A simple derivation of the waiting time distributions in a non-preemptive M/M/c queue with priorities

In this article we give a new derivation for the waiting time distributions in an M=M=c queue with multiple priorities and a common service rate by using elementary lattice paths counting. An advantage of the approach is that it does not require inversion of the Laplace-Stieltjes transform

A base-stock inventory model with service differentiation and response time guarantees

In response to customer specific service time guarantee requirements, service providers can offer differentiated services. Although response time agreements offer more flexibility, most of the theoretical models for customer differentiation are based on fill rates, due to the difficulty of calculating the response time distribution in the presence of priorities. In this paper we focus on the (S−1,S,K) model with two customer classes, in which low priority customers are served only if the inventory level is above K. For this model, we derive the exact distribution of the response time (within lead time) for the lower priority class and provide a new closed-form approximation for the fill rate for high priority customers. Via numerical experiments, we show that the fill rate approximation performs comparable to the best approximations in the literature, while its implementation requires only elementary operations