Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Understanding TCP vegas: a duality model
Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Using approximate majorization to characterize protocol fairness
Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Fairness in routing and load balancing
Journal of Computer and System Sciences - Special issue on Internet algorithms
Combining fairness with throughout: online routing with multiple objectives
Journal of Computer and System Sciences - Special issue on Internet algorithms
Global Optimization Using Local Information with Applications to Flow Control
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Fairness measures for resource allocation
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
All-norm approximation algorithms
Journal of Algorithms
Approximate majorization and fair online load balancing
ACM Transactions on Algorithms (TALG)
Leontief economies encode nonzero sum two-player games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Pricing for fairness: distributed resource allocation for multiple objectives
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Improved Bounds for Online Routing and Packing Via a Primal-Dual Approach
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Exchange market equilibria with leontief’s utility: freedom of pricing leads to rationality
WINE'05 Proceedings of the First international conference on Internet and Network Economics
Market equilibrium for CES exchange economies: existence, multiplicity, and computation
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Bandwidth allocation in networks: a single dual update subroutine for multiple objectives
CAAN'04 Proceedings of the First international conference on Combinatorial and Algorithmic Aspects of Networking
Hi-index | 0.00 |
We analyze several distributed, continuous time protocols for a fair allocation of bandwidths to flows in a network (or resources to agents). Our protocols converge to an allocation that is a logarithmic approximation, simultaneously, to all canonical social welfare functions (i.e., functions that are symmetric, concave, and nondecreasing). These protocols can be started in an arbitrary state. Although a similar protocol was known before, it only applied to the simple bandwidth allocation problem, and its stability and convergence time were not understood. In contrast, our protocols also apply to the more general case of Leontief utilities, where each user may place a different requirement on each resource. Furthermore, we prove that our protocols converge in polynomial time. The best convergence time we prove is O (n log ncMAX aMAX/cMINaMIN), where n is the number of agents in the network, cMAX and cMIN are the maximum and minimum capacity of the links, and amax, amin are respectively the largest and smallest Leontief coefficients. This time is achieved by a simple Multiplicative Increase, Multiplicative Decrease (MIMD) protocol that had not been studied before in this setting. We also identify combinatorial properties of these protocols that may be useful in proving stronger convergence bounds. The final allocations by our protocols are supported by usage-sensitive dual prices that are fair in the sense that they shield light users of a resource from the impact of heavy users. Thus, our protocols can also be thought of as efficient distributed schemes for computing fair prices.