Performance of a Synchronisation Station with Abandonment

Dieter Fiems ()
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Dieter Fiems: Department of Telecommunication Systems and Information Processing, Ghent University, St-Pietersnieuwstraat 41, 9000 Gent, Belgium

Mathematics, 2024, vol. 12, issue 5, 1-12

Abstract: The paper presents a Markovian queueing model for assessing the performance of synchronisation between stations in a production system. The system at hand consists of K distinct buffers, each buffer storing an item that is needed for the next production stage. Departures are immediate when all items are present. Due to the presence of multiple buffers, there is no reasonably fast way to calculate the stationary distribution of the Markov chain. Therefore, we focused on the series expansion of the stationary distribution in terms of the arrival rate. We provide a fast algorithm for calculating these terms. Comparing our results with stochastic simulation, we show that the expansion approach converges to the simulated values for a wide range of arrival rates.

Keywords: Markov chain; queueing system; synchronisation; Taylor series expansion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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