One to Rule Them All: A General Randomized Algorithm for Buffer Management with Bounded Delay

  • Łukasz Jeż
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)


We give a memoryless scale-invariant randomized algorithm Mix-R for buffer management with bounded delay that is e/(e − 1)-competitive against an adaptive adversary, together with better performance guarantees for many restricted variants, including the s-bounded instances. In particular, Mix-R attains the optimum competitive ratio of 4/3 on 2-bounded instances.

Both Mix-R and its analysis are applicable to a more general problem, called Item Collection, in which only the relative order between packets’ deadlines is known. Mix-R is the optimal memoryless randomized algorithm against adaptive adversary for that problem in a strong sense.

While some of the provided upper bounds were already known, in general, they were attained by several different algorithms.


Competitive Ratio Online Algorithm Deterministic Algorithm Packet Schedule Adversary Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Andelman, N., Mansour, Y., Zhu, A.: Competitive queueing policies for qos switches. In: Proc. of the 14th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 761–770 (2003)Google Scholar
  2. 2.
    Azar, Y.: Online packet switching. In: Persiano, G., Solis-Oba, R. (eds.) WAOA 2004. LNCS, vol. 3351, pp. 1–5. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Ben-David, S., Borodin, A., Karp, R.M., Tardos, G., Wigderson, A.: On the power of randomization in online algorithms. Algorithmica 11(1), 2–14 (1994); also appeared in Proc. of the 22nd STOC, pp. 379–386 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bienkowski, M., Chrobak, M., Dürr, C., Hurand, M., Jeż, A., Jeż, Ł., Stachowiak, G.: Collecting weighted items from a dynamic queue. In: Proc. of the 20th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 1126–1135 (2009)Google Scholar
  5. 5.
    Bienkowski, M., Chrobak, M., Jeż, Ł.: Randomized algorithms for buffer management with 2-bounded delay. In: Bampis, E., Skutella, M. (eds.) WAOA 2008. LNCS, vol. 5426, pp. 92–104. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)zbMATHGoogle Scholar
  7. 7.
    Chin, F.Y.L., Chrobak, M., Fung, S.P.Y., Jawor, W., Sgall, J., Tichý, T.: Online competitive algorithms for maximizing weighted throughput of unit jobs. Journal of Discrete Algorithms 4, 255–276 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Chin, F.Y.L., Fung, S.P.Y.: Online scheduling for partial job values: Does timesharing or randomization help? Algorithmica 37, 149–164 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Chrobak, M., Jawor, W., Sgall, J., Tichý, T.: Improved online algorithms for buffer management in QoS switches. ACM Transactions on Algorithms 3(4) (2007); also appeared in Proc. of the 12th ESA, pp. 204–215 (2004)Google Scholar
  10. 10.
    Englert, M., Westermann, M.: Considering suppressed packets improves buffer management in QoS switches. In: Proc. of the 18th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 209–218 (2007)Google Scholar
  11. 11.
    Epstein, L., van Stee, R.: Buffer management problems. Sigact News 35, 58–66 (2004)Google Scholar
  12. 12.
    Goldwasser, M.: A survey of buffer management policies for packet switches. SIGACT News 41(1), 100–128 (2010)CrossRefGoogle Scholar
  13. 13.
    Hajek, B.: On the competitiveness of online scheduling of unit-length packets with hard deadlines in slotted time. In: Conference in Information Sciences and Systems, pp. 434–438 (2001)Google Scholar
  14. 14.
    Jeż, Ł.: Randomised buffer management with bounded delay against adaptive adversary. CoRR abs/0907.2050 (2009)Google Scholar
  15. 15.
    Jeż, Ł.: Randomized algorithm for agreeable deadlines packet scheduling. In: Proc. of the 27th Symp. on Theoretical Aspects of Computer Science (STACS), pp. 489–500 (2010)Google Scholar
  16. 16.
    Kesselman, A., Lotker, Z., Mansour, Y., Patt-Shamir, B., Schieber, B., Sviridenko, M.: Buffer overflow management in QoS switches. SIAM Journal on Computing 33(3), 563–583 (2004); also appeared in Proc.of the 33rd STOC, pp 520–529, (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Li, F., Sethuraman, J., Stein, C.: An optimal online algorithm for packet scheduling with agreeable deadlines. In: Proc. of the 16th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 801–802 (2005)Google Scholar
  18. 18.
    Zhu, A.: Analysis of queueing policies in QoS switches. Journal of Algorithms 53(2), 137–168 (2004)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Łukasz Jeż
    • 1
  1. 1.Institute of Computer ScienceUniversity of WrocławWrocławPoland

Personalised recommendations