Abstract
The following online problem arises in network devices, e.g., switches, with quality of service (QoS) guarantees. In each time step, an arbitrary number of packets arrive at a single buffer and only one packet can be transmitted. The differentiated service concept is implemented by attributing each packet with a non-negative value corresponding to its service level. The goal is to maximize the total value of transmitted packets. We consider two models of this problem, the FIFO and the bounded-delay model. In the FIFO model, the buffer can store a limited number of packets and the sequence of transmitted packets has to be a subsequence of the arriving packets. In this model, a buffer management algorithm can reject arriving packets and preempt buffered packets. In the bounded-delay model, the buffer has unbounded capacity, but each packet has a deadline and packets can only be transmitted before their deadlines. Here, a buffer management algorithm determines the packet to be sent in each time step. We study comparison-based buffer management algorithms, i.e., algorithms that make their decisions based solely on the relative order between packet values with no regard to the actual values. This kind of algorithm proves to be robust in the realm of QoS switches. Kesselman et al. (SIAM J Comput 33(3):563–583, 2004) present two deterministic comparison-based online algorithms, one for each model, which are 2-competitive. For a long time, it has been an open problem, whether a comparison-based online algorithm exists, in either model, with a competitive ratio below 2. In the FIFO model, we present a lower bound of \(1+1/\sqrt{2} \approx 1.707\) on the competitive ratio of any deterministic comparison-based algorithm and give an algorithm that matches this lower bound in the case of monotonic sequences, i.e., packets arrive in a non-decreasing order according to their values. In the bounded-delay model, we show that no deterministic comparison-based algorithm exists with a competitive ratio below 2. In the special s-uniform case, where the difference between the arrival time and deadline of any packet equals s, we present a randomized comparison-based algorithm that is 5 / 3-competitive.
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References
Aiello, W.A., Mansour, Y., Rajagopolan, S., Rosén, A.: Competitive queue policies for differentiated services. J. Algorithms 55(2), 113–141 (2005)
Andelman, N., Mansour, Y.: Competitive management of non-preemptive queues with multiple values. In: Proceedings of the 17th International Conference on Distributed Computing (DISC), pp. 166–180 (2003)
Andelman, N., Mansour, Y., Zhu, A.: Competitive queueing policies for QoS switches. In: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 761–770 (2003)
Andelman, N.: Randomized queue management for DiffServ. In: Proceedings of the 17th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 1–10 (2005)
Azar, Y., Cohen, I.R.: Serving in the dark should be done non-uniformly. In: Proceedings of the 42nd International Colloquium on Automata, Languages and Programming (ICALP), pp. 91–102 (2015)
Azar, Y., Cohen, I.R., Gamzu, I.: The loss of serving in the dark. In: Proceedings of the 45th ACM Symposium on Theory of Computing (STOC), pp. 951–960 (2013)
Azar, Y., Richter, Y.: The zero-one principle for switching networks. In: Proceedings of the 36th ACM Symposium on Theory of Computing (STOC), pp. 64–71 (2004)
Bansal, N., Fleischer, L., Kimbrel, T., Mahdian, M., Schieber, B., Sviridenko, M.: Further improvements in competitive guarantees for QoS buffering. In: Proceedings of the 31st International Colloquium on Automata, Languages and Programming (ICALP), pp. 196–207 (2004)
Bienkowski, M., Chrobak, M., Jeż, Ł.: Randomized algorithms for buffer management with 2-bounded delay. In: Proceedings of the 6th Workshop on Approximation and Online Algorithms (WAOA), pp. 92–104 (2008)
Bienkowski, M., Chrobak, M., Jeż, Ł.: Randomized competitive algorithms for online buffer management in the adaptive adversary model. Theor. Comput. Sci. 412(39), 5121–5131 (2011)
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. J. Discret. Algorithms 4(2), 255–276 (2006)
Chin, F.Y.L., Fung, S.P.Y.: Online scheduling for partial job values: does timesharing or randomization help? Algorithmica 37, 149–164 (2003)
Chrobak, M., Jawor, W., Sgall, J., Tichý, T.: Improved online algorithms for buffer management in QoS switches. ACM Trans. Algorithms 3(4), 50 (2007)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press, Cambridge (2009)
Englert, M., Westermann, M.: Lower and upper bounds on FIFO buffer management in QoS switches. Algorithmica 53(4), 523–548 (2009)
Englert, M., Westermann, M.: Considering suppressed packets improves buffer management in quality of service switches. SIAM J. Comput. 41(5), 1166–1192 (2012)
Goldwasser, M.H.: A survey of buffer management policies for packet switches. SIGACT News 41, 100–128 (2010)
Jeż, Ł., Li, F., Sethuraman, J., Stein, C.: Online scheduling of packets with agreeable deadlines. ACM Trans. Algorithms 9(1), 5 (2012)
Kesselman, A., Mansour, Y., van Stee, R.: Improved competitive guarantees for QoS buffering. Algorithmica 43(1–2), 97–111 (2005)
Kesselman, A., Lotker, Z., Mansour, Y., Patt-Shamir, B., Schieber, B., Sviridenko, M.: Buffer overflow management in QoS switches. SIAM J. Comput. 33(3), 563–583 (2004)
Li, F., Sethuraman, J., Stein, C.: An optimal online algorithm for packet scheduling with agreeable deadlines. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 801–802 (2005)
Li, F., Sethuraman, J., Stein, C.: Better online buffer management. In: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 199–208 (2007)
Paxson, V., Floyd, S.: Wide-area traffic: the failure of Poisson modeling. IEEE/ACM Trans. Netw. 3(3), 226–244 (1995)
Reingold, N., Westbrook, J., Sleator, D.D.: Randomized competitive algorithms for the list update problem. Algorithmica 11(1), 15–32 (1994)
Sleator, D., Tarjan, R.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985)
Veres, A., Boda, M.: The chaotic nature of TCP congestion control. In: Proceedings of the 19th Annual IEEE International Conference on Computer Communications (INFOCOM), pp. 1715–1723 (2000)
Zhu, A.: Analysis of queueing policies in QoS switches. J Algorithms 53(2), 137–168 (2004)
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Matthias Englert and Matthias Westermann’s work was supported by ERC Grant Agreement No. 307696. A preliminary version appeared in Proceedings of the 12th Latin American Theoretical Informatics Symposium (LATIN), pages 27–40, 2016.
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Al-Bawani, K., Englert, M. & Westermann, M. Comparison-Based Buffer Management in QoS Switches. Algorithmica 80, 1073–1092 (2018). https://doi.org/10.1007/s00453-017-0393-2
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DOI: https://doi.org/10.1007/s00453-017-0393-2