Abstract:
A heterogeneous queuing system with an infinite number of servers is considered in this paper. Customers arrive in the system according to a Markov Modulated Poisson Process. The type of incoming customer is defined as i-type with probability pi(i=1,2). Each customer carries a random quantity of work (capacity of the customer). In this study service time does not depend on the customers capacities. It is shown that the joint probability distribution of the customers number and total capacities in the system is multidimensional Gaussian distribution under the asymptotic condition of an infinitely growing service time. Simulation results allow us to determine an applicability area of the asymptotic result.
Keywords:
infinite-server queueing system, random capacity of customers, Markov Modulated Poisson Process.
Received: 28.11.2018 Received in revised form: 14.01.2019 Accepted: 20.02.2019
Bibliographic databases:
Document Type:
Article
UDC:
517.9
Language: English
Citation:
Ekaterina V. Pankratova, Svetlana P. Moiseeva, Mais P. Farhadov, Alexandr N. Moiseev, “Heterogeneous system MMPP/GI(2)/∞ with random customers capacities”, J. Sib. Fed. Univ. Math. Phys., 12:2 (2019), 231–239
\Bibitem{PanMoiFar19}
\by Ekaterina~V.~Pankratova, Svetlana~P.~Moiseeva, Mais~P.~Farhadov, Alexandr~N.~Moiseev
\paper Heterogeneous system MMPP/GI(2)/$\infty$ with random customers capacities
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2019
\vol 12
\issue 2
\pages 231--239
\mathnet{http://mi.mathnet.ru/jsfu752}
\crossref{https://doi.org/10.17516/1997-1397-2019-12-2-231-239}
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Linking options:
https://www.mathnet.ru/eng/jsfu752
https://www.mathnet.ru/eng/jsfu/v12/i2/p231
This publication is cited in the following 3 articles:
Ekaterina Pankratova, Ekaterina Pakulova, Svetlana Moiseeva, Lecture Notes in Computer Science, 15460, Distributed Computer and Communication Networks, 2025, 339
S. P. Moiseeva, T. V. Bushkova, E. V. Pankratova, M. P. Farkhadov, A. A. Imomov, “Asymptotic analysis of resource heterogeneous QS (MMPP+2M)(2,ν)/GI(2)/∞ under equivalently increasing service time”, Autom. Remote Control, 83:8 (2022), 1213–1227
Ekaterina Lisovskaya, Ekaterina Pankratova, Svetlana Moiseeva, Michele Pagano, Lecture Notes in Computer Science, 12563, Distributed Computer and Communication Networks, 2020, 335
Citation in format AMSBIB
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