Multiclass GI/GI/∞ queueing systems with random resource requirements E. Y. Lisovskaya, S. P. Moiseeva, M. Pagano
Material type:
ArticleContent type: Текст Media type: электронный Subject(s): cистемы массового обслуживания | различные типы серверов | асимптотический анализGenre/Form: статьи в сборниках Online resources: Click here to access online
In:
Information Technologies and Mathematical Modelling. Queueing Theory and Applications : 17th International Conference, ITMM 2018, named after A. F. Terpugov and 12th Workshop on Retrial Queues and Related Topics, WRQ 2018, Tomsk, Russia, September 10-15, 2018 : selected papers P. 129-142Abstract: In the paper we consider a GI/GI/∞ queuing system with n types of customers under the assumptions that customers arrive at the queue according to a renewal process and occupy random resource amounts, which are independent of their service times. Since, in general, the analytical solution of the corresponding Kolmogorov differential equations is not available, we focus on the amount of resources occupied by each class of customers under the assumption of infinitely growing arrival rate, and derive its first and second-order asymptotic approximations. In more detail, we show that the n-dimensional probability distribution of the total resource amount is asymptotically n-dimensional Gaussian, and we verify the accuracy of the asymptotics (in terms of Kolmogorov distance) by means of discrete event simulation.
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In the paper we consider a GI/GI/∞ queuing system with n types of customers under the assumptions that customers arrive at the queue according to a renewal process and occupy random resource amounts, which are independent of their service times. Since, in general, the analytical solution of the corresponding Kolmogorov differential equations is not available, we focus on the amount of resources occupied by each class of customers under the assumption of infinitely growing arrival rate, and derive its first and second-order asymptotic approximations. In more detail, we show that the n-dimensional probability distribution of the total resource amount is asymptotically n-dimensional Gaussian, and we verify the accuracy of the asymptotics (in terms of Kolmogorov distance) by means of discrete event simulation.
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