Unreliable M/g/1 Queue with Multi-optional Services and Multi-optional Vacations under N-policy

A multiple optional vacation policy for the unreliable server batch arrival queueing system with essential and multi optional services under N-policy is investigated. According to vacation policy, the server takes an essential phase of vacation after the completion of service of an individual customer when queue becomes empty. On returning from the vacation, if the server finds the queue empty, then he again goes for second phase of vacation with some probability. This process is continued for at most ’m’ phases of vacations. The server follows N-policy according to which the server turns on and starts the service only when the queue size reaches or exceeds N. Once the queue size reaches N, the server provides ”essential” service to all the arriving units whereas ”multioptional” services to only a few of them who demand for the same. By employing generating function and supplementary variable techniques, the system size distribution and other performance indices such as average queue length and long run probabilities of the system states have been derived. The effects of the system parameters on various performance measures are examined by taking an illustration.