Optimal control of \((N, F)\) policy for unreliable server queue with multi-optional phase repair and start-up
Summary: In this paper, we study the modelling and analysis of unreliable M/M/K queuing system under \(N\)- and \(F\)-policy with multi-optional phase repair and start-up. According to the \((N, F)\) policy, the first server is turned on only when there are `\(N\)' or more customers are available in the system. The second server is turned on when the queue length of the customers reaches its system capacity \(K\). Furthermore, no more customers are allowed in the system till the number of the customers again drops up to a certain threshold level `\(F\)'. The servers may break down during busy period. There is a provision of `\(l\)' phase repairs to restore the servers. The first-phase repair is necessary but remaining (\(l\)--1) phases are optional. The lifetime, start-up time and repair time of the servers are assumed to be exponentially distributed. Using matrix method, transient probabilities of the system states are determined. To examine the effect of different parameters on various performance indices, the numerical results are provided by taking an illustration.
scientific article; zbMATH DE number 6875983