Time Dependent Probabilities of M/M/1 Queue with Working Vacation Subject to Disasters and Repair
B. Janani1, M. Lakshmi Priya2
1B. Janani, Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai, India.
2M. Lakshmi Priya, Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai, India.
Manuscript received on 20 August 2019. | Revised Manuscript received on 08 September 2019. | Manuscript published on 30 September 2019. | PP: 3585-3589 | Volume-8 Issue-11, September 2019. | Retrieval Number: K24770981119/2019©BEIESP | DOI: 10.35940/ijitee.K2477.0981119
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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 Markovian queueing model with working vacation subject to disaster and repair is considered. Whenever the server finds nobody in the system, the server is allowed to take a working vacation where, the server provides service at a slower rate than usual. Also disaster can occur either during busy state or during working vacation state. Whenever the system met with disaster all customers are flushed out and the system transits to repair state. Customers are allowed to join the queue even during repair time. After repair, if the server finds customer then the server moves to busy state otherwise the server moves to working vacation state. Using generating function and Laplace transform techniques explicit time dependent probabilities for various states have been obtained.
Keywords: Disaster, Repair, Vacation, Working vacation, Generating functions, Laplace transform.
Scope of the Article: Aggregation, Integration, and Transformation