Optimal strategy analysis of N-policy Two-Phase M/Ek/1 Vacation Queueing system with Server Start-Up, Time-Out and Breakdown

Abstract

This article presents optimalstrategy N-Policy M/Ek/1 vacation queueingsystem when the server is in Start-up, Time-out and Breakdown for two-phase. The individual arrivals considered to follow Poisson process and receive batch service of k-stages in the first phase, individual service in the second phase. During the service arrivals are allowed to enter the batch. On completion of the second phase service to all customers in the second phase, the server come back to the first phaseand do the service to the customers who have arrived by providing them first phase service of k-stages followed by second phase service. If there is no customer waiting in the phase one service, the server waits for a fixed time ‘C’ is called server Time-out. If units arrived during this fixed time, then the server provides first phase followed by second phase service, otherwise after expiration of fixed time he takes a vacation. After N-customers accumulate in the system the server returns from vacation. Before going to first phase service, the server spends a random startup period for pre-service after coming back from vacation. During individual service the server is susceptible to random breakdown according to a Poisson process and the repair time follows an exponential distribution. After repair the server resumes individual service. Exact notations for steady state distribution of the number of customers in the system are derived. Developed a cost model for determining the optimal operating policy at a minimum cost. By using numerical illustrations the sensitivity analysis is also presented.