Informatics and Applications2019, Volume 13, Issue 4, pp 42-47
THE OUTPUT STREAMS IN THE SINGLE SERVER QUEUEING SYSTEM WITH A HEAD OF THE LINE PRIORITY
AbstractThe paper studies a single server queuing system with two types of customers, head of the line 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 time 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 of customers are selected. From the practical perspective, an accurate characterization of the interdeparture time process is necessary when studying open networks of queues.
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TitleTHE OUTPUT STREAMS IN THE SINGLE SERVER QUEUEING SYSTEM WITH A HEAD OF THE LINE PRIORITY
JournalInformatics and Applications
2019, Volume 13, Issue 4, pp 42-47
PublisherInstitute of Informatics Problems, Russian Academy of Sciences
Key wordsoutput stream; head of the line priority; embedded Markov chain; single server
AuthorsV. G. Ushakov, and N. G. Ushakov,
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, Moscow 119991, GSP-1, 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