On transient and stationary regimes for multi-channel networks with periodic inputs

In this paper, a multi-channel queuing network with a periodic input flow is considered. The multivariate service process is studied in transient and stationary regimes as the number of calls at network nodes. A special form of Jackson's law is obtained. In heavy traffic regime, functional limit theorems of diffusion approximation type are formulated under the condition of convergence in the uniform topology. A limit non-Markov Gaussian process is constructed and its correlation characteristics are represented explicitly via the network parameters.