Infinite-server tandem queue with renewal arrivals and random capacity of customers

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.