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.
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Lisovskaya, E., Moiseeva, S., Pagano, M. (2017). Infinite–Server Tandem Queue with Renewal Arrivals and Random Capacity of Customers. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2017. Communications in Computer and Information Science, vol 700. Springer, Cham. https://doi.org/10.1007/978-3-319-66836-9_17
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DOI: https://doi.org/10.1007/978-3-319-66836-9_17
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