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Published in:
2017 | Supplement | Chapter
Infinite–Server Tandem Queue with Renewal Arrivals and Random Capacity of Customers
Authors : Ekaterina Lisovskaya, Svetlana Moiseeva, Michele Pagano
Published in: Distributed Computer and Communication Networks
Publisher: Springer International Publishing
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Abstract
A tandem of two queues with infinite number of servers is considered. Customers arrive at the first stage of the tandem according to a renewal process, and, after the completion of their services, go to the second stage. Each customer carries a random quantity of work (capacity of the customer). In this study service time does not depend on the customer capacities; the latter are used just to fix some additional features of the system evolution. It is shown that the two-dimensional probability distribution of the total capacities at the stages of the system is two-dimensional Gaussian under the asymptotic condition of a high arrival rate. Numerical experiments and simulations allow us to determine the applicability area for the asymptotic result.