OPTIMAL N-POLICY FOR UNRELIABLE SERVER QUEUE WITH IMPATIENT CUSTOMER AND VACATION INTERRUPTION

  • Richa Sharma Department of Mathematics, J. K. Lakshmipat University, Jaipur, India
Keywords: Unreliable Server, N-Policy, Working Vacation, Vacation Interruption, Balking, Reneging, Average Cost, Queue Size

Abstract

This study deals with animpatient behavior of the customers for unreliable server queue under N-policy and vacation interruption. N-policy states that the server is turned on only when there are ‘N’ or more customers encountered in the system. Further, we assume two types of vacation namely (i) working vacation and (ii) vacation interruptions. The working vacation queueing models are those wherein the server works at a lower rate rather than stopping the service completely during the dormant period. In vacation interruption, it is assumed that the server can come back to the normal working level immediately if he finds at least one customer waiting in the queue for its service. The server is subject to random breakdowns while rendering service to the customers. The broken-down and repair times of the server are assumed to be exponentially distributed. Using the recursive method, we obtain various performance measures of the concerned queueing system. Special cases are deduced in order to match our results with the existing results. Moreover, cost analysis of the model is also carried out. To examine the effect of different parameters on various performance indices, the numerical results are provided.

 

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Published
2017-05-26
Section
Articles