The N-policy for an unreliablequeue (M^x/G1G2/1 queue) with optional repeated service and delayed repair

Abstract

In this paper, we consider the N-policy for an unreliable M^X/G/1 queue with two types of general heterogeneous service under optional repeated service and delayed repair. The server is unreliable and turned off each time until the queue size (including one being served, if any) becomes$\mathrm{ }N\mathrm{ }$(threshold). As soon as the queue size exceeds$\mathrm{ }N\mathrm{ }$($\ge 1$), the server is turned on and begin to serve all the arriving units. For this model, we derive the joint distribution of state of the server and queue size by considering both elapsed and remaining time, as well as various system characteristics.

Keywords:

• Two types of service
• repeated service
• N-policy and optimal cost