On the stationary workload distribution of work-conserving single-server queues: A general formula via stochastic intensity (Q2774459)

The paper deals with the general work-conserving single server queueing system, where it is assumed that the stationary marked point process of the sequence of arrival epochs and service times has a stochastic intensity kernel. This allows to consider the case where the service time distribution of a customer depends on the past queueing behavior until his/her arrival. For the stationary workload distribution a closed-form formula is proved, being of a similar structure as in the well known M/GI/1 queue. The proof is based on the Palm-martingale calculus (connection of Palm probability and that of stochastic intensity) and the preemptive-resume last-come first-served discipline.