Abstract
In this paper asymptotic behavior of the service process for the multi-channel network with input flow controlled by semi-Markov process is studied. Conditions in which a stationary regime exists are pointed out. Integral representation for generating function of the stationary distribution is constructed. In case of exponentially distributed service times limit Gaussian and diffusion Ornstein–Uhlenbeck processes for normalized service process of network processing under heavy traffic conditions are obtained.
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Lebedev, E., Livinska, H. Multi-channel Queueing Networks with Input Flow Controlled by Semi-Markov Process. Math.Comput.Sci. 13, 333–340 (2019). https://doi.org/10.1007/s11786-019-00398-4
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DOI: https://doi.org/10.1007/s11786-019-00398-4