2011
DOI: 10.1007/s12243-011-0246-y
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On the optimality of max–min fairness in resource allocation

Abstract: In this work, a basic resource allocation (RA) problem is considered, where a fixed capacity must be shared among a set of users. The RA task can be formulated as an optimization problem, with a set of simple constraints and an objective function to be minimized. A fundamental relation between the RA optimization problem and the notion of max-min fairness is established. A sufficient condition on the objective function that ensures the optimal solution is max-min fairness is provided. Notably, some important o… Show more

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Cited by 23 publications
(20 citation statements)
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“…We initially apply here RR scheduling to divide the resources equally among RUEs so that we can observe throughput gap between backhaul and access. In the case that the backhaul presents a capacity bottleneck (R r < R a ), the initially allocated resources using RR scheduling are redistributed among the RUEs using max-min fair scheduling which priorities RUEs with lower throughputs [43]. Otherwise, if backhaul is not a bottleneck (R r ≥ R a ), the resource allocation for the RUEs from RR scheduling is retained.…”
Section: Scheduling and Throughput Formulamentioning
confidence: 99%
“…We initially apply here RR scheduling to divide the resources equally among RUEs so that we can observe throughput gap between backhaul and access. In the case that the backhaul presents a capacity bottleneck (R r < R a ), the initially allocated resources using RR scheduling are redistributed among the RUEs using max-min fair scheduling which priorities RUEs with lower throughputs [43]. Otherwise, if backhaul is not a bottleneck (R r ≥ R a ), the resource allocation for the RUEs from RR scheduling is retained.…”
Section: Scheduling and Throughput Formulamentioning
confidence: 99%
“…The effect that different types of objective functions in NUM-based resource management have on fairness has been questioned in recent research. Collucia et al [2] identify and study a number of objective function families that can be used to achieve max-min fairness.…”
Section: Termmentioning
confidence: 99%
“…However, its computational complexity deems it unfit for real-time operation and precipitates the need for heuristic algorithms that follow the same intra-class fairness, interclass differentiation policy. URM maximises the total per-client utility, a logarithmic function of the allocated throughput, different for every class and mathematically bound to follow the defined policy and provide Max-Min fairness [2]. The heuristics however, provide sub-optimal solutions that are not guaranteed to perfectly adhere to the policy.…”
Section: Introductionmentioning
confidence: 99%
“…The proposed functional form also provides a network-wide tendency to max-min fairness among clients of the same class [6].…”
Section: Class-based Utility Functionsmentioning
confidence: 99%