Informatics and Applications2016, Volume 10, Issue 3, pp 15-22
ANALYSIS OF A QUEUEING SYSTEM WITH AUTOREGRESSIVE ARRIVALS AND NONPREEMPTIVE PRIORITY
AbstractThe paper studies a single server queueing system with infinite capacity and with two arrival streams, one of which is Poisson and the other is batch Poisson. The customers from the first stream have nonpreemptive priority over the customers from the second. A feature of the system under study is autoregressive dependence of the sizes of the batches from the second arrival stream: the size of the nth batch is equal to the size of the (n - 1)st batch with a fixed probability and is an independent random variable with complementary probability Service times of the customers from each stream are supposed to be independent random variables with specified distributions. The main object of the study is the number of the customers from each stream in the system at an arbitrary moment.
The relations derived make it possible to find Laplace transorm in time of probability generating function of the transient queue length and also a number of additional characteristics.
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TitleANALYSIS OF A QUEUEING SYSTEM WITH AUTOREGRESSIVE ARRIVALS AND NONPREEMPTIVE PRIORITY
JournalInformatics and Applications
2016, Volume 10, Issue 3, pp 15-22
PublisherInstitute of Informatics Problems, Russian Academy of Sciences
Key wordsqueueing theory; transient behavior; batch arrivals; nonpreemptive priority
AuthorsN. D. Leontyev and V. G. Ushakov,
Author AffiliationsDepartment 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 Sciences and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str.,Moscow 119333, Russian Federation