Multiplexing Packets with Arbitrary Deadlines in Bounded Buffers

  • Yossi Azar
  • Nir Levy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4059)


We study the online problem of multiplexing packets with arbitrary deadlines in bounded multi-buffer switch. In this model, a switch consists of m input buffers each with bounded capacity B and one output port. Each arriving packet is associated with a value and a deadline that specifies the time limit till the packet can be transmitted. At each time step the switch can select any non-empty buffer and transmit one packet from that buffer. In the preemptive model, stored packets may be preempted from their buffers due to lack of buffer space or discarded due to the violation of the deadline constraints. If preemption is not allowed, every packet accepted and stored in the buffer must be transmitted before its deadline has expired. The goal is to maximize the benefit of the packets transmitted by their deadlines. To date, most models for packets with deadlines assumed a single buffer. To the best of our knowledge this is the first time a bounded multi-buffer switch is used with arbitrary deadline constraints.

Our main result is a 9.82-competitive deterministic algorithm for packets with arbitrary values and deadlines. Note that the greedy algorithm is not competitive. For the non-preemptive model we present a 2-competitive deterministic algorithm for the unit value packets. For arbitrary values we present a randomized algorithm whose competitiveness is logarithmic in the ratio between the largest and the smallest value of the packets in the sequence.


Competitive Ratio Online Algorithm Deterministic Algorithm Outgoing Link Transmission Phase 
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.
    Albers, S., Schmidt, M.: On the performance of greedy algorithms in packet buffering. In: Proc. 36th ACM Symp. on Theory of Computing, pp. 35–44 (2004)Google Scholar
  2. 2.
    Andelman, N., Mansour, Y., Zhu, A.: Competitive queueing policies for QoS switches. In: Proc. 14th ACM-SIAM Symp. on Discrete Algorithms, pp. 761–770 (2003)Google Scholar
  3. 3.
    Azar, Y., Litichevskey, A.: Maximizing throughput in multi-queue switches. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 53–64. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Azar, Y., Richter, Y.: Management of multi-queue switches in QoS networks. In: Proc. 35th ACM Symp. on Theory of Computing, pp. 82–89 (2003)Google Scholar
  5. 5.
    Azar, Y., Richter, Y.: The zero-one principle for switching networks. In: Proc. 36th ACM Symp. on Theory of Computing, pp. 64–71 (2004)Google Scholar
  6. 6.
    Bartal, Y., Chin, F.Y.L., Chrobak, M., Fung, S.P.Y., Jawor, W., Lavi, R., Sgall, J., Tichý, T.: Online competitive algorithms for maximizing weighted throughput of unit jobs. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 187–198. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Chin, F.Y.L., Fung, S.P.Y.: Online scheduling for partial job values: Does timesharing or randomization help? Algorithmica 37, 149–164 (2003)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Chrobak, M., Jawor, W., Sgall, J., Tichy, T.: Improved online algorithms for buffer management in QoS switches. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 204–215. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    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
  10. 10.
    Kesselman, A., Lotker, Z., Mansour, Y., Patt-Shamir, B., Schieber, B., Sviri-denko, M.: Buffer overflow management in QoS switches. In: Proc. 33rd ACM Symp. on Theory of Computing, pp. 520–529 (2001)Google Scholar
  11. 11.
    Li, F., Sethuraman, J., Stein, C.: An optimal online algorithm for packet scheduling with agreeable deadlines. In: Proc. 16th Symp. on Discrete Algorithms (SODA), pp. 801–802 (2005)Google Scholar
  12. 12.
    Schmidt, M.: Packet buffering: Randomization beats deterministic algorithms. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 293–304. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yossi Azar
    • 1
  • Nir Levy
    • 1
  1. 1.School of Computer ScienceTel Aviv UniversityTel AvivIsrael

Personalised recommendations