Synchronous working vacation policy for finite-buffer multiserver queueing system

摘要

This paper presents modeling and analysis of unreliable Markovian multiserver finite-buffer queue with discouragement and synchronous working vacation policy. According to this policy, c servers keep serving the customers until the number of idle servers reaches the threshold level d; then d idle servers take vacation altogether. Out of these d vacationing servers, dW servers may opt for working vacation i.e. they serve the secondary customers with different rates during the vacation period. On the other hand, the remaining d − dW = dV servers continue to be on vacation. During the vacation of d servers, the other e = c − d servers must be present in the system even if they are idle. On returning from vacation, if the queue size does not exceed e, then these d servers take another vacation together; otherwise start serving the customers. The servers may undergo breakdown simultaneously both in regular busy period and working vacation period due to the failure of a main control unit. This main unit is then repaired by the repairman in at most two phases. We obtain the stationary performance measures such as expected queue length, average balking and reneging rate, throughput, etc. The steady state and transient behaviours of the arriving customers and the servers are examined by using matrix analytical method and numerical approach based on Runge–Kutta method of fourth order, respectively. The sensitivity analysis is facilitated for the transient model to demonstrate the validity of the analytical results and to examine the effect of different parameters on various performance indices.