Analysis of an SPP/G/1 system with multiple vacations and E-limited service discipline |
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Authors: | Shoji Kasahara Tetsuya Takine Yutaka Takahashi Toshiharu Hasegawa |
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Affiliation: | (1) Division of Applied Systems Science, Faculty of Engineering, Kyoto University, 606-01 Kyoto, Japan;(2) Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, 606-01 Kyoto, Japan |
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Abstract: | Many researchers have studied variants of queueing systems with vacations. Most of them have dealt with M/G/1 systems and have explicitly analyzed some of their performance measures, such as queue length, waiting time, and so on. Recently, studies on queueing systems whose arrival processes are not Poissonian have appeared. We consider a single server queueing system with multiple vacations and E-limited service discipline, where messages arrive to the system according to a switched Poisson process. First, we consider the joint probability density functions of the queue length and the elapsed service time or the elapsed vacation time. We derive the equations for these pdf's, which include a finite number of unknown values. Using Rouché's theorem, we determine the values from boundary conditions. Finally, we derive the transform of the stationary queue length distribution explicitly. |
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Keywords: | Switched Poisson process multiple vacation queue length E-limited service Rouché 's theorem |
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