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A Multi Server Markovian Working Vacation queue with Breakdown, N-policy and with Server State Dependent Rates |
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PP: 21-28 |
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doi:10.18576/sjm/090201
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Author(s) |
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R. Kalyanaraman,
A. Sundaramoorthy,
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Abstract |
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| A multi-server Markovian queueing system with alternatives between regular busy state, repair state and working vacation state has been considered. When the system is busy, it functions as a multi-server Markovian queue. When it is on vacation, again it functions as a multi-server Markovian queue but with different arrival and service rates. The vacation policy is multiple vacation policy and the vacation period follows a negative exponential distribution. Also, the servers return to the queue only if there are N customers in the queue at a vacation completion point. Besides, during service the server may break down, the repair of the server starts immediately. The repair period follows a negative exponential distribution. The steady-state probability vector of the number of customers in the queue and the stability condition are obtained using the Matrix-Geometric method. Some performance measures and some illustrative examples are also provided. |
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