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Optimal Server Allocation in a System of Multi-Server Stations

Author

Listed:
  • J. George Shanthikumar

    (School of Business Administration, University of California, Berkeley, California 94720)

  • David D. Yao

    (Division of Applied Sciences, Harvard University, Cambridge, Massachusetts 02138)

Abstract

Consider a closed queueing network (Gordon and Newell [Gordon, W. J., G. F. Newell. 1967. Closed queueing networks with exponential servers. Oper. Res. 15 252--267.]) with a set of stations. The service rate at each station is an increasing concave function of the number of jobs at that station. Suppose there also exists a station that has c (\ge 1) parallel servers, each of which has a fixed service rate. We show that the throughput of this network is an increasing concave function with respect to c. This result is then applied to solve the optimal server allocation problem in a system of multi-server stations with a fixed buffer capacity (for the total number of jobs) at each station. For a single-station system, the simultaneous optimal allocation of both servers and buffer capacity is also studied.

Suggested Citation

  • J. George Shanthikumar & David D. Yao, 1987. "Optimal Server Allocation in a System of Multi-Server Stations," Management Science, INFORMS, vol. 33(9), pages 1173-1180, September.
    • Handle: RePEc:inm:ormnsc:v:33:y:1987:i:9:p:1173-1180
    DOI: 10.1287/mnsc.33.9.1173
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    Citations

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    Cited by:

    1. Moshe Shaked & J. Shanthikumar, 1990. "Parametric stochastic convexity and concavity of stochastic processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(3), pages 509-531, September.
    2. Frenk, J.B.G. & Labbé, M. & van Vliet, M. & Zhang, S., 1994. "Improved algorithms for machine allocation in manufacturing systems," Econometric Institute Research Papers 11742, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Aksin, O. Zeynep & Harker, Patrick T., 2003. "Capacity sizing in the presence of a common shared resource: Dimensioning an inbound call center," European Journal of Operational Research, Elsevier, vol. 147(3), pages 464-483, June.
    4. Waal, P.R. & Dijk, N.M. van, 1988. "Monotonicity of performance measures in a processor sharing queue," Serie Research Memoranda 0051, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    5. Kochel, Peter, 2004. "Finite queueing systems--structural investigations and optimal design," International Journal of Production Economics, Elsevier, vol. 88(2), pages 157-171, March.
    6. Hsieh, Chung-Chi & Chiu, Kuo-Chang, 2002. "Optimal maintenance policy in a multistate deteriorating standby system," European Journal of Operational Research, Elsevier, vol. 141(3), pages 689-698, September.
    7. Kochel, Peter & Kunze, Sophie & Nielander, Ulf, 2003. "Optimal control of a distributed service system with moving resources: Application to the fleet sizing and allocation problem," International Journal of Production Economics, Elsevier, vol. 81(1), pages 443-459, January.
    8. Xiuli Chao & Liming Liu & Shaohui Zheng, 2003. "Resource Allocation in Multisite Service Systems with Intersite Customer Flows," Management Science, INFORMS, vol. 49(12), pages 1739-1752, December.
    9. Kochel, Peter, 1996. "On queueing models for some multi-location problems," International Journal of Production Economics, Elsevier, vol. 45(1-3), pages 429-433, August.
    10. Michelle Opp & Kevin Glazebrook & Vidyadhar G. Kulkarni, 2005. "Outsourcing warranty repairs: Dynamic allocation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(5), pages 381-398, August.
    11. Subba Rao, S. & Gunasekaran, A. & Goyal, S. K. & Martikainen, T., 1998. "Waiting line model applications in manufacturing," International Journal of Production Economics, Elsevier, vol. 54(1), pages 1-28, January.
    12. Vincent W. Slaugh & Bahar Biller & Sridhar R. Tayur, 2016. "Managing Rentals with Usage-Based Loss," Manufacturing & Service Operations Management, INFORMS, vol. 18(3), pages 429-444, July.
    13. Xiuli Chao & Carlton Scott, 2000. "Several Results on the Design of Queueing Systems," Operations Research, INFORMS, vol. 48(6), pages 965-970, December.
    14. Gautam, N., 2002. "Performance analysis and optimization of web proxy servers and mirror sites," European Journal of Operational Research, Elsevier, vol. 142(2), pages 396-418, October.
    15. Refael Hassin & Yair Y. Shaki & Uri Yovel, 2015. "Optimal service‐capacity allocation in a loss system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(2), pages 81-97, March.
    16. Bitran, Gabriel R. & Morabito, Reinaldo., 1994. "Open queueing networks : optimization and performance evaluation models for discrete manufacturing systems," Working papers 3743-94., Massachusetts Institute of Technology (MIT), Sloan School of Management.

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