Analysis Of A FCFS Queue With Two Types Of Customers And Order-Dependent Service Times

In this paper, we study a discrete-time first-comefirst-served queueing system with a single server and two types (classes) of customers, where the (average) service time of a customer is longer if its type differs from the type of the preceding customer. As opposed to traditional literature, the different types of customers do not occur randomly and independently in the arrival stream: we include a Markovian type of correlation in the types of consecutive customers instead. We deduce the probability generating function of the system content, from which we extract various performance measures, such as the mean values of the system content and the customer delay. We demonstrate that the interclass correlation in the arrival stream has a tremendous impact on the system performance, which highlights the necessity to include it in the performance assessment of the system.