Skip to main content
SpringerLink
Log in

Dynamic Routing Problems with Delayed Information

  • Conference paper
  • First Online:
Performance Evaluation Methodologies and Tools (VALUETOOLS 2021)

  • 474 Accesses

Abstract

The problem of routing jobs to parallel servers is known as the dispatching problem. A typical objective is to minimize the mean response time, which according to Little’s result is equivalent to minimizing the mean number in the system. Dynamic dispatching policies are based on information about the state of each server. In large or real-time systems, up-to-date and accurate system state may not be available to dispatcher. We consider, cases where state information at some time in the past is available, or completed jobs are acknowledged after some propagation delay, and give efficient dispatching policies based on the incomplete state information. The dynamic dispatching policies tailored to this setting are evaluated numerically.

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

Access this chapter

Log in via an institution
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 EPUB and 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

Notes

  1. 1.

    The results for the distribution of N, and therefore also the corresponding policies, hold for any arrival pattern, even non-renewal, though in our numerical examples we consider only Poisson arrival processes.

  2. 2.

    In principle, it is possible that no job has departed from a busy server since the start. That is, the number of possible states increases without bound as the process continues, and evaluating the distribution and its mean eventually becomes cumbersome. As a workaround, our implementation of JSQe truncates the state-space to \(k_{\max }=20\) jobs (per server), and updates the state probabilities accordingly whenever a new job arrives. Given the load is reasonable, the effect of this modification will be negligible.

References

  1. Altman, E., Gaujal, B., Hordijk, A.: Balanced sequences and optimal routing. J. ACM 47(4), 752–775 (2000)

    Article  MathSciNet  Google Scholar 

  2. Altman, E., Kofman, D., Yechiali, U.: Discrete time queues with delayed information. Queueing Syst. 19, 361–376 (1995)

    Article  MathSciNet  Google Scholar 

  3. Artiges, D.: Optimal routing into two heterogeneous information. In: Proceedings of the 32nd Conference on Decision and Control, San Antonio, Texas (1993)

    Google Scholar 

  4. Buzen, J.P., Chen, P.P.: Optimal load balancing in memory hierarchies. In: Proceedings of the 6th IFIP Congress, pp. 271–275, Stockholm, Sweden, August 1974

    Google Scholar 

  5. Ephremides, A., Varaiya, P., Walrand, J.: A simple dynamic routing problem. IEEE Trans. Automatic Control 25(4), 690–693 (1980)

    Article  MathSciNet  Google Scholar 

  6. Haight, F.A.: Two queues in parallel. Biometrika 45(3–4), 401–410 (1958)

    Article  MathSciNet  Google Scholar 

  7. Lipschutz, D.: Open problem-load balancing using delayed information. Stochas. Syst. 9(3), 305–306 (2019)

    Article  MathSciNet  Google Scholar 

  8. Litvak, N., Yechiali, U.: Routing in queues with delayed information. Queueing Syst. 43, 147–165 (2003)

    Article  MathSciNet  Google Scholar 

  9. Liu, Z., Righter, R.: Optimal load balancing on distributed homogeneous unreliable processors. Oper. Res. 46(4), 563–573 (1998)

    Article  Google Scholar 

  10. Liu, Z., Towsley, D.: Optimality of the round-robin routing policy. J. Appl. Probab. 31(2), 466–475 (1994)

    Article  MathSciNet  Google Scholar 

  11. Mitzenmacher, M.: How useful is old information? IEEE Trans. Parallel Distrib. Syst. 11(1), 6–20 (2000)

    Article  Google Scholar 

  12. Novitzky, S., Pender, J., Rand, R.H., Wesson, E.: Nonlinear dynamics in queueing theory: determining the size of oscillations in queues with delay. SIAM J. Appl. Dyn. Syst. 18(1), 279–311 (2019)

    Article  MathSciNet  Google Scholar 

  13. Pender, J., Rand, R., Wesson, E.: A stochastic analysis of queues with customer choice and delayed information. Math. Oper. Res. 45(3), 1104–1126 (2020)

    Article  MathSciNet  Google Scholar 

  14. Selen, J., Adan, I., Kapodistria, S., van Leeuwaarden, J.: Steady-state analysis of shortest expected delay routing. Queueing Syst. 84(3), 309–354 (2016)

    Google Scholar 

  15. Whitt, W.: On the many-server fluid limit for a service system with routing based on delayed information. Oper. Res. Lett. 49, 316–319 (2021)

    Article  MathSciNet  Google Scholar 

  16. Winston, W.: Optimality of the shortest line discipline. J. Appl. Probab. 14, 181–189 (1977)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Iceland, Reykjavik, Iceland

    Esa Hyytiä

  2. Department of Industrial Engineering and Operations Research, University of California Berkeley, Berkeley, CA, USA

    Rhonda Righter

Authors
  1. Esa Hyytiä
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rhonda Righter
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Esa Hyytiä .

Editor information

Editors and Affiliations

  1. Tsinghua University, Beijing, China

    Qianchuan Zhao

  2. Sun Yat-sen University, Guangzhou, China

    Li Xia

Rights and permissions

Reprints and permissions

Copyright information

© 2021 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Hyytiä, E., Righter, R. (2021). Dynamic Routing Problems with Delayed Information. In: Zhao, Q., Xia, L. (eds) Performance Evaluation Methodologies and Tools. VALUETOOLS 2021. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 404. Springer, Cham. https://doi.org/10.1007/978-3-030-92511-6_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-92511-6_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92510-9

  • Online ISBN: 978-3-030-92511-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation