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Queueing models with optional cooperative services

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  • Chakravarthy, Srinivas R.

Abstract

In this paper we consider a single-server queueing model in which the customers arrive according to a versatile point process that includes correlated arrivals. An arriving customer can either request for an individual service or for a cooperative service (to be offered along with other customers with similar requests) with some pre-specified probabilities. There is a limit placed on the number of customers requiring cooperative services at any given time. Assuming the service times to be exponentially distributed with possibly different parameters depending on individual or cooperative services, we analyze this model using matrix-analytic method. Second, we simulate this model to obtain a couple of key performance measures which are difficult to compute analytically as well as numerically to show the benefit of cooperative services in queueing. Interesting numerical examples from both analytical and simulated models are discussed. We believe this type of queueing model, which is very much applicable in service areas, has not been studied in the literature.

Suggested Citation

  • Chakravarthy, Srinivas R., 2016. "Queueing models with optional cooperative services," European Journal of Operational Research, Elsevier, vol. 248(3), pages 997-1008.
    • Handle: RePEc:eee:ejores:v:248:y:2016:i:3:p:997-1008
    DOI: 10.1016/j.ejor.2015.08.015
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    References listed on IDEAS

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    1. Garcia-Sanz, M.D. & Fernandez, F.R. & Fiestras-Janeiro, M.G. & Garcia-Jurado, I. & Puerto, J., 2008. "Cooperation in Markovian queueing models," European Journal of Operational Research, Elsevier, vol. 188(2), pages 485-495, July.
    2. Warren B. Powell & Pierre Humblet, 1986. "The Bulk Service Queue with a General Control Strategy: Theoretical Analysis and a New Computational Procedure," Operations Research, INFORMS, vol. 34(2), pages 267-275, April.
    3. Fiestras-Janeiro, M.G. & García-Jurado, I. & Meca, A. & Mosquera, M.A., 2015. "Cooperation on capacitated inventory situations with fixed holding costs," European Journal of Operational Research, Elsevier, vol. 241(3), pages 719-726.
    4. Shoshana Anily & Moshe Haviv, 2010. "Cooperation in Service Systems," Operations Research, INFORMS, vol. 58(3), pages 660-673, June.
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    Cited by:

    1. Anuradha Banerjee & Priti Lata, 2024. "Complete Analysis of $$M/G_{r}^{(a,b)}/1/N$$ M / G r ( a , b ) / 1 / N Queue with Second Optional Service," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-33, December.
    2. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2019. "Performance improvement of a service system via stocking perishable preliminary services," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1000-1011.
    3. Liebmann, Thomas & Kassberger, Stefan & Hellmich, Martin, 2017. "Sharing and growth in general random multiplicative environments," European Journal of Operational Research, Elsevier, vol. 258(1), pages 193-206.

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