THE CORRELATED M/G/1 QUEUE

This paper considers a single server queue in which the service time of each customer depends on the length of the preceding interarrival interval. The dependence structure corresponds to the situation where work arrives at a gate according to a process with independent increments, while at exponential intervals the gate is opened and - after the addition of an independent component - the work is delivered to the server as a single customer. This model unifies and generalizes other recently studied M/G/1 queues with dependence between interarrival and service times. The main result is the joint steady-state distribution of the waiting and service time of a customer. As a by-result, the sojourn time distribution is obtained; a decomposition for its Laplace-Stieltjes transform is presented and interpreted.