Combining fairness with throughput: online routing with multiple objectives

This paper presents online algorithms for routing and bandwidth allocation which simultaneously approximate fair and max-throughput solutions. In fact, the algorithms solve a more difficult problem: for any bandwidth b , the number of sessions that get bandwidth b in the online algorithm is not smaller than the number of sessions receiving γb offline, where γ is the competitive ratio. This problem is provably harder than the problem of maximizing throughput (e.g., [4]) or the problem of maximizing the bandwidth assigned to the most starved session (e.g., [3]). For the case where the algorithm assigns bandwidths, we present an O (log 2 n log 1+ ε U / ε )-competitive algorithm, for any ε , where U is the minimum (over all choices of routes) of the maximum number of sessions routed along any single link. We also show an Ω (log 1+ ε U / ε ) lower bound in this model. For a more practically interesting model where the algorithm assigns routes and weights , and where these weights are used to drive the Weighted Fair Queuing policy in the routers, we present an O (log 2 n log U )-competitive algorithm. We also show that the dependence on U is necessary by presenting an Ω ( log U ) lower bound. Previous upper and lower bounds for online maximization of throughput become invalid if we are allowed to assign weights. We prove an Ω (log n ) lower bound for this model and present an O (log n log log n )-competitive online algorithm. We present preliminary simulation results which show that our algorithm is effective in attaining high throughput without significantly sacrificing fairness. References REFERENCES 1 Y. Afek Y. Mansour Z. Ostfeld Convergence complexity of optimistic rate based flow control algorithms Proceedings of the 28th ACM Symposium on Theory of Computing 1996 p. 89–98 2 Y. Afek Y. Mansour Z. Ostfeld Phantom: A simple and effective flow control scheme ACM SIGCOMM 1996 p. 169–182 3 J. Aspnes Y. Azar A. Fiat S. Plotkin O. Waarts On-line load balancing with applications to machine scheduling and virtual circuit routing 25th ACM Symposium on Theory of Computing 1993 p. 623–31 4 B. Awerbuch Y. Azar S. Plotkin Throughput competitive online routing 34th IEEE Symposium on Foundations of Computer Science 1993 p. 32–40 5 B. Awerbuch Y. Shavitt Converging to approximated max–min flow fairness in logarithmic time Proceedings of the 17th IEEE Infocom Conference 1998 p. 1350–57 6 Y. Bartal J. Byers D. Raz Global optimization using local information with applications to flow control 38th Annual Symposium on Foundations of Computer Science 1997 p. 303–312 7 Y. Bartal M. Farach-Colton M. Andrews L. Zhang Fast fair and frugal bandwith allocation in atm networks Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms 1999 p. 92–101 8 D. Bertsekas R. Gallager Data Networks 1992 Prentice Hall New York 9 A. Demers S. Keshav S. Shenker Analysis and simulation of a fair queueing algorithm Internetworking: Res. Exper. 1 1990 3 26 10 A. Kamath O. Palmon S. Plotkin Routing and admission control in general topology networks with poisson arrivals 7th ACM-SIAM Symposium on Discrete Algorithms 1996 p. 269–278 11 J. Kleinberg Y. Rabani E. Tardos Fairness in routing and load balancing Proceedings of the 35th Annual Symposium on Foundations of Computer Science 1999 12 N. Megiddo Optimal flows in networks with sources and sinks Math Programming 1974 13 A.K. Parekh R.G. Gallager A generalized processor sharing approach to flow control in integrated services networks—The single node case IEEE/ACM Trans. Networking 1 1993 344 357