Skip to main content

Polling Models with Two-Stage Gated Service: Fairness Versus Efficiency

  • Conference paper
Managing Traffic Performance in Converged Networks (ITC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 4516))

Included in the following conference series:

  • 1410 Accesses

Abstract

We consider an asymmetric cyclic polling system with general service-time and switch-over time distributions with so-called two-stage gated service at each queue, an interleaving scheme that aims to enforce fairness among the different customer classes. For this model, we (1) obtain a pseudo-conservation law, (2) describe how the mean delay at each of the queues can be obtained recursively via the so-called Descendant Set Approach, and (3) present a closed-form expression for the expected delay at each of the queues when the load tends to unity (under proper heavy-traffic scalings), which is the main result of this paper. The results are strikingly simple and provide new insights into the behavior of two-stage polling systems, including several insensitivity properties of the asymptotic expected delay with respect to the system parameters. Moreover, the results provide insight in the delay-performance of two-stage gated polling compared to the classical one-stage gated service policies. The results show that the two-stage gated service policy indeed leads to better fairness compared to one-stage gated service, at the expense of a decrease in efficiency. Finally, the results also suggest simple and fast approximations for the expected delay in stable polling systems. Numerical experiments demonstrate that the approximations are highly accurate for moderately and heavily loaded systems.

A preliminary version of this paper has also been presented at the Second Korea-Netherlands Conference on Queueing Theory and its Applications to Telecommunication Systems (Amsterdam, October 24-27, 2006).

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Boxma, O.J., Groenendijk, W.P.: Pseudo-conservation laws in cyclic-service systems. J. Appl. Prob. 24, 949–964 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  2. Coffman, E.G., Puhalskii, A.A., Reiman, M.I.: Polling systems with zero switch-over times: a heavy-traffic principle. Ann. Appl. Prob. 5, 681–719 (1995)

    MATH  MathSciNet  Google Scholar 

  3. Coffman, E.G., Puhalskii, A.A., Reiman, M.I.: Polling systems in heavy-traffic: a Bessel process limit. Math. Oper. Res. 23, 257–304 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Fricker, C., Jaïbi, M.R.: Monotonicity and stability of periodic polling models. Queueing Systems 15, 211–238 (1994)

    Article  MATH  Google Scholar 

  5. Konheim, A.G., Levy, H., Srinivasan, M.M.: Descendant set: an efficient approach for the analysis of polling systems. IEEE Trans. Commun. 42, 1245–1253 (1994)

    Article  Google Scholar 

  6. Kramer, G., Muckerjee, B., Pesavento, G.: Ethernet PON: design and analysis of an optical access network. Phot. Net. Commun. 3, 307–319 (2001)

    Article  Google Scholar 

  7. Kramer, G., Muckerjee, B., Pesavento, G.: Interleaved polling with adaptive cycle time (IPACT): a dynamic bandwidth allocation scheme in an optical access network. Phot. Net. Commun. 4, 89–107 (2002)

    Article  Google Scholar 

  8. Kramer, G., Muckerjee, B., Pesavento, G.: Supporting differentiated classes of services in Ethernet passive optical networks. J. Opt. Netw. 1, 280–290 (2002)

    Google Scholar 

  9. Levy, H., Sidi, M.: Polling models: applications, modeling and optimization. IEEE Trans. Commun. 38, 1750–1760 (1991)

    Article  Google Scholar 

  10. Park, C.G., Han, D.H., Kim, B., Jung, H.-S.: Queueing analysis of symmetric polling algorithm for DBA schemes in an EPON. In: Choi, B.D. (ed.) Proceedings 1st Korea-Netherlands Joint Conference on Queueing Theory and its Applications to Telecommunuication Systems, Seoul, Korea, pp. 147–154 (2005)

    Google Scholar 

  11. Takagi, H.: Analysis of Polling Systems. MIT Press, Cambridge (1986)

    Google Scholar 

  12. 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 

  13. 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 

  14. van der Mei, R.D., Levy, H.: Expected delay in polling systems in heavy traffic. Adv. Appl. Prob. 30, 586–602 (1998)

    Article  MATH  Google Scholar 

  15. van der Mei, R.D.: Polling systems in heavy traffic: higher moments of the delay. Queueing Systems 31, 265–294 (1999)

    Article  MATH  Google Scholar 

  16. van der Mei, R.D.: Delay in polling systems with large switch-over times. J. Appl. Prob. 36, 232–243 (1999)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Lorne Mason Tadeusz Drwiega James Yan

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

van der Mei, R.D., Resing, J.A.C. (2007). Polling Models with Two-Stage Gated Service: Fairness Versus Efficiency. In: Mason, L., Drwiega, T., Yan, J. (eds) Managing Traffic Performance in Converged Networks. ITC 2007. Lecture Notes in Computer Science, vol 4516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72990-7_49

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72990-7_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72989-1

  • Online ISBN: 978-3-540-72990-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics