A Markovian Working Vacation Queue with Server State Dependent Arrival Rateand with Partial Breakdown
R. Kalyanaraman1, A. Sundaramoorthy2
1R. Kalyanaraman, Department of Mathematics, Annamalai University, Annamalainagar (Tamil Nadu), India.
2A. Sundaramoorthy, Department of Mathematics, Annamalai University, Annamalainagar (Tamil Nadu), India.
Manuscript received on 26 March 2019 | Revised Manuscript received on 05 April 2019 | Manuscript Published on 27 April 2019 | PP: 664-668 | Volume-7 Issue-6S2 April 2019 | Retrieval Number: F10800476S219/2019©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: A single server Markovianqueueing system with the system alternates between regular busy state, repair state and working vacation state has been considered. If the system is busy, it functions as a single server Markovian queue. When it is on repair/vacation, again it functions as a single server Markovian queue but with different arrival and service rates. The vacation policy is multiple vacation policy and the vacation period follows negative exponential. In addition, during service the server may break down, the repair of the server starts immediately. The breakdown period and repair period follows two different negative exponential distributions. During the repair period the server serves the customer with service period follows negative exponential of different service rate. Some illustrative examples are also provided.
Keywords: Working Vacation, State Dependent Arrival Rate, Matrix-Geometric Method. 2000 Mathematics Subject Classification: 90B22, 60K25 and 60K30.
Scope of the Article: Cryptography and Applied Mathematics