G/M/1 queues with delayed vacations |
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Authors: | Dong Hwan Han Doo Il Choi |
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Affiliation: | 1. Department of Mathematics, Sunmoon University, Asan, 336 - 840, ChungNam, Korea 2. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, 60607-7045, Chicago, Illinois, USA
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Abstract: | We considerG/M/1 queues with multiple vacation discipline, where at the end of every busy period the server stays idle in the system for a period of time called changeover time and then follows a vacation if there is no arrival during the changeover time. The vacation time has a hyperexponential distribution. By using the methods of the shift operator and supplementary variable, we explicitly obtain the queue length probabilities at arrival time points and arbitrary time points simultaneously. |
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