A markov-modulated M/M/1 queue with group arrivals |
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| Authors: | Yixin Zhu |
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| Institution: | (1) Department of Operations Research, School of Engineering and Applied Science, The George Washington University, 20052 Washington, DC, USA;(2) Present address: Department of Industrial Engineering, SUNY, 14260 Buffalo, NY, USA |
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| Abstract: | We study anM/M/1 group arrival queue in which the arrival rate, service time distributions and the size of each group arrival depend on
the state of an underlying finite-state Markov chain. Using Laplace transforms and matrix analysis, we derive the results
for the queue length process, its limit distribution and the departure process. In some special cases, explicit results are
obtained which are analogous to known classic results. |
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| Keywords: | M/M/1 queue Markov-modulated Laplace transform matrix analysis queue length departure process limit distribution |
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