Multiplexing Packets with Arbitrary Deadlines in Bounded Buffers
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.
KeywordsCompetitive Ratio Online Algorithm Deterministic Algorithm Outgoing Link Transmission Phase
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- 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.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
- 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.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.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
- 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.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.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