient mean queue length and queue length distributions are given.
doi_str_mv 10.1155/S104895330100034
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title The MX/G/1 queue with queue length dependent service times
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