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Stochastic Comparisons

  • Hong Chen
  • David D. Yao
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 46)

Abstract

We continue our study of Jackson networks, but shift to focusing on their structural properties: those that describe the qualitative behavior of the network. We want to demonstrate that the Jackson network has the capability to capture the essential qualitative behavior of the system, to make it precise, and to bring out explicitly the role played by different resources and control parameters.

Keywords

Service Rate Equilibrium Rate Service Completion Jackson Network Stochastic Comparison 
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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References

  1. [1]
    Chang, C.S. and Yao, D.D. 1993. Rearrangement, Majorization, and Stochastic Scheduling. Mathematics of Operations Research, 18, 658–684.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Chang, C.S., Shanthikumar, J.G., and Yao, D.D. 1994. Stochastic Convexity and Stochastic Majorization. In: Stochastic Modeling and Analysis of Manufacturing Systems, D.D. Yao (ed.), Springer-Verlag, New York, 189–231.CrossRefGoogle Scholar
  3. [3]
    Glasserman, P. and Yao, D.D. 1994. A GSMP Framework for the Analysis of Production Lines. In: Stochastic Modeling and Analysis of Manufacturing Systems, D.D. Yao (ed.), Springer-Verlag, New York, 1994, 131–186.Google Scholar
  4. [4]
    Glasserman, P. and Yao, D.D. 1994. Monotone Structure in Discrete-Event Systems. Wiley, New York.MATHGoogle Scholar
  5. [5]
    Glasserman, P. and Yao, D.D. 1995. Subadditivity and Stability of a Class of Discrete-Event Systems. IEEE Transactions on Automatic Control, 40, 1514–1527.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Gordon, W.J. and Newell, G. F. 1967. Closed Queueing Networks with Exponential Servers. Operations Research, 15, 252–267.Google Scholar
  7. [7]
    Kamae, T. Krengel, U., and O’Brien, G.L. 1977. Stochastic Inequalities on Partially Ordered Spaces. Annals of Probability, 5, 899–912.MathSciNetMATHGoogle Scholar
  8. [8]
    Karlin, S. and Proschan, F. 1960. Polya-Type Distributions of Convolutions. Ann. Math. Stat., 31, 721–736.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    Keilson, J. and Sumita, U. 1982. Uniform Stochastic Ordering and Related Inequalities. Canadian Journal of Statistics, 10, 181–198.MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    Marshall, A.W. and Olkin, I. 1979. Inequalities: Theory of Majorization and Its Applications. Academic Press, New York.MATHGoogle Scholar
  11. [11]
    Ross, S.M. 1983. Stochastic Processes. Wiley, New York.MATHGoogle Scholar
  12. [12]
    Shaked, M. and Shanthikumar, J.G. 1988. Stochastic Convexity and Its Applications. Advances in Applied Probability, 20, 427–446.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    Shaked, M. and Shanthikumar, J.G. 1990. Convexity of a Set of Stochastically Ordered Random Variables. Advances in Applied Probability, 22, 160–167.MathSciNetMATHCrossRefGoogle Scholar
  14. [14]
    Shanthikumar, J.G. 1987. Stochastic Majorization of Random Variables with Proportional Equilibrium Rates. Advances in Applied Probability, 19, 854–872.MathSciNetMATHCrossRefGoogle Scholar
  15. [15]
    Shanthikumar, J.G. and Stecke, K.E. 1986. Reducing the Work-in-Process Inventory in Certain Class of Flexible Manufacturing Systems. European J. of Operational Res., 26, 266–271.MATHCrossRefGoogle Scholar
  16. [16]
    Shanthikumar, J.G. and Yao, D.D. 1986. The Preservation of Likelihood Ratio Ordering under Convolution. Stochastic Processes and Their Applications, 23, 259–267.MathSciNetMATHCrossRefGoogle Scholar
  17. [17]
    Shanthikumar, J.G. and Yao, D.D. 1986. The Effect of Increasing Service Rates in Closed Queueing Networks. Journal of Applied Probability, 23, 474–483.MathSciNetMATHCrossRefGoogle Scholar
  18. [18]
    Shanthikumar, J.G. and Yao, D.D. 1987. Optimal Server Allocation in a System of Multiserver Stations. Management Science, 34, 1173 1180.Google Scholar
  19. [19]
    Shanthikumar, J.G. and Yao, D.D. 1988. On Server Allocation in Multiple-Center Manufacturing Systems. Operations Research, 36, 333–342.MathSciNetMATHCrossRefGoogle Scholar
  20. [20]
    Shanthikumar, J.G. and Yao, D.D. 1988. Second-Order Properties of the Throughput in a Closed Queueing Network. Mathematics of Operations Research, 13, 524–534.MathSciNetCrossRefGoogle Scholar
  21. [21]
    Shanthikumar, J.G. and Yao, D.D. 1988. Throughput Bounds for Closed Queueing Networks with Queue-Dependent Service Rates. Performance Evaluation, 9, 69–78.MathSciNetMATHCrossRefGoogle Scholar
  22. [22]
    Shanthikumar, J.G. and Yao, D.D. 1991. Strong Stochastic Convexity: Closure Properties and Applications. Journal of Applied Probability, 28 (1991), 131–145.MathSciNetMATHCrossRefGoogle Scholar
  23. [23]
    Stoyan, D. 1983. Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.MATHGoogle Scholar
  24. [24]
    Yao, D.D. 1984. Some Properties of the Throughput Function of Closed Networks of Queues. Operations Research Letters, 3, 313–317.CrossRefGoogle Scholar
  25. [25]
    Yao, D.D. 1987. Majorization and Arrangement Orderings in Open Networks of Queues. Annals of Operations Research, 9, 531–543.CrossRefGoogle Scholar
  26. [26]
    Yao, D.D. and Kim, S.C. 1987. Reducing the Congestion in a Class of Job Shops, Management Science, 34, 1165–1172.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Hong Chen
    • 1
  • David D. Yao
    • 2
  1. 1.Faculty of Commerce and Business AdministrationUniversity of British ColumbiaVancouverCanada
  2. 2.Department of Operations Research and Industrial EngineeringColumbia UniversityNew YorkUSA

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