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zbMATH Open
Article . 2014
Data sources: zbMATH Open
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Price-based protocols for fair resource allocation

Convergence time analysis and extension to leontief utilities
Authors: Goel, Ashish; Nazerzadeh, Hamid;

Price-based protocols for fair resource allocation

Abstract

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 nc MAX a MAX / c MIN a MIN ), where n is the number of agents in the network, c MAX and c MIN are the maximum and minimum capacity of the links, and a max , a min 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.

Related Organizations
Keywords

fairness, decentralized algorithms, Approximation algorithms, Resource and cost allocation (including fair division, apportionment, etc.), shadow prices, network protocols, Deterministic network models in operations research, majorization, Network protocols, Leontief utilities

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average