Skip to main content

Optimal Service Capacities in a Competitive Multiple-Server Queueing Environment

  • Conference paper

Abstract

The study of economic behavior of service providers in a competition environment is an important and interesting research issue. A two-server queueing model has been proposed in Kalai et al. [11] for this purpose. Their model aims at studying the role and impact of service capacity in capturing larger market share so as to maximize the long-run expected profit. They formulate the problem as a two-person strategic game and analyze the equilibrium solutions. The main aim of this paper is to extend the results of the two-server queueing model in [11] to the case of multiple servers. We will only focus on the case when the queueing system is stable.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Altman, E.: Non-zero-sum Stochastic Games in Admission, Service and Routing Control in Queueing Systems. Queueing Systems Theory Appl. 23, 259–279 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  2. Andradotir, S., Ayhan, H., Down, D.: Server Assignment Policies for Maximizing the Steady-State Throughput of Finite Queueing Systems. Manag. Sci. 47, 1421–1439 (2001)

    Article  MATH  Google Scholar 

  3. Ben-Daya, M., Hariga, M.: Integrated Single Vendor Single Buyer Model with Stochastic Demand and Variable Lead Time. International Journal of Production Economics 92, 75–80 (2004)

    Article  Google Scholar 

  4. Bernstein, F., Chen, F., Federgruen, A.: Coordinating Supply Chains with Simple Pricing Schemes: The Role of Vendor-Managed Inventories. Manag. Sci. 52, 1483–1492 (2006)

    Article  MATH  Google Scholar 

  5. Ching, W.: On Convergence of Asynchronous Greedy Algorithm with Relaxation in Multiclass Queueing Environment. IEEE Communication Letters 3, 34–36 (1999)

    Article  Google Scholar 

  6. Ching, W.: Iterative Methods for Queuing and Manufacturing Systems. Springer Monographs in Mathematics. Springer, London (2001)

    Book  MATH  Google Scholar 

  7. Ching, W., Ng, M.: Markov Chains: Models, Algorithms and Applications. International Series on Operations Research and Management Science. Springer, New York (2006)

    MATH  Google Scholar 

  8. Ching, W., Choi, S., Huang, M.: Optimal Service Capacity in a Multiple-server Queueing System: A Game Theory Approach (preprint) (2008), http://hkumath.hku.hk/papers/~wkc/cchpaper1.pdf

  9. Crabill, C., Gross, D., Magazine, M.: A Classified Bibliography of Research on Optimal Control of Queues. Oper. Res. 25, 219–232 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  10. El-Taha, M., Maddah, B.: Allocation of Service Time in a Multiserver System. Manag. Sci. 52, 623–637 (2006)

    Article  MATH  Google Scholar 

  11. Kalai, E., Kamien, M., Rubinovitch, M.: Optimal Service Speeds in a Competitive Environment. Manag. Sci. 38(8), 1154–1163 (1992)

    Article  MATH  Google Scholar 

  12. Gilbert, S., Weng, Z.: Incentive Effects Favor Nonconsolidating Queues in a Service System: The Principal-Agent Perspective. Manag. Sci. 44(12), 1662–1669 (1998)

    Article  MATH  Google Scholar 

  13. Laffont, J., Martimort, D.: The Theory of Incentives: the Principal-agent Model. Princeton University Press, Princeton (2002)

    Google Scholar 

  14. Mishra, B., Raghunathan, S.: Retailer vs. Vendor-Managed Inventory and Brand Competition. Manag. Sci. 50, 445–457 (2004)

    Article  MATH  Google Scholar 

  15. Morries, P.: Introduction to Game Theory. Springer, New York (1994)

    Book  Google Scholar 

  16. Tai, A., Ching, W.: A Quantity-time-based Dispatching Policy for a VMI System. In: Gervasi, O., Gavrilova, M.L., Kumar, V., Laganá, A., Lee, H.P., Mun, Y., Taniar, D., Tan, C.J.K. (eds.) ICCSA 2005. LNCS, vol. 3483, pp. 342–349. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  17. Teghem, J.: Control of the Service Process in a Queueing System. Euro. J. of Oper. Res. 23, 141–158 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  18. Thomas, D.: Coordinated Supply Chain Management. European Journal of Operational Research 94, 1–15 (1996)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering

About this paper

Cite this paper

Ching, WK., Choi, SM., Huang, M. (2009). Optimal Service Capacities in a Competitive Multiple-Server Queueing Environment. In: Zhou, J. (eds) Complex Sciences. Complex 2009. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02466-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02466-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02465-8

  • Online ISBN: 978-3-642-02466-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics