Skip to main content
Log in

Inequalities and an approximation formula for the mean delay time in tandem queueing systems

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Avi-Itzhak, B. and Yadin, M. (1965). A sequence of two servers with no intermediate queue,Management science,11, 553–564.

    MathSciNet  Google Scholar 

  2. Hildebrand, D. K. (1967). Stability of finite queue, tandem server system,J. Appl. Prob.,4, 571–583.

    Article  MathSciNet  MATH  Google Scholar 

  3. Hunt, G. C. (1956). Sequential arrays of waiting lines,Operat. Res. Quart.,4, 674–683.

    Google Scholar 

  4. Kawashima, Y. (1976). Reverse ordering of services in tandem queues,Memoirs of Defense Academy,15, 151–159.

    MathSciNet  Google Scholar 

  5. Kingman, J. F. C. (1962). On queues in heavy traffic,J. R. Statist. Soc., B-24, 383–392.

    MathSciNet  MATH  Google Scholar 

  6. Kingman, J. F. C. (1970). Inequalities in the theory of queues,J. R. Statist. Soc., B-32, 102–110.

    MathSciNet  MATH  Google Scholar 

  7. Kishi, T. (1960). Queues with parallel phases (in Japanese),Keiei-Kagaku,3, 156–165.

    Google Scholar 

  8. Lindley, D. V. (1952). The theory of queues with a single server,Proc. Camb. Phil. Soc.,48, 277–289.

    Article  MathSciNet  Google Scholar 

  9. Marshall, K. T. (1968). Some inequalities in queuing,Operat. Res. Quart.,16, 651–665.

    Article  MathSciNet  MATH  Google Scholar 

  10. Sakasegawa, H. (1976). An approximation formulaL qα·ρ β /(1-ρ),Ann. Inst. Statist. Math.,29, 67–75.

    MathSciNet  Google Scholar 

  11. Suzuki, T. (1964a). On a tandem queue with blocking,J. Operat. Res. Soc. Japan 6, 137–157.

    Google Scholar 

  12. Suzuki, T. (1964b). Ergodicity of a tandem queue with blocking,J. Operat. Res. Soc. Japan,7, 48–75.

    Google Scholar 

  13. Yamazaki, G. and Sakasegawa, H. (1975). Properties of duality in tandem queueing systems,Ann. Inst. Statist. Math.,27, 201–212.

    MathSciNet  MATH  Google Scholar 

  14. Queueing Tables (in Japanese), (1970), Iwanami.

Download references

Author information

Authors and Affiliations

Authors

Additional information

The Institute of Statistical Mathematics

About this article

Cite this article

Sakasegawa, H., Yamazaki, G. Inequalities and an approximation formula for the mean delay time in tandem queueing systems. Ann Inst Stat Math 29, 445–466 (1977). https://doi.org/10.1007/BF02532805

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02532805

Keywords

Navigation