2024, Vol. 5, Issue 2, Part A
Analysis of M/M/1 queueing model with removable and unreliable server, partial breakdown during working vacation, setup with repair
Author(s): Rachna Rathore and Dr. RK Shrivastava
Abstract: This paper investigates a M/M/1 queueing Model with unreliable and removable server in which Partial breakdown happens during working vacation, set up and repair. Customers arrival follow Poisson’s distribution with rate λ. When system becomes empty server moves for a single working vacation with rate θ. During working vacation, server faces an unpredictable partial breakdown due to which server provides service at some reduced rate η. On completion of vacation, if server find customers waiting for service, then server resumes normal busy period otherwise moves to closed down state with rate γ. If customers come during closed down state, the server needs to restart. During restarting of server, the server may fail with probability q otherwise join regular busy period with probability p. The closed form expression of various steady state probabilities along with various performance measures like waiting time in system, expected queue length, system probabilities at different server states have been evaluated. The impact of some parameters on various system performances have been presented numerically in tabular form and illustrated graphically.
DOI: https://doi.org/10.22271/math.2024.v5.i2a.141
Pages: 01-07 | Views: 211 | Downloads: 106
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How to cite this article:
Rachna Rathore and Dr. RK Shrivastava. Analysis of M/M/1 queueing model with removable and unreliable server, partial breakdown during working vacation, setup with repair. Journal of Mathematical Problems, Equations and Statistics. 2024; 5(2): 01-07. DOI: 10.22271/math.2024.v5.i2a.141
