Abstract
In this paper, we analyze a tandem queueing system consisting of R multi-server stations without buffers. The input flow at the first station is a MAP (Markovian arrival process). The customers from this flow aim to be served at all R stations of the tandem. For any r-th station, besides transit customers proceeding from the (r − 1)-th station, an additional MAP flow of new customers arrives at the r-th station directly, not entering the previous stations of the tandem. Customers from this flow aim to be served at the r-th station and all subsequent stations of the tandem. The service time of any customer arriving at the r-th station is exponentially distributed with the service rate depending of r. We present the recursive scheme for calculating the stationary distributions and the loss probabilities associated with the tandem.
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Klimenok, V., Dudin, A., Vishnevsky, V. (2013). Tandem Queueing System with Correlated Input and Cross-Traffic. In: Kwiecień, A., Gaj, P., Stera, P. (eds) Computer Networks. CN 2013. Communications in Computer and Information Science, vol 370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38865-1_42
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DOI: https://doi.org/10.1007/978-3-642-38865-1_42
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