Waiting times in classical priority queues via elementary lattice path counting

In this paper we describe an elementary combinatorial approach for deriving the waiting and response time distributions in a few classical priority queueing models. By making use of lattice paths that are linked in a natural way to the stochastic processes analysed, the proposed method offers new insights and complements the results previously obtained by inverting the associated Laplace Transforms

Enabling customer satisfaction and stock reduction through service differentiation with response time guarantees

In response to customer specific service time guarantee requirements, service providers can offer differentiated services. However, conventional customer differentiation models based on fill rate constraints do not take full advantage of the stock reduction that can be achieved by differentiating customers based on agreed response times. 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. We employ lattice paths combinatorics to derive the exact distribution of the response time (within leadtime) for the lower priority class and provide a simple and accurate approximation for the response time of the high priority class. We show that the stock levels chosen based on agreed response times can be significantly lower than the ones chosen based on fillrates. This indicates that response time guarantees are an efficient tool in negotiating after-sale contracts, as they improve customer satisfaction and reduce investment costs