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On Gaussian approximation of multi-channel networks with input flows of general structure. (English) Zbl 1478.60250

Summary: In this paper, a multi-channel queueing network with input flow of a general structure is considered. The multi-dimensional service process is introduced as the number of customers at network nodes. In the heavy-traffic regime, a functional limit theorem of diffusion approximation type is proved under the condition that the input flows converge to their limits in the uniform topology. A limit Gaussian process is constructed and its correlation characteristics are represented explicitly via the network parameters. A network with nonhomogeneous Poisson input flow is studied as a particular case of the general model, and a correspondent Gaussian limit process is built.

MSC:

60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
90B15 Stochastic network models in operations research
90B18 Communication networks in operations research
90B22 Queues and service in operations research
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