Ergodicity of Two Class Priority Queues with Preemptive Priority

Well-known results on the ergodicity of queues with preemptive priority were obtained under the assumption that jobs arrive according to the Poisson process. This assumption, however, does not always hold true in practice. In our work we find sufficient ergodicity conditions for queues with two prio...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-10, Vol.267 (2), p.255-259
Main Authors: Mistryukov, A. V., Ushakov, V. G.
Format: Article
Language:English
Subjects:
Ergodic processes
Mathematics
Mathematics and Statistics
Preempting
Queues
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Summary:Well-known results on the ergodicity of queues with preemptive priority were obtained under the assumption that jobs arrive according to the Poisson process. This assumption, however, does not always hold true in practice. In our work we find sufficient ergodicity conditions for queues with two priority classes with a single server, where interarrival times of high-priority jobs have either Erlang or hyperexponential distribution and interarrival times of low-priority jobs and service times of jobs of both classes have arbitrary continuous distributions. We present results in disciplines with loss of an interrupted job and with retrial of an interrupted job.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-06130-1