Multi-server system with single working vacation |
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| Authors: | Chuen-Horng Lin Jau-Chuan Ke |
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| Institution: | 1. Graduate School of Computer Science and Information Technology, National Taichung Institute of Technology, Taichung 404, Taiwan, ROC;2. Department of Applied Statistics, National Taichung Institute of Technology, No. 129, Sec. 3, Sanmin Rd., Taichung 404, Taiwan, ROC |
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| Abstract: | We consider an M/M/R queue with vacations, in which the server works with different service rates rather than completely terminates service during his vacation period. Service times during vacation period, service times during service period and vacation times are all exponentially distributed. Neuts’ matrix–geometric approach is utilized to develop the computable explicit formula for the probability distributions of queue length and other system characteristics. A cost model is derived to determine the optimal values of the number of servers and the working vacation rate simultaneously, in order to minimize the total expected cost per unit time. Under the optimal operating conditions, numerical results are provided in which several system characteristics are calculated based on assumed numerical values given to the system parameters. |
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| Keywords: | Cost Matrix&ndash geometric approach Optimization Queue Single working vacations |
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