Systems and Means of Informatics
2020, Volume 30, Issue 3, pp 32-38
ERGODICITY OF SINGLE SERVER QUEUES WITH PREEMPTIVE PRIORITY
Abstract
Well known results on ergodicity of queues with preemptive priority were obtained under the assumption that jobs arrive according to Poisson process. However, this assumption does not always hold true in practice. In this paper, the author finds sufficient ergodicity conditions for queues with two priority classes with 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. To formulate desired conditions, the authors use Lindley's recursion for waiting times of each priority class queue. Using Lyapunov-Foster criteria, the authors obtain sufficient conditions for a given recursion to be Harris-ergodic Markov chain.
[+] References (6)
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[+] About this article
Title
ERGODICITY OF SINGLE SERVER QUEUES WITH PREEMPTIVE PRIORITY
Journal
Systems and Means of Informatics
Volume 30, Issue 3, pp 32-38
Cover Date
2020-11-10
DOI
10.14357/08696527200303
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
preemptive priority; ergodicity; Lyapunov-Foster criteria; hyperexponential arrivals; Erlang arrivals
Authors
A. V. Mistryukov 
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
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