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A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

Author

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  • Ekaterina Evdokimova
  • Sabine Wittevrongel
  • Dieter Fiems

Abstract

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

Suggested Citation

  • Ekaterina Evdokimova & Sabine Wittevrongel & Dieter Fiems, 2017. "A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-10, April.
    • Handle: RePEc:hin:jnlmpe:3298605
    DOI: 10.1155/2017/3298605
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    Cited by:

    1. Dieter Fiems & Eline De Cuypere & Koen De Turck & Dieter Claeys, 2020. "Performance Analysis of Hybrid MTS/MTO Systems with Stochastic Demand and Production," Mathematics, MDPI, vol. 8(11), pages 1-16, November.
    2. Dieter Fiems, 2024. "Performance of a Synchronisation Station with Abandonment," Mathematics, MDPI, vol. 12(5), pages 1-12, February.

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