Проведено исследование системы массового обслуживания с неограниченным числом приборов. Заявки поступают в систему в виде марковски-модулированного пуассоновского потока. Каждая заявка несет в себе произвольное количество данных (объем заявки). В этом исследовании время обслуживания не зависит от объема заявок. Показано, что совместное распределение вероятностей числа заявок в системе и их суммарного объема является двумерным гауссовским при асимптотическом условии растущего времени обслуживания. Имитационное моделирование и численные эксперименты позволили определить область применимости асимптотического результата.
In this paper a queuing system with an infinite number of servers is considered. Customers arrive in the system according to a Markov Modulated Poisson Process. 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 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 to determine an applicability area of the asymptotic result
Study of the MMPP/GI/∞MMPP/GI/∞ queueing system with random customers' capacities
M. Pagano;
2017-01-01
Abstract
In this paper a queuing system with an infinite number of servers is considered. Customers arrive in the system according to a Markov Modulated Poisson Process. 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 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 to determine an applicability area of the asymptotic resultFile | Dimensione | Formato | |
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Descrizione: DOI: https://doi.org/10.14357/19922264170414
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