Heterogeneous system GI/GI(n)/∞ with random customers capacities E. Y. Lisovskaya, S. P. Moiseeva, M. Pagano, E. V. Pankratova
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ArticleContent type: Текст Media type: электронный Subject(s): системы массового обслуживания | Колмогорова интегро-дифференциальные уравнения | время ожиданияGenre/Form: статьи в сборниках Online resources: Click here to access online
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Applied probability and stochastic processes P. 507-521Abstract: In the paper, we consider a queuing system with n types of customers. We assume that each customer arrives at the queue according to a renewal process and takes a random resource amount, independent of their service time. We write Kolmogorov integro-differential equation, which, in general, cannot be analytically solved. Hence, we look for the solution under the condition of infinitely growing a service time, and we obtain multi-dimensional asymptotic approximations. We show that the n-dimensional probability distribution of the total resource amounts is asymptotically Gaussian, and we look at its accuracy via Kolmogorov distance.
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In the paper, we consider a queuing system with n types of customers. We assume that each customer arrives at the queue according to a renewal process and takes a random resource amount, independent of their service time. We write Kolmogorov integro-differential equation, which, in general, cannot be analytically solved. Hence, we look for the solution under the condition of infinitely growing a service time, and we obtain multi-dimensional asymptotic approximations. We show that the n-dimensional probability distribution of the total resource amounts is asymptotically Gaussian, and we look at its accuracy via Kolmogorov distance.
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