Dobrushin mean-field approach for queueing large-scale networks with a small parameter

In this paper it is considered a system that consists of infinite number of servers with a Poisson input flow of requests of intensity Nλ. Each requests arriving to the system randomly selects two servers and is instantly sent to the one with the shorter queue. In this case a share u:k (t) of the servers that have the queues lengths with not less than k can be described using an infinite system of differential equations. It is possible to investigate Tikhonov type Cauchy problem for this system with small parameter μ for building the solutions u:k (t). The evolution analysis of u:k (t) (k=1,2, …) be applied to application in queueing large-scale networks analysis. © 2017, Springer International Publishing AG.