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A model for equilibrium in some service-provider user-set interactions

Author

Listed:
  • Nandyala Hemachandra

    (Indian Institute of Technology Bombay)

  • Kamma Sri Naga Rajesh

    (Carnegie Mellon University)

  • Mohd. Abdul Qavi

    (JDA Software)

Abstract

We propose a model for interaction between a user-set (market) and a service-provider (firm) when the offered demand is sensitive to the offered Quality of Service which in turn depends on the offered demand. We show that, under fairly mild conditions, an equilibrium point or an equilibrium set exists either when the service-provider bases its operational decisions as per a revenue optimal policy of an average reward Markov decision model or when it uses a discounted reward Markov decision model. We also consider the cases when the firm has to meet functional constraints on consumption of resources for its operations. If an equilibrium set exists, then the interaction can suitably be interpreted as one explanation of the business cycles phenomena. We illustrate these and related issues via a model for vehicle relocation system which may be of independent interest.

Suggested Citation

  • Nandyala Hemachandra & Kamma Sri Naga Rajesh & Mohd. Abdul Qavi, 2016. "A model for equilibrium in some service-provider user-set interactions," Annals of Operations Research, Springer, vol. 243(1), pages 95-115, August.
    • Handle: RePEc:spr:annopr:v:243:y:2016:i:1:d:10.1007_s10479-015-2037-8
    DOI: 10.1007/s10479-015-2037-8
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    References listed on IDEAS

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    1. Krishnamurthy Iyer & Nandyala Hemachandra, 2010. "Sensitivity analysis and optimal ultimately stationary deterministic policies in some constrained discounted cost models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 401-425, June.
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    3. repec:cdl:itsrrp:qt0850h6r5 is not listed on IDEAS
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    6. Eugene A. Feinberg & Adam Shwartz, 1996. "Constrained Discounted Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 922-945, November.
    7. Lodewijk Kallenberg, 2013. "Derman’s book as inspiration: some results on LP for MDPs," Annals of Operations Research, Springer, vol. 208(1), pages 63-94, September.
    8. Sinha, Sudhir K. & Rangaraj, N. & Hemachandra, N., 2010. "Pricing surplus server capacity for mean waiting time sensitive customers," European Journal of Operational Research, Elsevier, vol. 205(1), pages 159-171, August.
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    Cited by:

    1. N. Hemachandra & Kishor Patil & Sandhya Tripathi, 2020. "Equilibrium points and equilibrium sets of some $$\textit{GI}/M/1$$ GI / M / 1 queues," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 245-284, December.

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