Informatics and Applications2021, Volume 15, Issue 2, pp 26-29
THE MULTIVARIATE DISTRIBUTIONS OF OUTPUT STREAMS IN A QUEUEING SYSTEM WITH PREEMPTIVE REPEAT PRIORITY
AbstractThe paper studies a single server queuing system with r types of customers, preemptive repeat priority and an infinite number of positions in the queue. The arrival stream of customers of each type is a Poisson stream.
Each type has its own generally distributed service time characteristics. The main result is the Laplace-Stieltjes transform of one- and two-dimensional stationary distribution functions of the interdeparture times for each type of customers. The analysis of the output process is carried out by the method of embedded Markov chains.
As embedded times, successive moments of the end of service of the same type customers are selected. From a practical perspective, an accurate characterization of the interdeparture time process is necessary when studying open networks of queues.
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TitleTHE MULTIVARIATE DISTRIBUTIONS OF OUTPUT STREAMS IN A QUEUEING SYSTEM WITH PREEMPTIVE REPEAT PRIORITY
JournalInformatics and Applications
2021, Volume 15, Issue 2, pp 26-29
PublisherInstitute of Informatics Problems, Russian Academy of Sciences
Key wordsoutput stream; preemptive repeat priority; embedded Markov chain; single server
AuthorsV. G. Ushakov, and N. G. Ushakov,
Author AffiliationsDepartment of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Institute of Microelectronics Technology and High-Purity Materials of the Russian Academy of Sciences, 6 Academician Osipyan Str., Chernogolovka, Moscow Region 142432, Russian Federation
Norwegian University of Science and Technology, 15A S. P. Andersensvei, Trondheim 7491, Norway