On the stationary workload distribution of work-conserving single-server queues: A general formula via stochastic intensity (Q2774459)
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scientific article; zbMATH DE number 1713759
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the stationary workload distribution of work-conserving single-server queues: A general formula via stochastic intensity |
scientific article; zbMATH DE number 1713759 |
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23 October 2002
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single server queue
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work conserving discipline
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stationary workload distribution
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Palm-martingale calculus
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stochastic intensity kernel
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LCFS-PR discipline
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0.90797806
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0.89946854
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0.8984786
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0.8919678
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On the stationary workload distribution of work-conserving single-server queues: A general formula via stochastic intensity (English)
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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.
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