Subscribe
Issue No.04 - April (2008 vol.19)
pp: 462-475
ABSTRACT
Fairness in traffic management can improve the isolation between traffic streams, offer a more predictable performance, eliminate transient bottlenecks, mitigate the effect of certain kinds of denial-of-service attacks, and serve as a critical component of a quality-of-service strategy to achieve certain guaranteed services such as delay bounds and minimum bandwidths. In this paper, we choose a popular notion of fairness called max-min fairness and provide a rigorous definition in the context of input-queued switches. We show that being fair at the output ports alone, or at the input ports alone, or even at both input and output ports, does not actually achieve overall max-min fair allocation of bandwidth in a switch. Instead, we propose a new algorithm that computes the exact max-min fair allocation of rates for the flows through the switch. In addition to proving the correctness of the algorithm, we show that it can be implemented in a distributed fashion at the input and output ports to determine the max-min fair rates. We further propose a practical scheduling strategy based on our algorithm and present simulation results, using both real traffic traces as well synthetic traffic, to evaluate the fairness of a variety of popular scheduling algorithms for input-queued switches. The results show that our scheduling strategy achieves better fairness than other known algorithms for input-queued switches and, in addition, achieves throughput performance very close to that of the best schedulers.
INDEX TERMS
Routers, input-queued switches, fairness, quality-of-service
CITATION
Madhusudan Hosaagrahara, Harish Sethu, "Max-Min Fair Scheduling in Input-Queued Switches", IEEE Transactions on Parallel & Distributed Systems, vol.19, no. 4, pp. 462-475, April 2008, doi:10.1109/TPDS.2007.70746
REFERENCES
 [1] S. Keshav, An Engineering Approach to Computer Networking: ATM Networks, the Internet, and the Telephone Network, first ed. Addison-Wesley, May 1997. [2] T. Bonald and L. Massouli, “Impact of Fairness on Internet Performance,” Proc. ACM SIGMETRICS '01, vol. 29, no. 1, pp. 82-91, June 2001. [3] D. Cohen and K. Narayanaswamy, “A Fair Service Approach to Defenses against Packet Flooding Attacks,” white paper, http://www.cs3-inc.comddos.html, June 2006. [4] J. Xu and W. Lee, “Sustaining Availability of Web Services under Distributed Denial of Service Attacks,” IEEE Trans. Computers, vol. 52, no. 2, pp. 195-208, Feb. 2003. [5] D.K.Y. Yau, J.C.S. Lui, F. Liang, and Y. Yam, “Defending against Distributed Denial of Service Attacks with Max-Min Fair Server-Centric Router Throttles,” IEEE/ACM Trans. Networking, vol. 13, no. 1, pp. 29-42, Feb. 2005. [6] F. Kelly, “Charging and Rate Control for Elastic Traffic,” European Trans. Telecomm., vol. 8, no. 1, pp. 33-37, 1997. [7] Z. Cao and E.W. Zegura, “Utility Max-Min: An Application-Oriented Bandwidth Allocation Scheme,” Proc. IEEE INFOCOM '99, vol. 2, pp. 793-801, Mar. 1999. [8] D. Bertsekas and R. Gallager, Data Networks, second ed. Prentice Hall, 1992. [9] B. Vandalore, S. Fahmy, R. Jain, R. Goyal, and M. Goyal, “General Weighted Fairness and Its Support in Explicit Rate Switch Algorithms,” Computer Comm., vol. 23, no. 2, pp. 149-161, Jan. 2000. [10] D. Liu, N. Ansari, and E. Hou, “Fairness Criterion for Allocating Resources in Input Queued Switches,” IEE Electronic Letters, vol. 37, no. 19, pp. 1205-1206, Sept. 2001. [11] A.K. Parekh and R.G. Gallager, “A Generalized Processor Sharing Approach to Flow Control in Integrated Services Networks: The Single-Node Case,” IEEE/ACM Trans. Networking, vol. 1, no. 3, pp.344-357, June 1993. [12] D.C. Stephens, J.C.R. Bennett, and H. Zhang, “Implementing Scheduling Algorithms in High-Speed Networks,” IEEE J. Selected Areas in Comm., vol. 17, no. 6, pp. 1145-1158, June 1999. [13] Cisco Systems Inc., Cisco IOS Software Release 12.0(5)T, http://www.cisco.com/univercd/cc/td/doc/ product/software/ios% 120/120newft/120t/ 120t5cbwfq.pdf, 1999. [14] J.M. Kleinberg, E. Tardos, and Y. Rabani, “Fairness in Routing and Load Balancing,” Proc. 40th Ann. Symp. Foundations of Computer Science (FOCS '99), pp. 568-578, 1999. [15] L. Tassiulas and S. Sarkar, “Maxmin Fair Scheduling in Wireless Networks,” Proc. IEEE INFOCOM '02, vol. 2, pp. 763-772, June 2002. [16] S. Sarkar and K.N. Sivarajan, “Fairness in Wireless Mobile Networks,” IEEE Trans. Information Theory, vol. 48, no. 8, pp.2412-2426, Aug. 2002. [17] M. Pióro, G. Fodor, P. Nilsson, and E. Kubilinskas, “On Efficient Max-Min Fair Routing Algorithms,” Proc. Eighth IEEE Int'l Symp. Computers and Comm. (ISCC '03), p. 365, 2003. [18] A. Kam and K.-Y. Siu, “Linear Complexity Algorithms for QoS Support in Input-Queued Switches with No Speedup,” IEEE J.Selected Areas in Comm., vol. 17, no. 6, pp. 1040-1056, June 1999. [19] X. Zhang and L. Bhuyan, “Deficit Round-Robin Scheduling for Input-Queued Switches,” IEEE J. Selected Areas in Comm., vol. 21, no. 4, pp. 584-594, May 2003. [20] Y. Tamir and G.L. Frazier, “High-Performance Multi-Queue Buffers for VLSI Communication Switches,” Proc. 15th Ann. Int'l Symp. Computer Architecture (ISCA '88), pp. 343-354, 1988. [21] M. Shreedhar and G. Varghese, “Efficient Fair Queueing Using Deficit Round-Robin,” IEEE/ACM Trans. Networking, vol. 4, no. 3, pp. 275-285, June 1996. [22] S.-T. Chuang, A. Goel, N. McKeown, and B. Prabhakar, “Matching Output Queueing with a Combined Input/Output-Queued Switch,” IEEE J. Selected in Areas Comm., vol. 17, no. 6, pp. 1030-1039, June 1999. [23] J.E. Hopcroft and R.M. Karp, “An $n^{{{5}\over{2}}}$ Algorithm for Maximum Matchings in Bipartite Graphs,” SIAM J. Computing, vol. 2, no. 4, p.225, Dec. 1973. [24] I. Keslassy, R. Zhang-Shen, and N. McKeown, “Maximum Size Matching Is Unstable for Any Packet Switch,” IEEE Comm. Letters, vol. 7, no. 10, pp. 496-498, Oct. 2003. [25] N. McKeown, A. Mekkittikul, V. Anantharam, and J. Walrand, “Achieving 100% Throughput in an Input-Queued Switch,” IEEE Trans. Comm., vol. 47, no. 8, pp. 1260-1267, Aug. 1999. [26] A. Charny, P. Krishna, N. Patel, and R. Simcoe, “Algorithms for Providing Bandwidth and Delay Guarantees in Input-Buffered Crossbars with Speedup,” Proc. Sixth Int'l Workshop Quality of Service (IWQoS '98), pp. 235-244, May 1998. [27] E. Leonardi, F. Neri, and B. Yener, “Algorithms for Virtual Output Queued Switching,” Proc. IEEE GLOBECOM '99, vol. 2, pp. 1203-1210, Dec. 1999. [28] T.E. Anderson, S.S. Owicki, J.B. Saxe, and C.P. Thacker, “High-Speed Switch Scheduling for Local-Area Networks,” ACM Trans. Computer Systems, vol. 11, no. 4, pp. 319-352, Nov. 1993. [29] N. McKeown, “$i{\rm SLIP}$ : A Scheduling Algorithm for Input-Queued Switches,” IEEE/ACM Trans. Networking, vol. 7, no. 2, pp. 188-201, Apr. 1999. [30] R. Sivaram, C.B. Stunkel, and D.K. Panda, “HIPIQS: A High-Performance Switch Architecture Using Input Queuing,” IEEE Trans. Parallel and Distributed Systems, vol. 13, no. 3, pp. 275-289, Mar. 2002. [31] D.C. Stephens and H. Zhang, “Implementing Distributed Packet Fair Queueing in a Scalable Switch Architecture,” Proc. IEEE INFOCOM '98, pp. 282-290, Apr. 1998. [32] D.C. Stephens, “Implementing Distributed Packet Fair Queueing in a Scalable Switch Architecture,” Master's thesis, Carnegie Mellon Univ., 1998. [33] S. Li, J.-G. Chen, and N. Ansari, “Fair Queueing for Input-Buffered Switches with Back Pressure,” Proc. First IEEE Int'l Conf. ATM (ICATM '98), pp. 252-259, June 1998. [34] N. Ni and L.N. Bhuyan, “Fair Scheduling in Internet Routers,” IEEE Trans. Computers, vol. 51, no. 6, pp. 686-701, June 2002. [35] D. Cavendish, M. Goudreau, and A. Ishii, “On the Fairness of Scheduling Algorithms for Input-Queued Switches,” Proc. 17th Int'l Teletraffic Congress, vol. 4, pp. 829-841, Dec. 2001. [36] D. Cavendish, M. Lajolo, and H. Liu, “On the Evaluation of Fairness for Input Queued Switches,” Proc. IEEE Int'l Conf. Comm. (ICC '02), vol. 2, pp. 996-1000, May 2002. [37] N. Kumar, R. Pan, and D. Shah, “Fair Scheduling in Input-Queued Switches under Inadmissible Traffic,” Proc. IEEE GLOBECOM '04, vol. 3, no. 29, pp. 1713-1717, Dec. 2004. [38] R. Yim, N. Devroye, V. Tarokh, and H.T. Kung, “Achieving Fairness in Generalized Processor Sharing for Network Switches,” Proc. 22nd Biennial Symp. Comm., pp. 185-187, 2004. [39] NLANR, Passive Measurement and Analysis, http://pma.nlanr.netPMA/, June 2006. [40] COS-1069192584-1.tsh.gz, taken from the NLANR Colorado State Univ. OC3c Tap on 18 Nov. 2003, this trace may be requested from the PMA HPSS repository, http://pma.nlanr.net/PMA/SitesCOS.html, June 2006. [41] S.S. Kanhere and H. Sethu, “Anchored Opportunity Queueing: A Low-Latency Scheduler for Fair Arbitration among Virtual Channels,” J. Parallel and Distributed Processing, vol. 63, no. 12, pp. 1288-1299, 2003.