Optimal D-policy for an Unreliable Single Server Queueing Model with Bulk Arrivals

The single server queueing model with control policies has a wide range of applications in the quality control of telephone switching systems and production systems. As a result, several variations of the controlled queueing model have been studied extensively in the literature. These studies give rise to several types of control policies. To name a few, Yadin and Naor [1] analyzed the control policy in which the server doesn’t start service in idle period unless there are N customers in queue, which is called the N-policy. The T-policy is another control policy, introduced by Heyman [2] . The T-policy suggests turning the server into active state after a time interval of length T when the server is in the idle state. Later, the D-policy is proposed by Balachendran [3] which is the focus of this research. In the D-policy, the server remains inactive until a total of D service times are accumulated in the queue. Many variations of these control policies were suggested in the literature. A comprehensive survey paper in this topic is found in Crabill et al. [4] and Doshi [5,6] .