Allocation of Customer Types to Servers: Clustering is Optimal

  • S. C. Borst
Part of the Esprit Basic Research Series book series (ESPRIT BASIC)


The model under consideration consists of n customer types attended by m parallel non-identical servers. Customers are allocated to the servers in a probabilistic manner; upon arrival customers are sent to one of the servers according to an m x n matrix of routing probabilities. We consider the problem of finding an allocation that minimizes a weighted sum of the mean waiting times. We expose the structure of an optimal allocation and describe for some special cases in detail how the structure may be exploited in actually computing an optimal allocation.


Service Time Traffic Intensity Optimal Allocation Total Load Distribute Computer System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    S.C. Borst, “Optimal probabilistic allocation of customer types to servers”, CWI Report BS-R9415, 1994.Google Scholar
  2. 2.
    J.A. Buzacott and J.G. Shanthikumar, “Design of manufacturing systems using queueing models”, Queueing Systems 12, Special Issue on Queueing Models of Manufacturing Systems, pp. 135–213, 1992.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    J.P. Buzen and P.P.-S. Chen, “Optimal load balancing in memory hierarchies”, In: Proc. IFIP 1974, ed. J.L. Rosenfeld (North-Holland, Amsterdam), pp. 271-275, 1974.Google Scholar
  4. 4.
    W.C. Cheng and R.R. Muntz, “Optimal routing for closed queueing networks”, In: Perf’ 90, eds. P.J.B. King, I. Mitrani, R.J. Pooley (North-Holland, Amsterdam), pp. 3-17, 1990.Google Scholar
  5. 5.
    E. De Souza e Silva and M. Gerla, “Load balancing in distributed systems with multiple classes and site constraints”, In: Perf.’ 84, ed. E. Gelenbe (North-Holland, Amsterdam), pp. 17-33, 1984.Google Scholar
  6. 6.
    M.R. Garey and D.S. Johnson, “Computers and Intractability: a Guide to the Theory of NP-Completeness”, (Freeman, San Francisco), 1979.Google Scholar
  7. 7.
    I. Meilijson and U. Yechiali, “On optimal right-of-way policies at a single-server station when insertion of idle times is permitted”, Stock. Proc. Appl. 6, pp. 25–32, 1977.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    A.N. Tantawi and D. Towsley, “A general model for optimal static load balancing in star network configurations”, In: Perf.’ 84, ed. E. Gelenbe (North-Holland, Amsterdam), pp. 277-291, 1984.Google Scholar
  9. 9.
    A.N. Tantawi and D. Towsley, “Optimal static load balancing in distributed computer systems”, J. ACM 32, pp. 445–465, 1985.MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    S.K. Tripathi and C.M. Woodside, “A vertex-allocation theorem for resources in queueing networks”, J. ACM 35, pp. 221–230, 1988.MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    C.M. Woodside and S.K. Tripathi, “Optimal allocation of file servers in a local network environment”, IEEE Trans. Soflw. Eng. 12, pp. 844–848, 1986.Google Scholar
  12. 12.
    Y.-T. Wang and R.J.T. Morris, “Load sharing in distributed systems”, IEEE Trans. Comp. 34, pp. 204–217, 1985.CrossRefGoogle Scholar

Copyright information

© ECSC-EC-EAEC, Brussels-Luxembourg 1995

Authors and Affiliations

  • S. C. Borst
    • 1
  1. 1.CWIThe Netherlands

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