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On the Aloha Throughput-Fairness Tradeoff
Journal article   Open access   Peer reviewed

On the Aloha Throughput-Fairness Tradeoff

Nan Xie and Steven Weber
IEEE transactions on information theory, v 63(9), pp 6085-6112
Sep 2017
DOI: https://doi.org/10.1109/TIT.2017.2705029
Featured in Collection :   UN Sustainable Development Goals @ Drexel
url
http://arxiv.org/abs/1605.01557View
Submitted Open Open Access (License Unspecified)

Abstract

Aloha Jain’s fairness Media Access Protocol Multiple access network utility maximization (NUM) Optimal control proportional fairness Queueing analysis random access Resource management stability Stability analysis Throughput throughput-fairness tradeoff α-fair (isoelastic) utility function
A well-known inner bound of the stability region of the finite-user slotted Aloha protocol (with fixed contention probabilities) on the collision channel with n users assumes worst case service rates (all user queues non-empty). Using this inner bound as a feasible set of achievable rates, a characterization of the throughput-fairness tradeoff over this set is obtained, where the throughput is defined as the sum of the individual user rates, and two definitions of fairness are considered: the Jain-Chiu-Hawe function and the sum-user α-fair (isoelastic) utility function. This characterization is obtained using both an equality constraint and an inequality constraint on the throughput, and properties of the optimal controls, the optimal rates, and the maximum fairness as a function of the target throughput are established. A key structural property underpinning all theorems is the observation that the vector of contention probabilities that extremizes both fairness objectives has its nonzero components taking at most two distinct values.

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7 citations in Web of Science
8 citations in Scopus

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Web of Science research areas
Computer Science, Information Systems
Computer Science, Theory & Methods
Engineering, Electrical & Electronic
Mathematics, Applied
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