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.

本文考虑了一个多通道排队网络及其节点集合的渐近合并问题。到达网络的输入流速率取决于时间。网络节点中的服务时间通常是分布式的。我们引入了一个多元服务过程，作为节点中正在处理的呼叫数。在交通繁忙的情况下，证明了高斯近似类型的功能极限定理可用于原始网络和合并网络的规范化服务过程。构造极限高斯过程，并通过网络参数写入它们的相关特性。在合并网络节点集的情况下，限制过程是多维扩散高斯过程。而且，由于采用合并的方法，限制过程的尺寸减小了。