Skip to main content

An Analysis of Asymmetrical Threshold Polling Systems

  • Conference paper
Computational Intelligence and Intelligent Systems (ISICA 2010)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 107))

Included in the following conference series:

  • 750 Accesses

Abstract

Asymmetric polling systems have been found many applications in production environments. We provide a unified analytic framework for studying asymmetric polling system. This differ-service analysis (DSA) framework allows analysis of mean queue length and packet waiting time in classical asymmetric polling systems with gated service, by use the imbedded Markov-chain theory and the probability generating function. A simulation study is undertaken to evaluate these mathematical analysis.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Mack, C., Murphy, T., Webb, N.L.: The efficiency of N machines uni-directionally patrolled by one operative when walking time and repair times are constants. Journal of the Royal Statistical Society Series B 19(1), 166–172 (1957)

    MathSciNet  MATH  Google Scholar 

  2. Mack, C.: The efficiency of N machines uni-directionally patrolled by one operative when walking time is constant and repair times are variable. Journal of the Royal Statistical Society Series B 19(1), 173–178 (1957)

    MathSciNet  MATH  Google Scholar 

  3. Boxma, O.: Workloads and waiting times in single-server systems with multiple customer classes. Queueing Systems 5, 185–214 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. Levy, H., Sidi, M.: Polling systems: Applications, modeling and optimization. IEEE Transactions on Communications 38(10), 1750–1760 (1990)

    Article  Google Scholar 

  5. Takagi, H.: Queueing analysis of polling models: An update. In: Takagi, H. (ed.) Stochastic Analysis of Computer and Communication Systems, pp. 267–318. North-Holland, Amsterdam (1990)

    Google Scholar 

  6. Takagi, H.: Queueing analysis of polling models: progress in 1990-1994. In: Dshalalow, J.H. (ed.) Frontiers in Queueing: Models, Methods and Problems, pp. 119–146. CRC Press, Boca Raton (1997)

    Google Scholar 

  7. Takagi, H.: Analysis and application of polling models. In: Reiser, M., Haring, G., Lindemann, C. (eds.) Dagstuhl Seminar 1997. LNCS, vol. 1769, pp. 423–442. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  8. Vishnevskii, V., Semenova, O.: Mathematical methods to study the polling systems. Automation and Remote Control 67, 173–220 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dongfeng, Z.: Study on Asymmetric Scheme for Token Bus and Token Ring Networks. Journal of China Institute of Communications 9(1), 75–80 (1998) (in Chinese)

    Google Scholar 

  10. Coman Jr., E., Puhalskii, A., Reiman, M.: Polling systems in heavy-tra5c: a Bessel process limit. Math. Oper. Res. 23, 257–304 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  11. van der Mei, R.D.: Distribution of the delay in polling systems in heavy traffic. Performance Evaluation 38, 133–148 (1999)

    Article  MATH  Google Scholar 

  12. van der Mei, R.D., Winands, E.M.M.: Mean value analysis for polling models in heavy traffic. In: Proc. Int. Conf. on Performance Evaluation Methodologies and Tools, ValueTools, Pisa (2006)

    Google Scholar 

  13. van der Mei, R.D., Winands, E.M.M.: Polling models with renewal arrivals: A new method to derive heavy-traffic asymptotics. Performance Evaluation 64, 1029–1040 (2007)

    Article  Google Scholar 

  14. Van der mei, R.D., Resing, J.A.C.: Polling systems with two-phase gated service: Heavy traffic results for the waiting time distribution. Probability in the Engineering and Informational Sciences 22(4), 623–651 (2008)

    Google Scholar 

  15. Dongfeng, Z., Sunmin, Z.: Message Waiting Time Analysis for a Polling System with Gated Service. Journal of China Institute of Communications 15(2), 18–23 (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Guan, Z., Zhao, D. (2010). An Analysis of Asymmetrical Threshold Polling Systems. In: Cai, Z., Tong, H., Kang, Z., Liu, Y. (eds) Computational Intelligence and Intelligent Systems. ISICA 2010. Communications in Computer and Information Science, vol 107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16388-3_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-16388-3_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16387-6

  • Online ISBN: 978-3-642-16388-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics