A queueing approach to a multi class M/G/1 make-to-stock with backlog

This paper studies an M/G/1 production system serving several customer classes. We show that the Multilevel Rationing (MR) policy, that has been shown to be optimal in the M/M/1 case is not optimal in general. We propose another policy, which we call the extended MR (EMR). The EMR policy exploits the information on the number of all waiting customers at arrival epochs to assess the residual service time. We establish conditions under which the EMR policy is optimal and extend the conditions under which the MR policy is optimal.