SIMULATION OF LARGE-SCALE QUEUEING SYSTEMS

In this paper we consider the dynamics of large-scale queueing systems with an infinite number of servers. We assume that a Poisson input flow of requests with intensity N lambda. We suppose that each incoming request selects two any servers randomly and a next step of an algorithm includes sending this request to the server with the shorter queue instantly. A share u(k)(t) of the servers that have the queues lengths with not less than k can be described using an system of ordinary differential equations of infinite order. We investigate this system of ordinary differential equations of infinite order with a small real parameter. A small real parameter allows us to describe the processes of rapid changes in large-scale queueing systems. We use the simulation methods for this large-scale queueing systems analysis.