Abstract
This paper focuses on an M/M/s queue with multiple working vacations such that the server works with different service rates rather than no service during the vacation period. We show that this is a generalization of an M/M/1 queue with working vacations in the literature. Service times during vacation period, or during service period and vacation times are all exponentially distributed. We obtain the useful formula for the rate matrix R through matrix-geometric method. A cost function is formulated to determine the optimal number of servers subject to the stability conditions. We apply the direct search algorithm and Newton-Quasi algorithm to heuristically find an approximate solution to the constrained optimization problem. Numerical results are provided to illustrate the effectiveness of the computational algorithm.
Original language | English |
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Pages (from-to) | 1-17 |
Number of pages | 17 |
Journal | Journal of Industrial and Management Optimization |
Volume | 8 |
Issue number | 1 |
DOIs | |
State | Published - 1 Feb 2012 |
Keywords
- Newton-quasi algorithm
- Optimization
- Rate matrix
- Sensitivity analysis
- Working vacations