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 vb offiine, where V 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+~ U/e)-competit ive algorithm, for any e, 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 ~(log 1+~ U/e) 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(log2nlogU) competitive algorithm. We also show that the dependence on U is necessary by presenting an ~ ( ~ ) lower bound. The upper and lower bounds presented in [4] for online maximization of throughput become invalid if we *Depar tment of Computer Science, University of Southern California, Los Angeles CA 90089-0781. Emaih agoel@cs.usc.edu. t Depar tment of Computer Science, Stanford University CA 94305. Emaih awm@cs.stanford.edu. $Supported by ARO Grants DAAG55-98-1-0170 and ONR Grant N00014-98-1-0589. Depar tment of Computer Science, Stanford University CA 94305. Emaih plotkin@cs.stanford.edu. Permission to make digital or hard copies of all or par(of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the thll citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. STOC 2000 Portland Oregon USA Copyright ACM 2000 1-58113-184-4/00/5...$5.00 are allowed to assign weights. We prove an ~(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.