Max-min Fair Allocation Research Articles

Efficient and Lightweight Model-Predictive IoT Energy Management

Multi-sensor IoT devices often rely on renewable energy and batteries to support diverse field deployments. A device’s sensors use significant energy, so careful energy management is needed to maximize its operating time while meeting application requirements. Model Predictive Control (MPC), a successful energy management technique for other application domains, requires significant computational resources usually not available in typical IoT sensing devices. We develop and evaluate a low-complexity approximation to MPC for IoT device operations powered by renewable (solar) energy, where the approximation is guided by the charging characteristics of real batteries. The complex MPC optimization problem is solved by decomposing it into a time-dependent energy allocation problem, and a task-dependent sensor scheduling problem, each of which is solvable with cubic time complexity. We utilize a novel combination of an incremental max-min fair allocation method and a recursive dynamic programming-like procedure. This low-complexity predictive optimization step is integrated with a very simple parabola-based adaptive solar prediction to provide a full system solution, termed Predictive EneRgy Management for IoT (PERMIT) , that can be implemented in lightweight IoT devices. PERMIT is evaluated through experiments on a solar-powered Raspberry Pi device with multiple sensors. We also complement our evaluations with simulations based on real device data traces. Results show that PERMIT’s low-complexity algorithm approximates the exact MPC solution very closely. PERMIT also performs significantly better than Signpost, a comparable IoT energy management solution.

A distributed end-to-end fair bandwidth allocation algorithm for multi-path networks

Multi-path transmission significantly improves network performance, yet it complicates the problem of fair resource allocation. While traditional fair bandwidth allocation schemes thrive in single-path settings, they often falter when applied to multi-path environments, highlighting the challenge of achieving fair bandwidth sharing in such networks. To tackle this issue, the concept of "max-min similarity" of queuing delays has been introduced based on insight into the intrinsic interactions between queuing packets, delays, and bandwidth allocation, which leads to a formal definition of max-min fair bandwidth allocation for multi-path environments. Theoretical analysis shows that the max-min similarity of queuing delays is a sufficient condition for max-min fair bandwidth allocation in single bottleneck environments. A novel distributed end-to-end fair bandwidth allocation algorithm, named DMFBA, is then proposed, which separates the control into flow-level and transmission path-level. In achieving max-min similarity in queuing delays by dynamically adjusting the distribution of flows’ queuing packet quotas across paths it achieves the goal of max-min fair bandwidth allocation. Two sets of numerical simulation experiments were conducted and the results show that DMFBA has less overhead and faster convergence than the traditional utility fair algorithms.

Traffic-based adaptive bandwidth adjustment for flexible OTN connectivity in optical networks.

In conventional optical transport networks, the service form is the fixed bandwidth connectivity, which is not flexible for carrying bursting traffic. To support the time-varying traffic in an efficient way, researchers are studying the optical service units for building the more flexible optical transport network (OTN) connectivity, which is capable of dynamic hitless bandwidth adjustment. To better utilize the benefits of flexible connectivity, network operators need efficient algorithms to adjust the flexible connectivity bandwidth, especially in the network with a massive number of connections. In this paper, based on max-min fair bandwidth allocation criteria, we propose two traffic-based adaptive bandwidth adjustment algorithms to make bandwidth adjustment decisions, with the aim to improve bandwidth effectiveness. Simulation results show that the proposed algorithms can improve bandwidth utilization by up to 16%. Additionally, under high load conditions, it can reduce the loss in traffic bitrate by a maximum of 10%.

Polynomial-time Combinatorial Algorithm for General Max–Min Fair Allocation

Polynomial-time Combinatorial Algorithm for General Max–Min Fair Allocation

Fair and efficient allocation with few agent types, few item types, or small value levels

In fair division of indivisible goods, allocations that satisfy fairness and efficiency simultaneously are highly desired but may not exist or, even if they do exist, are computationally hard to find. Conditions under which such allocations, or allocations satisfying specific levels of fairness and efficiency simultaneously, can be efficiently found have thus been explored. Following this line of research, this study is concerned with the problem in a high-multiplicity setting where instances come with certain parameters, including agent types, item types, and value levels. Particularly, we address two computational problems. First, we wish to compute fair and Pareto-optimal allocations, w.r.t. any of the common fairness criteria: proportionality, maximin share, and max-min fairness. Second, we seek to find a max-min fair allocation that is efficient in the sense of maximizing utilitarian social welfare. We show that the first problem is tractable for most of the fairness criteria when the number of item types is fixed, or when at least two of the three parameters are fixed. For the second problem, we model it as a bi-criteria optimization problem that is solved approximately by determining an approximate Pareto set of bounded size. Our results are obtained based on dynamic programming and linear programming approaches. Our techniques strengthen known methods and can be potentially applied to other notions of fairness and efficiency.

An Experimental Study of Fast Greedy Algorithms for Fair Allocation Problems

This paper is concerned with two salient allocationproblems in fair division of indivisible goods, aiming atmaximizing egalitarian and Nash product social welfare.These problems are computationally NP-hard, meaning thatachieving polynomial time algorithms is impossible, unlessP = NP. Approximation algorithms, which return near-optimalsolution with a theoretical guarantee, have been widely usedfor tackling the problems. However, most of them are often ofhigh computational complexity or not easy to implement. It istherefore of great interest to explore fast greedy methods thatcan quickly produce a good solution. This paper presents anempirical study of the performance of several such methods.Interestingly, the obtained results show that fair allocationproblems can be practically approximated by greedy algorithms.Keywords: Fair allocation, exact algorithm, greedy algorithm,mixed-integer linear program, NP-hard.I. INTRODUCTIONIn this paper, we study the fair allocation problem, whichhas shown its growing interest during last decades, with awide range of real-world applications [1]. In short, this is acombinatorial optimization problem which asks to allocate???? discrete items amongst a set of ???? agents (or players)so as to meet a certain notion of fairness. It is assumedthat every item is “indivisible” and “non-sharable”, thatis, i) it cannot be broken in pieces before allocating toagents, and ii) it cannot be shared by two or more agents.For example, laptops and cell-phones are indivisible itemswhich agents might not want to share with others. Anallocation of items to agents is simply a partition of thewhole set of items into ???? disjoint subsets. There are up to???????? such partitions, making the solution space large enoughso that an exhaustive search for an optimal solution isimpossible.It now remains to define what a fair allocation is, aconcept that is of independent interest in the field ofEconomic and Social Choice Theory [2, 3]. In general, thereare many different ways of defining fairness, depending onparticular applications. The most common way is to eitheruse a so-called Collective Utility Function (CUF), which isa function for aggregating individual agents’ utilities in afair manner, or to follow an orthogonal method relying ondetermining the fair share of agents. Since we are focusingon the first method in this paper, we refer the reader tothe paper [4] and the references therein for more details ofthe second method. Suppose that every agent evaluates thevalue of items through a utility function, which maps eachsubset of items to a numerical value representing the utilityof the agent for the subset. Then, one can define a maxmin fair allocation to be the one that maximizes the 
 
 

Cross-Layer Optimization for Heterogeneous MU-MIMO/OFDMA Networks.

To enable the full benefits from MU-MIMO (Multiuser-Multiple Input Multiple Output) and OFDMA (Orthogonal Frequency Division Multiple Access) to be achieved, the optimal use of these two technologies for a given set of network resources has been investigated in a rich body of literature. However, most of these studies have focused either on maximizing the performance of only one of these schemes, or have considered both but only for single-hop networks, in which the effect of the interference between nodes is relatively limited, thus causing the network performance to be overestimated. In addition, the heterogeneity of the nodes has not been sufficiently considered, and in particular, the joint use of OFDMA and MU-MIMO has been assumed to be always available at all nodes. In this paper, we propose a cross-layer optimization framework that considers both OFDMA and MU-MIMO for heterogeneous wireless networks. Not only does our model assume that the nodes have different capabilities, in terms of bandwidth and the number of antennas, but it also supports practical use cases in which nodes can support either OFDMA or MU-MIMO, or both at the same time. Our optimization model carefully takes into account the interactions between the key elements of the physical layer to the network layer. In addition, we consider multi-hop networks, and capture the complicated interference relationships between nodes as well as multi-path routing via multi-user transmissions. We formulate the proposed model as a Mixed Integer Linear Programming (MILP) problem, and initially model the case in which each node can selectively use either OFDMA or MU-MIMO; we then extend this to scenarios in which they are jointly used. As a case study, we apply the proposed model to sum-rate maximization and max–min fair allocation, and verify through MATLAB numerical evaluations that it can take appropriate advantage of each technology for a given set of network resources. Based on the optimization results, we also observe that when the two technologies are jointly used, more multi-user transmissions are enabled thanks to flexible resource allocation, meaning that greater use of the link capacity is achieved.

Distributed Traffic Engineering for Multi-Domain SDN Without Trust

In software defined networking, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">flat</i> design of distributed control plane enables the management of multi-domain networks that are incapable of deploying a root controller. However, it is very difficult to avoid policy conflicts between independent local controllers due to the lack of centralized arbitration. Moreover, domains without trust may not be always cooperative and could even cheat to maximize their own interests. In this article, we first consider the cooperative scenario and address the problem of traffic engineering in a flat distributed control plane. We propose a fully distributed algorithm, called <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DisTE</monospace> , which can provide max-min fair bandwidth allocation for flows and maximize resource utilization. <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DisTE</monospace> also preserves the local topology of each domain and achieves policy consistency by multiple rounds of synchronization. We then consider the non-cooperative scenario, where selfish domains may discriminate bandwidth requests from other domains or overstate theirs owns to squeeze more bandwidths.

Efficient Downlink Power Allocation Algorithms for Cell-Free Massive MIMO Systems

Cell-free Massive MIMO systems consist of a large number of geographically distributed access points (APs) that serve the users by coherent joint transmission. The spectral efficiency (SE) achieved by each user depends on the power allocation: which APs that transmit to which users and with what power. In this article, we revisit the max-min and sum-SE power allocation policies, which have previously been approached using high-complexity general-purpose solvers. We develop and compare several different high-performance low-complexity power allocation algorithms that are appropriate for use in large systems. We propose two new algorithms for sum-SE power optimization inspired by weighted minimum mean square error (WMMSE) minimization and fractional programming (FP). Further, one new FP-based algorithm is proposed for max-min fair power allocation. The alternating direction method of multipliers (ADMM) is used to solve specific convex subproblems in the proposed algorithms. Our ADMM reformulations lead to multiple small-sized subproblems with closed-form solutions. The proposed algorithms find global or local optimal power allocation solutions for large-scale systems but with reduced computational time compared to previous work.

Max–Min Fair Sensor Scheduling: Game-Theoretic Perspective and Algorithmic Solution

We consider the design of a fair sensor schedule for a number of sensors monitoring different linear time-invariant processes. The largest average remote estimation error among all processes is to be minimized. We first consider a general setup for the max-min fair allocation problem. By reformulating the problem as its equivalent form, we transform the fair resource allocation problem into a zero-sum game between a "judge" and a resource allocator. We propose an equilibrium seeking procedure and show that there exists a unique Nash equilibrium in pure strategy for this game. We then apply the result to the sensor scheduling problem and show that the max-min fair sensor scheduling policy can be achieved.

Max-min fair allocation for resources with hybrid divisibilities

Resource allocation is a classic problem in economics and computer science. The application scenarios of resource allocation include inheritance settlements, computation resource sharing and so on. This paper focuses on the max-min fair allocation of resources in which m resources need to be allocated to n agents while maximizing the minimum utility of any agent. When money transfer is not allowed, the existing work on max-min fair allocation only focuses on the fair allocation of indivisible resources. However, in real applications, the allocated resource set may simultaneously include indivisible resources and divisible resources, e.g., the allocated resources in distributed systems include the indivisible CPU resources, the divisible storage resource and the divisible bandwidth resource. The combination of indivisible resources and divisible resources creates a new challenge and requires us to consider how to coordinate the allocations of indivisible resources and divisible resources in the allocation process. Therefore, we investigate the combined max-min fair allocation problem in which the allocated resource set consists of both indivisible resources and divisible resources. We present a 6+210+ε (ε > 0)-factor approximation algorithm for the restricted case where uij ∈ {0, uj} (i.e., the utility of a resource j is either 0 or uj for each agent i) and the agent valuations for the divisible resources are in proximity to each other. Moreover, we propose an approximation algorithm for the general case based on the augmented flow idea. Experiments conducted on real data show that the average performance of the proposed approximation algorithm is better than 80% of the performance of the optimal algorithm, which requires exponential time in the worst case unless P = NP. To the best of our knowledge, the proposed algorithm is the first approximation algorithm for the general case of the combined max-min fair allocation problem when money transfer is not allowed. The proposed algorithm can be adopted to design more efficient expert systems that apply to resource allocation in distributed systems, inheritance settlements and so on. The adoption of the proposed algorithm contributes to promoting the broader application of expert systems in the fair allocation of computation resources and social resources. The experimental results show that the proposed algorithm can perform well in real applications.

On max-min fair allocation for multi-source transmission

Max-min fair is widely used in network traffic engineering to allocate available resources among different traffic transfers. Recently, as data replication technique developed, increasing systems enforce multi-source transmission to maximize network utilization. However, existing TE approaches fail to deal with multi-source transfers because the optimization becomes a joint problem of bandwidth allocation as well as flow assignment among different sources. In this paper, we present a novel allocation approach for multi-source transfers to achieve global max-min fairness. The joint bandwidth allocation and flow assignment optimization problem poses a major challenge due to nonlinearity and multiple objectives. We cope with this by deriving a novel transformation with simple equivalent canonical linear programming to achieve global optimality efficiently. We conduct data-driven simulations, showing that our approach is more max-min fair than other single-source and multi-source allocation approaches, meanwhile it outperforms others with substantial gains in terms of network throughput and transfer completion time.

Adaptive bandwidth binning for bandwidth management

In this paper, we present a novel bandwidth management scheme that we call adaptive bandwidth binning (ABB). ABB is presented in the context of a DOCSIS cable network, but it has obvious applicability to downstream service on any shared medium access network in which all downstream traffic is scheduled by a single headend device such as a CMTS or wireless base station or access point.ABB is capable of providing approximate weighted max-min fair sharing of downstream bandwidth via a low-overhead scheduler that requires only a small number of permanently allocated queues. A modern delay-based active queue management (AQM) technique is employed to control delays.The performance of ABB is evaluated via ns-2 simulations in which workloads include FTP, HTTP-based adaptive streaming (HAS), and web traffic targeted for different tiered service quality levels. Our results show that ABB is able to provide approximate weighted max-min fair bandwidth allocation among responsive high bandwidth flows while isolating them from low bandwidth and latency sensitive flows. The use of CoDel in each ABB queue is effective in managing latency as required. The use of flow weights in ABB supports service tiering in which subscribers pay more for higher service rates.

Fair Resource Allocation in an Intrusion-Detection System for Edge Computing: Ensuring the Security of Internet of Things Devices

The recent trend of edge computing extends cloud computing and the Internet of Things (IoT) to the edge of the network. Similar to most systems, an intrusion-detection system (IDS) is commonly used to mitigate cybersecurity threats in edge computing. Due to the limitations in edge nodes (e.g., in terms of computational and storage capabilities), efficient and fair resource allocation within an IDS is challenging. This article studies IDS architecture and resource allocation in edge computing. Specifically, the proposed system is designed to facilitate multiple resources sharing and heterogeneous resource-demanding allocation. A general edge computing IDS architecture is presented, and we use this as the basis for our model for allocating resources. Then, a single-layer dominant and max-min fair (SDMMF) allocation is used, which has been theoretically proven to satisfy all hierarchical resource allocation properties, and a multilayer resource allocation scheme [in our system, the multilayer dominant and max-min fair (MDMMF) allocation] is used to cope with the multiple resources fair allocation in multiple layers.

Fair Resource Allocation in Systems With Complete Information Sharing

In networking and computing, resource allocation is typically addressed using classical resource allocation protocols as the proportional rule, the max–min fair allocation, or solutions inspired by cooperative game theory. In this paper, we argue that, under awareness about the available resource and other users demands, a cooperative setting has to be considered in order to revisit and adapt the concept of fairness. Such a complete information sharing setting is expected to happen in 5G environments, where resource sharing among tenants (slices) need to be made acceptable by users and applications, which therefore need to be better informed about the system status via ad-hoc (northbound) interfaces than in legacy environments. We identify in the individual satisfaction rates the key aspect of the challenge of defining a new notion of fairness in systems with complete information sharing, consequently, a more appropriate resource allocation algorithm. We generalize the concept of user satisfaction considering the set of admissible solutions for bankruptcy games and we adapt to it the fairness indices. Accordingly, we propose a new allocation rule we call mood value: for each user, it equalizes our novel game-theoretic definition of user satisfaction with respect to a distribution of the resource. We test the mood value and a new fairness index through extensive simulations about the cellular frequency scheduling use-case, showing how they better support the fairness analysis. We complete the paper with further analysis on the behavior of the mood value in the presence of multiple competing providers and with cheating users.

On (1, $$\epsilon $$ ϵ )-Restricted Max–Min Fair Allocation Problem

We study the max–min fair allocation problem in which a set of m indivisible items are to be distributed among n agents such that the minimum utility among all agents is maximized. In the restricted setting, the utility of each item j on agent i is either 0 or some non-negative weight $$w_j$$ . For this setting, Asadpour et al. (ACM Trans Algorithms 8(3):24, 2012) showed that a certain configuration-LP can be used to estimate the optimal value to within a factor of $$4+\delta $$ , for any $$\delta >0$$ , which was recently extended by Annamalai et al. (in: Indyk (ed) Proceedings of the twenty-sixth annual ACMSIAM symposium on discrete algorithms, SODA 2015, San Diego, CA, USA, January 4–6, 2015) to give a polynomial-time 13-approximation algorithm for the problem. For hardness results, Bezakova and Dani (SIGecom Exch 5(3):11–18, 2005) showed that it is $$\mathsf {NP}$$ -hard to approximate the problem within any ratio smaller than 2. In this paper we consider the $$(1,\epsilon )$$ -restricted max–min fair allocation problem in which each item j is either heavy $$(w_j = 1)$$ or light $$(w_j = \epsilon )$$ , for some parameter $$\epsilon \in (0,1)$$ . We show that the $$(1,\epsilon )$$ -restricted case is also $$\mathsf {NP}$$ -hard to approximate within any ratio smaller than 2. Using the configuration-LP, we are able to estimate the optimal value of the problem to within a factor of $$3+\delta $$ , for any $$\delta >0$$ . Extending this idea, we also obtain a quasi-polynomial time $$(3+4\epsilon )$$ -approximation algorithm and a polynomial time 9-approximation algorithm. Moreover, we show that as $$\epsilon $$ tends to 0, the approximation ratio of our polynomial-time algorithm approaches $$3+2\sqrt{2}\approx 5.83$$ .

Rapid Calculation of Max-Min Fair Rates for Multi-Commodity Flows in Fat-Tree Networks

Max-min fairness is often used in the performance modeling of interconnection networks. Existing methods to compute max-min fair rates for multi-commodity flows have high complexity and are computationally infeasible for large networks. In this work, we show that by considering topological features, this problem can be solved efficiently for the fat-tree topology that is widely used in data centers and high performance compute clusters. Several efficient new algorithms are developed for this problem, including a parallel algorithm that can take advantage of multi-core and shared-memory architectures. Using these algorithms, we demonstrate that it is possible to find the max-min fair rate allocation for multi-commodity flows in fat-tree networks that support tens of thousands of nodes. We evaluate the run-time performance of the proposed algorithms and show improvement in orders of magnitude over the previously best known method. We further demonstrate a new application of max-min fair rate allocation that is only computationally feasible using our new algorithms.

Multi-layer Resources Fair Allocation in Big Data with Heterogeneous Demands

The resource fair allocation is very important for the most systems. This paper focuses on the resource allocation in a big data system. This system has the characteristics of multiple resources owning and heterogeneous resource demanding. Firstly, a basic allocation scheme is proposed. Some allocation properties are introduced including sharing incentive, strategy proofness, envy-freeness, Pareto optimality, resource efficiency, single-layer multi-resource fairness, multi-layer single-resource fairness. Secondly, a single layer dominant and max–min fair allocation (SDMMF) is proposed. The basic idea is that the resources are firstly allocated using dominant resource fairness scheme. If some resources are not fully allocated, using max–min fairness scheme allocate the surplus ones. The SDMMF is theoretically proved satisfying all the hierarchical resource allocation properties. Thirdly, a Multi-layer resource allocation scheme, namely multi-layer dominant and max–min fair allocation (MDMMF) is proposed. The basic idea is that a multi-layer resource demand hierarchy can be divided into a series of single layer resource demand. So a resource demand vector can be built in the hierarchy from down to top. Then, the resource allocation of first layer is calculated using SDMMF allocation. The result of such allocation is further allocating in the third layer. Recursively do the MDMMF allocation until the bottom layer nodes obtain resource allocation shares. Lastly, The MDMMF is also theoretically proved satisfying all the hierarchical resource allocation properties.

Constrained max-min fair scheduling of variable-length packet-flows to multiple servers

In this paper, we study a multi-server queuing system wherein each user is constrained to get service only from a specified subset of servers. Fair packet scheduling in such a setting poses novel challenges that we address in this paper. Specifically, we observe that max-min fair allocation of the available resource over different servers (notably bandwidth) in the presence of placement constraints results in different levels of fair service-rates. To achieve the max-min fair service rates, we propose a novel packet scheduler which is inspired by the deficit-round robin (DRR) algorithm. The scheduler allocates tokens to flows in a round-by-round manner, where token allocation to flows at the beginning of each round is weighted max-min fair. So, we have called it multi-server max-min fair DRR (MSMF-DRR). The performance of the MSMF-DRR algorithm in terms of achieving fairness is shown through a worst-case performance analysis. In addition to analytical results, numerical experiments are also carried out to illustrate service isolation and the delay guarantee that are provided by the algorithm. Generally, a scheduler for such a constrained multi-server queuing system can be applicable in many modern data-networking applications, especially in cloud computing wherein virtual machines and/or processes vie for different IT resources distributed over heterogenous servers, while different processes may have preferences over servers owing to their quality-of-service requirements and the heterogeneity of servers.

Combinatorial Algorithm for Restricted Max-Min Fair Allocation

We study the basic allocation problem of assigning resources to players to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, a certain Configuration-LP can be used to estimate the value of the optimal allocation to within a factor of 4+ ε. In contrast, however, the best-known approximation algorithm for the problem has an unspecified large constant guarantee. In this article, we significantly narrow this gap by giving a 13-approximation algorithm for the problem. Our approach develops a local search technique introduced by Haxell [13] for hypergraph matchings and later used in this context by Asadpour, Feige, and Saberi [2]. For our local search procedure to terminate in polynomial time, we introduce several new ideas, such as lazy updates and greedy players . Besides the improved approximation guarantee, the highlight of our approach is that it is purely combinatorial and uses the Configuration-LP only in the analysis.