Skip to main content
SpringerLink
Log in

Stochastic Comparisons

  • Chapter
Fundamentals of Queueing Networks

Part of the book series: Stochastic Modelling and Applied Probability ((SMAP,volume 46))

  • 1760 Accesses

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.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 99.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chang, C.S. and Yao, D.D. 1993. Rearrangement, Majorization, and Stochastic Scheduling. Mathematics of Operations Research, 18, 658–684.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Chapter  Google Scholar 

  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. Glasserman, P. and Yao, D.D. 1994. Monotone Structure in Discrete-Event Systems. Wiley, New York.

    MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  6. Gordon, W.J. and Newell, G. F. 1967. Closed Queueing Networks with Exponential Servers. Operations Research, 15, 252–267.

    Google Scholar 

  7. Kamae, T. Krengel, U., and O’Brien, G.L. 1977. Stochastic Inequalities on Partially Ordered Spaces. Annals of Probability, 5, 899–912.

    MathSciNet  MATH  Google Scholar 

  8. Karlin, S. and Proschan, F. 1960. Polya-Type Distributions of Convolutions. Ann. Math. Stat., 31, 721–736.

    Article  MathSciNet  MATH  Google Scholar 

  9. Keilson, J. and Sumita, U. 1982. Uniform Stochastic Ordering and Related Inequalities. Canadian Journal of Statistics, 10, 181–198.

    Article  MathSciNet  MATH  Google Scholar 

  10. Marshall, A.W. and Olkin, I. 1979. Inequalities: Theory of Majorization and Its Applications. Academic Press, New York.

    MATH  Google Scholar 

  11. Ross, S.M. 1983. Stochastic Processes. Wiley, New York.

    MATH  Google Scholar 

  12. Shaked, M. and Shanthikumar, J.G. 1988. Stochastic Convexity and Its Applications. Advances in Applied Probability, 20, 427–446.

    Article  MathSciNet  MATH  Google Scholar 

  13. Shaked, M. and Shanthikumar, J.G. 1990. Convexity of a Set of Stochastically Ordered Random Variables. Advances in Applied Probability, 22, 160–167.

    Article  MathSciNet  MATH  Google Scholar 

  14. Shanthikumar, J.G. 1987. Stochastic Majorization of Random Variables with Proportional Equilibrium Rates. Advances in Applied Probability, 19, 854–872.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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. Shanthikumar, J.G. and Yao, D.D. 1988. On Server Allocation in Multiple-Center Manufacturing Systems. Operations Research, 36, 333–342.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  22. Shanthikumar, J.G. and Yao, D.D. 1991. Strong Stochastic Convexity: Closure Properties and Applications. Journal of Applied Probability, 28 (1991), 131–145.

    Article  MathSciNet  MATH  Google Scholar 

  23. Stoyan, D. 1983. Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.

    MATH  Google Scholar 

  24. Yao, D.D. 1984. Some Properties of the Throughput Function of Closed Networks of Queues. Operations Research Letters, 3, 313–317.

    Article  Google Scholar 

  25. Yao, D.D. 1987. Majorization and Arrangement Orderings in Open Networks of Queues. Annals of Operations Research, 9, 531–543.

    Article  Google Scholar 

  26. Yao, D.D. and Kim, S.C. 1987. Reducing the Congestion in a Class of Job Shops, Management Science, 34, 1165–1172.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Commerce and Business Administration, University of British Columbia, V6T 1Z2, Vancouver, British Columbia, Canada

    Hong Chen

  2. Department of Operations Research and Industrial Engineering, Columbia University, 10027, New York, NY, USA

    David D. Yao

Authors
  1. Hong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David D. Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media New York

About this chapter

Cite this chapter

Chen, H., Yao, D.D. (2001). Stochastic Comparisons. In: Fundamentals of Queueing Networks. Stochastic Modelling and Applied Probability, vol 46. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-5301-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-5301-1_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-2896-2

  • Online ISBN: 978-1-4757-5301-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation