On the Stationary Workload Distribution of Work-conserving Single-server Queues: A General Formula via Stochastic Intensity
نویسنده
چکیده
It is well known that a simple closed-form formula exists for the stationary distribution of waiting times in the first-come, first-served (FCFS) M/GI/1 queue. In this paper, we extend this to the general stationary framework. Namely, we consider a work-conserving single-server queueing system, where the sequence of customers’ arrival epochs and their service times is described as a general stationary marked point process, and we give a closed-form formula for the stationary distribution of the workload in the system. The key to our proof is two-fold: One is the Palm-dynamic calculus, that is, the connection between the notion of Palm probability and that of stochastic intensity. The other is the last-come, first-service with preemptive-resume (LCFS-PR) queueing discipline.
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