Using Dobrushin mean-field approach for queueing large-scale networks analysis

In this paper it is considered a system that consists of in nite number of servers with a Poisson input ow 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 uk(t) of the servers that have the queues lengths with not less than k can be described using an in nite system of differential equations. It is possible to investigate Tikhonov type Cauchy problem for this system with small parameter μ for building the solutions uk(t). The evolution analysis of uk(t) (k = 1; 2;....) be applied to application in queueing large-scale networks analysis.