An information-theoretic characterization of weighted α-proportional fairness in network resource allocation

Uchida, Masato; Kurose, Jim

doi:10.1016/j.ins.2011.05.001

Cited by 7 publications

(7 citation statements)

References 35 publications

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“…The formulation is similar to that explored by Wildman et al and makes use of an α ‐proportional fairness utility function parametrized by α . The network utility maximization (NUM) problem can be formulated as

\max_{boldM \in scriptM} \sum_{l = 1}^{N_{U}} U_{α} false(R_{u_{l}} false(boldM false) false),

where

U_{α} false(R_{u_{l}} false(boldM false) false) = ({, \begin{matrix} \frac{{(R_{u_{l}} (M))}^{(1 - α)}}{1 - α} & , α \geq 0, α \neq 1, \\ normall normalo normalg (R_{u_{l}} (M)) & , α = 1, \end{matrix})

is the α ‐proportional fairness utility function,

R_{u_{l}} false(boldM false) = \sum_{k = 1}^{N_{B}} \frac{r_{u_{l}}^{S h a} m_{k l}}{1 + \sum_{\underset{q \neq k}{q=1}}^{N_{B}} m_{k q}}

is the sum DL rate for user u l , and

r_{u_{l}}^{S h a}

is the Shannon capacity, the theoretical maximum achievable rate ,

r_{u_{l}}^{S h a} = normal l o

…”

Section: Related Workmentioning

confidence: 99%

Near‐optimal user assignment in LTE mobile networks with evolutionary computing

Arco-Vega

Cuadra

Portilla-Figueras

et al. 2016

Trans. Emerging Tel. Tech.

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This paper tackles the problem of users assignment to evolved NodeBs in long‐term evolution mobile networks. We propose a model that aims at assigning users by minimizing a function called download time of the complete system, defined as the minimum time required for all the users in the system to complete their downloads. This strategy helps the network use its resources in a more balanced way, by assigning users from cells (which otherwise would be overloaded when using a simple signal‐to‐interference‐plus‐noise ratio‐based approach) to others with less load. The user‐cell association problem is, in general, a combinatorial NP hard problem. Although other approaches indirectly tackle this complexity by transforming the problem into another whose optimal solution is less difficult (but still with very high computational cost), we tackle directly our download time of the complete system minimization problem by finding an approximate solution provided by a specific implementation of an evolutionary algorithm, which is based on a long‐term evolution domain‐specific initial population along with fully tailored operators adapted to this assignment problem. A variety of experiments in different realistic scenarios point out that the proposed method outperforms the conventional signal‐to‐interference‐plus‐noise ratio‐based and load balancing approaches, specially in urban and dense urban environments (where the assignment is more critical in terms of capacity). We have also tested our approach in simple scenarios that mimic heterogeneous networks and ultra‐dense networks in which the number of users is similar to that of nodes, proving its beneficial properties. Our method is aimed at the design/dimensioning stage and not to the operation stage, and in this sense, it is an off‐line algorithm that could be useful to make better decisions on cost‐effective network dimensioning and upgrading.

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\max_{boldM \in scriptM} \sum_{l = 1}^{N_{U}} U_{α} false(R_{u_{l}} false(boldM false) false),

where

U_{α} false(R_{u_{l}} false(boldM false) false) = ({, \begin{matrix} \frac{{(R_{u_{l}} (M))}^{(1 - α)}}{1 - α} & , α \geq 0, α \neq 1, \\ normall normalo normalg (R_{u_{l}} (M)) & , α = 1, \end{matrix})

is the α ‐proportional fairness utility function,

R_{u_{l}} false(boldM false) = \sum_{k = 1}^{N_{B}} \frac{r_{u_{l}}^{S h a} m_{k l}}{1 + \sum_{\underset{q \neq k}{q=1}}^{N_{B}} m_{k q}}

is the sum DL rate for user u l , and

r_{u_{l}}^{S h a}

is the Shannon capacity, the theoretical maximum achievable rate ,

r_{u_{l}}^{S h a} = normal l o

…”

Section: Related Workmentioning

confidence: 99%

Near‐optimal user assignment in LTE mobile networks with evolutionary computing

Arco-Vega

Cuadra

Portilla-Figueras

et al. 2016

Trans. Emerging Tel. Tech.

View full text Add to dashboard Cite

show abstract

“…We now consider downlink delay minimization [19], which falls under a broader class of network utility maximization problems, particularly those that employ α-proportional fairness measures [17], [20]. When α = 2, each MU's rate is assigned a utility equal to the negation of its reciprocal: −1/R p (f ).…”

Section: Downlink Delay Minimizationmentioning

confidence: 99%

Delay minimizing user association in cellular networks via hierarchically well-separated trees

Wildman

Osmanlıoğlu

Weber

et al. 2015

2015 IEEE International Conference on Communications (ICC)

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Abstract-We study downlink delay minimization within the context of cellular user association policies that map mobile users to base stations. We note the delay minimum user association problem fits within a broader class of network utility maximization and can be posed as a non-convex quadratic program. This non-convexity motivates a split quadratic objective function that captures the original problem's inherent tradeoff: association with a station that provides the highest signal-tointerference-plus-noise ratio (SINR) vs. a station that is least congested. We find the split-term formulation is amenable to linearization by embedding the base stations in a hierarchically well-separated tree (HST), which offers a linear approximation with constant distortion. We provide a numerical comparison of several problem formulations and find that with appropriate optimization parameter selection, the quadratic reformulation produces association policies with sum delays that are close to that of the original network utility maximization. We also comment on the more difficult problem when idle base stations (those without associated users) are deactivated.

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“…We will consider a diverse family of NUM problems derived from α-proportional fairness measures [19], [22], defined as:…”

Section: A Single User Association (Sua)mentioning

confidence: 99%

A primal-dual approach to delay minimizing user association in cellular networks

Wildman

Osmanlıoğlu

Weber

et al. 2015

2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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We study network utility maximization (NUM) within the context of cellular single user association (SUA) policies that map each mobile user (MU) to a single base station (BS) and make use of the generalized α-proportional fairness utility measure across downlink rates. Finding an exact solution to many such centralized user association problem is known to be NP-hard, so we are motivated to consider the integer relaxation of the SUA NUM problem. On this front, we provide separate characterizations of i) the fairness measures under which the SUA NUM problem integrality gap is exactly 1, and ii) the fairness measures yielding non-convex SUA NUM problem formulations. Next, we analyze the fairness measure corresponding to delay minimization and find a more natural linearization of the non-convex minimum delay SUA problem compared to our related previous work. We propose and construct a primal-dual algorithm to approximate the linearized minimum delay SUA problem. Our primal-dual algorithm is shown to achieve smaller performance gaps and runtimes over i) an intuitive baseline rounding algorithm applied to the linearized min delay SUA problem, as well as ii) two greedy heuristics that emphasize associations with minimal MU-BS distances and maximal downlink SINR ratios, respectively.

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An information-theoretic characterization of weighted α-proportional fairness in network resource allocation

Cited by 7 publications

References 35 publications

Near‐optimal user assignment in LTE mobile networks with evolutionary computing

Near‐optimal user assignment in LTE mobile networks with evolutionary computing

Delay minimizing user association in cellular networks via hierarchically well-separated trees

A primal-dual approach to delay minimizing user association in cellular networks

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