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This article is cited in 6 scientific papers (total in 6 papers)
Study of the $\mathrm{MMPP/GI/}\infty$ queueing system with random customers' capacities
E. Lisovskayaa, S. Moiseevaa, M. Paganob, V. Potatuevaa a Tomsk State University, 36 Lenin ave., Tomsk 634050, Russian Federation
b University of Pisa, 16 Via Caruso, Pisa 56122, Italy
Abstract:
A queueing system with an infinite number of
servers is considered. Customers arrive in the system according to a Markov
Modulated Poisson Process (MMPP). Each customer carries a random quantity of
work (capacity of the customer). In this study, service time does not depend
on the customers' capacities; the latter are used just to fix some additional
features of the system's evolution. It is shown that the joint probability
distribution of the customers' number and total capacities in the system is
two-dimensional Gaussian under the asymptotic condition of an infinitely
growing service time.
Simulation results allow determining the applicability area of the asymptotic result.
Keywords:
infinite-server queueing system; random capacity of customers; Markov Modulated Poisson Process.
Received: 16.03.2017
Citation:
E. Lisovskaya, S. Moiseeva, M. Pagano, V. Potatueva, “Study of the $\mathrm{MMPP/GI/}\infty$ queueing system with random customers' capacities”, Inform. Primen., 11:4 (2017), 109–117
Linking options:
https://www.mathnet.ru/eng/ia508 https://www.mathnet.ru/eng/ia/v11/i4/p109
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