Proportional Fairness Research Articles

A Multidimensional System of Proportional Representation

ABSTRACT In a representative deliberative democracy, a subset of the population—a committee—is selected to enter into deliberations as well as to make decisions on its behalf. In order to make a system of proportional representation fair to individual voters, the deliberations and decisions of the committee should be as close to deliberations and decisions in the ideal direct democracy where all are able to participate. The Chamberlin-Courant system claims to achieve this with its committee selection rule and voting weight distribution among committee members. After offering a novel streamlined presentation of the Chamberlin-Courant system, I argue that it in fact does not guarantee fairness to the individual voter because it does not take sufficient account of the fact that the satisfactoriness of a representative for an individual may vary per issue. I then propose an alternative—the multidimensional system—that is able to do exactly this. I then connect formal political theory with statistics on the use of voting guides to further motivate the proposed system and show that it is feasible to implement.

Dynamic priority-based bandwidth allocation scheme for machine type communications

The burgeoning realm of Machine Type Communications (MTC) has ushered in a paradigm shift in wireless communication, necessitating innovative strategies to efficiently manage diverse application requirements. This paper presents a pioneering Dynamic Priority-based Bandwidth Allocation (DPBA) scheme tailored specifically for MTC scenarios, encompassing both MTC and Human Type Communications (HTC) coexistence. DPBA employs an adaptive framework addressing dynamic MTC traffic, optimizing resource use while meeting latency constraints and sporadic data patterns. By dynamically prioritizing MTC applications based on requirements, the scheme allocates bandwidth for reliable data delivery. DPBA extends to MTC and HTC coexistence, managing diverse quality demands. This underlines its versatility and capacity to serve distinct needs in a shared spectrum. To substantiate its performance, the DPBA scheme is rigorously evaluated against a spectrum of related allocation methods like Proportional Fairness (PF), Static Priority Scheduling (SPS), and the Machine Learning-based Scheme (MLS), DPBA excels in simulations, minimizing packet loss, latency, enhancing throughput and ensuring fairness, surpassing benchmarks. This research underscores the critical importance of tailored bandwidth allocation strategies in advancing MTC and HTC coexistent environments. With its adaptability, efficiency, and remarkable performance, the DPBA scheme emerges as a cornerstone in the trajectory of wireless communication networks, catering to the distinct requirements of both MTC and HTC applications.

A Unified Optimization Model with Proportional Fairness and Robustness of Fuzzy Multi-Objective Aggregate Production Planning in Supply Chain under Uncertain Environments

A Unified Optimization Model with Proportional Fairness and Robustness of Fuzzy Multi-Objective Aggregate Production Planning in Supply Chain under Uncertain Environments

Incentivizing Proportional Fairness for Multi-Task Allocation in Crowdsensing

Incentivizing Proportional Fairness for Multi-Task Allocation in Crowdsensing

Proportional Representation in Metric Spaces and Low-Distortion Committee Selection

We introduce a novel definition for a small set R of k points being "representative" of a larger set in a metric space. Given a set V (e.g., documents or voters) to represent, and a set C of possible representatives, our criterion requires that for any subset S comprising a theta fraction of V, the average distance of S to their best theta*k points in R should not be more than a factor gamma compared to their average distance to the best theta*k points among all of C. This definition is a strengthening of proportional fairness and core fairness, but - different from those notions - requires that large cohesive clusters be represented proportionally to their size. Since there are instances for which - unless gamma is polynomially large - no solutions exist, we study this notion in a resource augmentation framework, implicitly stating the constraints for a set R of size k as though its size were only k/alpha, for alpha > 1. Furthermore, motivated by the application to elections, we mostly focus on the "ordinal" model, where the algorithm does not learn the actual distances; instead, it learns only for each point v in V and each candidate pairs c, c' which of c, c' is closer to v. Our main result is that the Expanding Approvals Rule (EAR) of Aziz and Lee is (alpha, gamma) representative with gamma

Proportional Fairness for Long-Term Evolution-Licensed Assisted Access (LTE-LAA) with Wi-Fi Coexistence in Unlicensed Spectrum

Long-Term Evaluation-Licensed Assisted Access (LTE-LAA) has good potential for fair coexistence with Wi-Fi in an unlicensed spectrum. Though the LTE-LAA utilizes the same listen before-talk technique as the distributed coordination function in IEEE 802.11, it utilizes completely different parameters and transmission durations. For this reason, a fair coexistence between LTE-LAA and Wi-Fi leaves an open question on how the LTE-LAA network should choose its parameters. To tackle this issue, an analytical framework considering the effects of varying important parameters, which are the different initial back-off window sizes, the numbers of sensing durations, the maximum back-off stages, the number of retransmissions and the transmission opportunities for LTE-LAA and Wi-Fi nodes on their performances has been developed. The node and network airtime performances are evaluated by using the current standard parameters setting to see how this setting affects the node and network airtime performances. From there, optimal settings of the initial backoff window size and number of sensing durations are applied by using the obtained node airtime equation that is derived from the Markov renewal process and evaluated as functions of system parameters. The optimum initial backoff window size and number of sensing durations of LTE-LAA are evaluated and verified by the calculation and simulation using MATLAB software. The analysis shows that LTE-LAA maintained unfair coexistence with Wi-Fi by using the current standard parameter setting as its initial back off window size or sensing duration. But in contrast, using the optimum initial backoff window size and number of sensing durations of LTE-LAA shows that they can maintain proportional fairness. It is unconcealed that the initial backoff window size tuning of LTE-LAA carries a high possibility of achieving fairness because it needs less system data and achieves a higher exactness result.

Quadratic Optimization Models for Balancing Preferential Access and Fairness: Formulations and Optimality Conditions

Typically, within facility location problems, fairness is defined in terms of accessibility of users. However, for facilities perceived as undesirable by communities hosting them, fairness between the usage of facilities becomes especially important. Limited research exists on this notion of fairness. To close this gap, we develop a series of optimization models for the allocation of populations of users to facilities such that access for users is balanced with a fair utilization of facilities. The optimality conditions of the underlying nonconvex quadratic models state the precise balance between accessibility and fairness. We define new classes of fairness and a metric to quantify the extent to which fairness is achieved in both optimal and suboptimal allocations. We show that a continuous relaxation of our central model is sufficient to achieve a perfect extent of fairness, while a special case reduces to the classical notion of proportional fairness. Our work is motivated by pervasive ecological challenges faced by the waste management community as policymakers seek to reduce the number of recycling centers in the last few years. As a computational case study, applying our models on data for the state of Bavaria in Germany, we find that even after the closure of a moderate number of recycling centers, large degrees of access can be ensured, provided that the closures are conducted optimally. Fairness, however, is impacted more, with facilities in rural regions shouldering larger loads of visiting populations than those in urban regions. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: Computer resources and support provided by the Erlangen Regional Computing Center are gratefully acknowledged. B. Singh was partially financially supported by the Bavarian State Ministry for Science and Art (Bayerisches Staatsministerium für Wissenschaft und Kunst) under the Competence Network for Scientific High Performance Computing in Bavaria. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0308 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0308 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Comparative Study of Radio Resource Distribution Algorithms

The equitable distribution of radio resources among different users in wireless networks is a difficult problem and has attracted the interest of many studies. This study presents the Proportional Fair Q-Learning Algorithm (PFLA) to enable the equitable distribution of radio resources among diverse users through the integration of Q-learning and proportional fairness principles. The PFLA, Round Robin (RR), and Max Throughput (MaxTP) algorithms were compared to evaluate their effectiveness in resource allocation. Performance was measured in terms of sum-rate throughputs and fairness index. The comparison results showed an improvement in the fairness index metrics for PFLA compared to the other algorithms. PFLA showed gains of 11.62 and 43% in the fairness index compared to RR and MaxTP, respectively. These results show that PFLA is more efficient in utilizing available resources, leading to higher overall system throughput and demonstrating its ability to balance performance metrics between users, especially when the number of users increases.

Optimum Power Allocation for HARQ-Aided NOMA With Proportional Fairness on Fading Channels

Optimum Power Allocation for HARQ-Aided NOMA With Proportional Fairness on Fading Channels

Energy-Based Proportional Fairness in Cooperative Edge Computing

Energy-Based Proportional Fairness in Cooperative Edge Computing

Extending Causal Discovery to Live 5G NR Network With Novel Proportional Fair Scheduler Enhancements

Extending Causal Discovery to Live 5G NR Network With Novel Proportional Fair Scheduler Enhancements

Group efficiency and individual fairness tradeoff in making wise decisions

In group decision making, the consensus model with minimum cost has been researched with the aim of improving group efficiency and saving resources. However, one limitation of the minimum cost consensus model is that the reach of consensus is usually at the expense of some group members. We consider two issues that we see as keys in group consensus: efficiency and fairness. We propose the price of fairness in the opinion revision process and give two kinds of fairness schemes. According to the individual's perception of inequity, we introduce inequity aversion parameters and classify experts into two types: experts with non-cooperative behaviors and with altruistic behaviors. Experts with altruistic behaviors will be allowed to contribute more than the recommended number of modifications. Then, we discuss how to achieve the tradeoff between efficiency and fairness. Furthermore, with the rapid development of social media, cloud, and e-government platforms, collective intelligence (CI), i.e., groups of individuals doing things collectively that seem intelligent, has been a hot topic. We expand our work to a crowd context with many individuals. We investigate how the opinion revision process and fairness schemes can influence the emergence of CI. Results suggest that the proportional fairness and max-min fairness have similar performance in stimulating CI. Moreover, the improvement of group accuracy is mainly related to two factors: the group consensus level of initial opinions and the relative distance between group aggregated opinion and the ground truth.

Hierarchical Deep Reinforcement Learning for Age-of-Information Minimization in IRS-Aided and Wireless-Powered Wireless Networks

In this paper, we focus on a wireless-powered sensor network coordinated by a multi-antenna access point (AP). Each node can generate sensing information and report the latest information to the AP using the energy harvested from the AP’s signal beamforming. We aim to minimize the average age-of-information (AoI) by adapting the nodes’ scheduling and the transmission control strategies jointly. To reduce the transmission delay, an intelligent reflecting surface (IRS) is used to enhance the channel conditions by controlling the AP’s beamforming strategy and the IRS’s phase shifting matrix. Considering dynamic data arrivals at different sensing nodes, we propose a hierarchical deep reinforcement learning (DRL) framework to for AoI minimization in two steps. The users’ transmission scheduling is firstly determined by the outer-loop DRL approach, e.g. the DQN or PPO algorithm, and then the inner-loop optimization is used to adapt either the uplink information transmission or downlink energy transfer to all nodes. A simple and efficient approximation is also proposed to reduce the inner-loop rum time overhead. Numerical results verify that the hierarchical learning framework outperforms typical baselines in terms of the average AoI and proportional fairness among different nodes.

IRS-Aided Joint Spatial Division and Multiplexing for mmWave Multiuser MISO Systems

Intelligent reflecting surface (IRS)-aided millimeter wave (mmWave) communication systems have gained considerable attention recently. However, the benefits brought by IRS require the instantaneous channel state information (I-CSI) of the cascaded base station (BS)-IRS and IRS-user channel which is difficult to obtain in practice, especially for the multiuser scenario. To address this issue, in this paper, we combine two-timescale beamforming and multi-IRS aided joint spatial division and multiplexing (JSDM) in a mmWave multiuser system. Specifically, all the users are first divided into different groups and each group is associated with an IRS. Then, we propose a novel two-stage grouping-based randomized beamforming (TS-GRB) scheme, where the analog beamformer is designed based on the statistical CSI (S-CSI) in the first stage, and the short-term digital beamformer at the BS and long-term passive beam pattern control policy at the IRSs are jointly optimized in the second stage with both S-CSI and dimension-reduced effective I-CSI. In particular, in the first stage, the analog beamformer is designed to reduce the inter-group interference (IGI) and effective channel dimension, while in the second stage, a two-timescale randomized joint beamforming (TRJB) algorithm is proposed to maximize the proportional fairness utility (PFU). We show that through two-timescale beamforming, JSDM and proper problem reformulation, the pilot overhead of our TS-GRB scheme is significantly lower than existing schemes. Finally, simulation results are presented to illustrate the effectiveness of the proposed TS-GRB scheme.

An MFD approach to route guidance with consideration of fairness

This paper introduces two fair and efficient route guidance (RG) advisory control schemes for proactive control of a large-size urban network. The two developed fairness-centered concepts are proportional fairness and anticipatory control. These concepts are developed as distinct control frameworks to address inequity issues of earlier RG schemes in a model predictive control (MPC) scheme for a heterogeneous urban network, which is divided into multiple pockets of congestion. The modelling approach uses a macroscopic fundamental diagram (MFD), which relates aggregated traffic variables, such as vehicle accumulation and trip completion rate. The proportionally fair RG control (FC) scheme is developed as a two-level RG advisory controller that focuses on maximizing the proportion of travellers utilities to effectively prevent the network from becoming congested while also considering fairness in the distribution of network resources. In addition, an anticipatory control (AC) RG scheme is devised as a two-level optimization model by incorporating road users routing behaviour as an integral part of the control scheme. Intensive sensitivity analysis is conducted under high-demand profiles and for different compliance rates and MFD parameters to analyze and evaluate the performance of these two fairness-centered routing schemes compared to a basic MPC based control scenario. The results indicate that FC improves fairness in an urban network by increasing homogeneity while maintaining efficiency. For all examined compliance levels, even as low as 30%, a more homogenized traffic condition is achieved under FC and AC. When comparing the two schemes, AC advises a smoother RG ratios compared to FC.

Bit-Interleaved Multiple Access: Improved Fairness, Reliability, and Latency for Massive IoT Networks

Internet-of-Things (IoT) networks require massive connections in dense areas. Therefore, a resource efficient multiple access scheme seems inevitable to enable immense connectivity where multiple devices have to share the same resource block. Non-orthogonal multiple access (NOMA) has been considered as the strongest candidate in recent years. However, in this paper, by considering the practical implementation, we first provide a true power allocation (PA) constraint with finite alphabet inputs for conventional downlink NOMA and demonstrate that it cannot support massive connections in practical systems. To this end, we propose bit-interleaved multiple access (BIMA) scheme in downlink IoT networks. The proposed BIMA scheme implements bitwise multiaccess interleaving and deinterleaving at the transceiver ends and there are no strict PA constraints, unlike conventional NOMA, thus allowing a high number of devices in the same resource block. We provide a comprehensive analytical framework for BIMA by investigating all key performance indicators (KPIs) to present both information-theoretic (i.e., ergodic capacity EC and outage probability OP) and finite alphabet inputs (i.e., bit error rate BER) performance metrics with both instantaneous and statistical channel ordering. In addition, we define Jain’s fairness index and proportional fairness index in terms of all KPIs. Based on the extensive computer simulations, we reveal that BIMA outperforms conventional NOMA significantly, with a performance gain of up to 20-30 dB in terms of KPIs in some scenarios. In other words, compared to conventional NOMA schemes, the same KPIs are met in BIMA with 20-30 dB less transmit power, which is quite promising for energy-limited use cases. Moreover, this performance gain becomes greater when more IoT devices are supported. BIMA provides a full diversity order for all IoT devices and enables the implementation of an arbitrary number of devices and modulation orders, which is crucial for IoT networks where a huge number of devices should be supported in a single resource block in dense areas. In addition to the overall performance gain, BIMA guarantees a fairness system where none of the devices gets a severely degraded performance and the sum-rate is shared in a fair manner among devices. It guarantees QoS satisfaction for all devices. Finally, we provide an intense complexity and latency analysis for BIMA and demonstrate that it provides lower latency compared to conventional NOMA receivers, since it allows parallel computation at the receivers and no iterative operations are required. We show that compared to conventional NOMA receivers, BIMA reduces latency by up to 350% for specific IoT devices and 170% on average.

Generalized nash fairness solutions for bi‐objective minimization problems

AbstractIn this article, we consider a particular case of bi‐objective optimization (BOO), called bi‐objective minimization (BOM), where the two objective functions to be minimized take only positive values. As well as for BOO, most of the methods proposed in the literature for solving BOM focus on computing the Pareto‐optimal solutions representing different trade‐offs between two objectives. However, it may be difficult for a central decision‐maker to determine the preferred solutions due to the huge number of solutions in the Pareto set. We propose a novel criterion for selecting the preferred Pareto‐optimal solutions by introducing the concept of ‐Nash Fairness (‐) solutions inspired by the definition of proportional fairness. The ‐ solutions are the feasible solutions achieving some proportional nash equilibrium between the two objectives. The positive parameter is introduced to reflect the relative importance of the first objective to the second one. For this work, we will discuss existential and algorithmic questions about the ‐ solutions by first showing their existence for BOM. Furthermore, the ‐ solution set can be a strict subset of the Pareto set. As there are possibly many ‐ solutions, we focus on extreme ‐ solutions achieving the smallest values for one of the objectives. Then, we propose two Newton‐based iterative algorithms for finding extreme ‐ solutions. Finally, we present computational results on some instances of the bi‐objective travelling salesman problem (BOTSP) and the bi‐objective shortest path problem.

Proportionally fair load balancing with statistical quality of service provisioning for aerial base stations

AbstractAerial base stations (ABSs) seem promising to enhance the coverage and capacity of fifth‐generation and upcoming networks. With the flexible mobility of ABSs, they can be positioned in air to maximize the number of users served with a guaranteed quality of service (QoS). However, ABSs may be overloaded or underutilized given inefficient placement, and user association has not been well addressed. Hence, we propose a three‐dimensional ABS placement scheme with a delay‐QoS‐driven user association to balance loading among ABSs. First, a load balancing utility function is designed based on proportional fairness. Then, an optimization problem for joint ABS placement and user association is formulated to maximize the utility function subject to statistical delay QoS requirements and ABS collision avoidance constraints. To solve this problem, we introduce an efficient modified gray wolf optimizer for ABS placement with a greedy user association strategy. Simulation results demonstrate that the proposed scheme outperforms baselines in terms of load balancing and delay QoS provisioning.

Collaborative Management of Resource Allocation and Precoding for Dual-Mode Networks

A sub-6GHz (μWave) and millimeter wave (mmWave) dual-mode network can deliver high data rates while maintaining dependable coverage. This paper proposes a novel resource allocation and precoding algorithm based on collaborative sensing in the dual-mode network. We formulated the collaborative optimization problem of resource allocation and precoding, which maximizes the sum of data rates while meeting minimum acceptable rate requirements and ensuring proportional fairness. Considering the spatial similarity between mmWave channel and μWave channel, the prior information of mmWave channel predicted by μWave band is generated to process sensing weight (i.e., subchannel allocation weight of Markov algorithm), which realizes fast dual-mode network resource allocation. Furthermore, a low complexity two-stage precoding scheme for dual-mode networks is proposed based on μWave spatial information. Low-complexity analog precoding is realized in the first stage based on μWave spatial information. In the second stage, inspired by the correlation between minimum mean square error (MMSE) and mutual information, this paper proposes an alternating optimization algorithm to find a local weighted sum-rate (WSR) optimum with low complexity. Compared with other heuristic algorithms, simulation results demonstrate the apparent advantages of the proposed collaborative sensing optimization algorithm. Most importantly, it can be seen that we can achieve a performance that approaches an upper bound.

An eavesdropping and jamming dilemma with sophisticated players

Wireless networks are susceptible to malicious attacks, especially those involving eavesdropping and jamming. In this paper, we consider a communication scenario involving a transmitter who wishes to communicate secretly and reliably with a receiver, while an adversary wants to obstruct this communication by means of either eavesdropping or jamming. The transmitter as well as the adversary wants to achieve its own goal in a manner that is as unpredictable as possible to its rival. We model this problem by a non-zero sum game. The expected throughput that is delivered secretly and non-jammed to the receiver is considered as the metric that reflects communication secrecy and reliability. The entropy of the player’s strategies is considered as the metric to reflect the player’s unpredictability. The equilibrium is found in closed form, and parameters of the transmitter’s utility supporting both goals are optimized via a proportional fairness approach.