Abstract
In this paper, a multichannel queueing network and the problem of asymptotic merging for its set of nodes are considered. Rate of input flow arriving to the network depends on time. Service times in the network nodes are generally distributed. We introduce a multivariate service process as the number of calls being processed in the nodes. Under heavy traffic conditions, functional limit theorems of Gaussian approximation type are proved for the normalized service process of both original and merged networks. Limit Gaussian processes are constructed, and their correlation characteristics are written via the network parameters. In the case of the merging of the network nodes set, the limit process is a multidimensional diffusion Gaussian process. Moreover, due to the approach with merging, dimension of the limit process is reduced.
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