IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v52y2006i11p1778-1791.html
   My bibliography  Save this article

Dynamic Control of an M/M/1 Service System with Adjustable Arrival and Service Rates

Author

Listed:
  • Baric{s} Ata

    (Kellogg School of Management, Northwestern University, 2001 Sheridan Road, Evanston, Illinois 60208)

  • Shiri Shneorson

    (Intel Corporation, 2220 Mission College, Santa Clara, California 95054)

Abstract

We study a service facility in which the system manager dynamically controls the arrival and service rates to maximize the long-run average value generated. We initially consider a rate-setting problem where the service facility is modeled as an M/M/1 queue with adjustable arrival and service rates and solve this problem explicitly. Next, we use this solution to study a price-setting problem, where customers are utility maximizing and price- and delay-sensitive, and the system manager chooses state-dependent service rates and prices. We find that the optimal arrival rate is decreasing and the optimal service rate is increasing in the number of customers in the system; however, the optimal price need not be monotone. We also show that under the optimal policy, the service facility operates as one with a finite buffer. Finally, we study a numerical example to compare the social welfare achieved using a dynamic policy to that achieved using static policies and show the dynamic policy offers significant welfare gains.

Suggested Citation

  • Baric{s} Ata & Shiri Shneorson, 2006. "Dynamic Control of an M/M/1 Service System with Adjustable Arrival and Service Rates," Management Science, INFORMS, vol. 52(11), pages 1778-1791, November.
    • Handle: RePEc:inm:ormnsc:v:52:y:2006:i:11:p:1778-1791
    DOI: 10.1287/mnsc.1060.0587
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1060.0587
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1060.0587?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Philipp Afèche & Haim Mendelson, 2004. "Pricing and Priority Auctions in Queueing Systems with a Generalized Delay Cost Structure," Management Science, INFORMS, vol. 50(7), pages 869-882, July.
    2. Shaler Stidham, 2002. "Analysis, Design, and Control of Queueing Systems," Operations Research, INFORMS, vol. 50(1), pages 197-216, February.
    3. David W. Low, 1974. "Optimal Dynamic Pricing Policies for an M / M / s Queue," Operations Research, INFORMS, vol. 22(3), pages 545-561, June.
    4. Sanjeev Dewan & Haim Mendelson, 1990. "User Delay Costs and Internal Pricing for a Service Facility," Management Science, INFORMS, vol. 36(12), pages 1502-1517, December.
    5. Steven A. Lippman & Shaler Stidham, 1977. "Individual versus Social Optimization in Exponential Congestion Systems," Operations Research, INFORMS, vol. 25(2), pages 233-247, April.
    6. Jennifer M. George & J. Michael Harrison, 2001. "Dynamic Control of a Queue with Adjustable Service Rate," Operations Research, INFORMS, vol. 49(5), pages 720-731, October.
    7. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    8. Constantinos Maglaras & Assaf Zeevi, 2003. "Pricing and Capacity Sizing for Systems with Shared Resources: Approximate Solutions and Scaling Relations," Management Science, INFORMS, vol. 49(8), pages 1018-1038, August.
    9. J. Christopher Westland, 1992. "Congestion and Network Externalities in the Short Run Pricing of Information System Services," Management Science, INFORMS, vol. 38(7), pages 992-1009, July.
    10. Yasushi Masuda & Seungjin Whang, 1999. "Dynamic Pricing for Network Service: Equilibrium and Stability," Management Science, INFORMS, vol. 45(6), pages 857-869, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Philipp Afèche & Haim Mendelson, 2004. "Pricing and Priority Auctions in Queueing Systems with a Generalized Delay Cost Structure," Management Science, INFORMS, vol. 50(7), pages 869-882, July.
    2. S. Rao & E. R. Petersen, 1998. "Optimal Pricing of Priority Services," Operations Research, INFORMS, vol. 46(1), pages 46-56, February.
    3. Wang, E. T. G., 2000. "Information and incentives in computing services supply: The effect of limited system choices," European Journal of Operational Research, Elsevier, vol. 125(3), pages 503-518, September.
    4. Omar Besbes & Costis Maglaras, 2009. "Revenue Optimization for a Make-to-Order Queue in an Uncertain Market Environment," Operations Research, INFORMS, vol. 57(6), pages 1438-1450, December.
    5. Vernon N. Hsu & Susan H. Xu & Boris Jukic, 2009. "Optimal Scheduling and Incentive Compatible Pricing for a Service System with Quality of Service Guarantees," Manufacturing & Service Operations Management, INFORMS, vol. 11(3), pages 375-396, May.
    6. Vibhanshu Abhishek & Mustafa Dogan & Alexandre Jacquillat, 2021. "Strategic Timing and Dynamic Pricing for Online Resource Allocation," Management Science, INFORMS, vol. 67(8), pages 4880-4907, August.
    7. Gérard P. Cachon & Patrick T. Harker, 2002. "Competition and Outsourcing with Scale Economies," Management Science, INFORMS, vol. 48(10), pages 1314-1333, October.
    8. Balcıõglu, Barış & Varol, Yãgız, 2022. "Fair and profitable: How pricing and lead-time quotation policies can help," European Journal of Operational Research, Elsevier, vol. 299(3), pages 977-986.
    9. Jan A. Van Mieghem, 2000. "Price and Service Discrimination in Queuing Systems: Incentive Compatibility of Gc\mu Scheduling," Management Science, INFORMS, vol. 46(9), pages 1249-1267, September.
    10. Ke-Wei Huang & Arun Sundararajan, 2006. "Pricing Digital Goods: Discontinuous Costs and Shared Infrastructure," Working Papers 06-11, NET Institute, revised Sep 2006.
    11. Xuanming Su & Stefanos Zenios, 2004. "Patient Choice in Kidney Allocation: The Role of the Queueing Discipline," Manufacturing & Service Operations Management, INFORMS, vol. 6(4), pages 280-301, June.
    12. Mei Xue & Patrick T. Harker, 2003. "Service Co-Production, Customer Efficiency and Market Competition," Center for Financial Institutions Working Papers 03-03, Wharton School Center for Financial Institutions, University of Pennsylvania.
    13. Y Perlman & M Kaspi, 2007. "Centralized decision of internal transfer-prices with congestion externalities for two modes of repair with limited repair capacity," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(9), pages 1178-1184, September.
    14. Prabhudev Konana & Alok Gupta & Andrew B. Whinston, 2000. "Integrating User Preferences and Real-Time Workload in Information Services," Information Systems Research, INFORMS, vol. 11(2), pages 177-196, June.
    15. Zhou, Wenhui & Lian, Zhaotong & Wu, Jinbiao, 2014. "When should service firms provide free experience service?," European Journal of Operational Research, Elsevier, vol. 234(3), pages 830-838.
    16. Aktaran-KalaycI, Tûba & Ayhan, Hayriye, 2009. "Sensitivity of optimal prices to system parameters in a steady-state service facility," European Journal of Operational Research, Elsevier, vol. 193(1), pages 120-128, February.
    17. Larsen, Christian, 1998. "Investigating sensitivity and the impact of information on pricing decisions in an M/M/1/ [infinity] queueing model," International Journal of Production Economics, Elsevier, vol. 56(1), pages 365-377, September.
    18. Zhe George Zhang & Xiaoling Yin, 2021. "Designing a Sustainable Two‐Tier Service System with Customer's Asymmetric Preference for Servers," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 3856-3880, November.
    19. Philipp Afèche, 2013. "Incentive-Compatible Revenue Management in Queueing Systems: Optimal Strategic Delay," Manufacturing & Service Operations Management, INFORMS, vol. 15(3), pages 423-443, July.
    20. Philipp Afèche & J. Michael Pavlin, 2016. "Optimal Price/Lead-Time Menus for Queues with Customer Choice: Segmentation, Pooling, and Strategic Delay," Management Science, INFORMS, vol. 62(8), pages 2412-2436, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:52:y:2006:i:11:p:1778-1791. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.