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A Multi-Server Queueing Model With Markovian Arrivals And Multiple Thresholds

Author

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  • SRINIVAS R. CHAKRAVARTHY

    (Department of Industrial and Manufacturing Engineering, Kettering University, Flint, MI 48504, USA)

Abstract

We consider a multi-server queueing model in which arrivals occur according to a Markovian arrival process (MAP). There is a single-server and additional (backup) servers are added or removed depending on sets of thresholds. The service times are assumed to be exponential and the servers are assumed to be homogeneous. A comparison of this model to the classicalMAP/M/cqueueing model through an optimization problem yields some interesting results that are useful in practical applications. For example, we notice that positively correlated arrival process appears to benefit with the threshold type queueing model. We also give the minimum delay costs and the associated maximum setup costs so that the threshold type queueing model is to be preferred over the classicalMAP/M/cmodel.

Suggested Citation

  • Srinivas R. Chakravarthy, 2007. "A Multi-Server Queueing Model With Markovian Arrivals And Multiple Thresholds," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 223-243.
    • Handle: RePEc:wsi:apjorx:v:24:y:2007:i:02:n:s0217595907001164
    DOI: 10.1142/S0217595907001164
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    Cited by:

    1. Srinivas R. Chakravarthy & Alexander N. Dudin & Sergey A. Dudin & Olga S. Dudina, 2023. "Queueing System with Potential for Recruiting Secondary Servers," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    2. T. Harikrishnan & K. Jeganathan & S. Selvakumar & N. Anbazhagan & Woong Cho & Gyanendra Prasad Joshi & Kwang Chul Son, 2022. "Analysis of Stochastic M / M / c / N Inventory System with Queue-Dependent Server Activation, Multi-Threshold Stages and Optional Retrial Facility," Mathematics, MDPI, vol. 10(15), pages 1-37, July.

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