Abstract
In the work a multichannel queueing network with a general input flow is considered [3]. There are no restrictions on the structure of the input flow. Heavy traffic conditions on the network parameters are introduced. A functional limit theorem for the service process of the network is proved provided that the conditions are satisfied. Approximative Gaussian process is constructed. An additional splittability condition for the switching matrix of the network yields an opportunity to merge network nodes and to reduce dimension of the limit process at the Gaussian approximation scheme. Convergence is proved in the uniform topology, which enables solving optimization problems for correspondent functionals.
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Lebedev, E.A., Livinska, H. (2021). Reducing of Service Process Dimension for a General-Type Multichannel Network in Heavy Traffic. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2020. Communications in Computer and Information Science, vol 1391. Springer, Cham. https://doi.org/10.1007/978-3-030-72247-0_8
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