Routing-Independent Fairness in Capacitated Networks

Fairness and system throughput, influenced by wireless interference, are major objectives of resource allocation in wireless networks. Whereas traditionally max-min fairness protocols have been developed for wired networks (where interference is not a factor for network performance), in this paper we investigate the problem of flow routing and fair bandwidth allocation under the constraints of the physical interference model for multihop wireless networks. A max-min fair (MMF) routing algorithm under physical interference constraints is proposed where multiple candidate paths coexist for each user to the base station. The algorithm is formulated as a multicommodity flow problem where the lexicographically largest bandwidth allocation vector is found among all optimal allocation vectors. We compare our approach with two MMF interference routing algorithms in the literature that use the protocol interference model to garner fair bandwidth allocation. We show that our algorithm performs better in terms of blocking probability, bandwidth usage and link load.

The problem how to determine the capacity of and achieve fairness in mesh networks is one of the key topics in practical and theoretical research on mesh networks. Max-min fairness is one way to define fairness and several algorithms how to compute max-min fair rate allocations are already published. In this paper we make two major contributions to this area of research: First, we formulate an algorithm achieving max-min fairness among end-to-end flows based on the effective load of a collision domain. This allows us to determine max-min fair rate allocations in a multi-gateway, multi-channel mesh network with equal rates for all links. Second, we extend this algorithm for heterogeneous link rates.

Two food banks catering to populations of different sizes with different needs must divide among themselves a donation of food items. What constitutes a "fair" allocation of the items among them?

Fair resource allocation and SBS selection for MC-NOMA-based HetNets supporting D2D communications

It has been shown that as long as traffic sources adapt their rates to aggregate congestion measure in their paths, they implicitly maximize certain utility. In this paper we study some counter-intuitive throughput behaviors in such networks, pertaining to whether a fair allocation is always inefficient and whether increasing capacity always raises aggregate throughput. A bandwidth allocation policy can be defined in terms of a class of utility functions parameterized by a scalar a that can be interpreted as a quantitative measure of fairness. An allocation is fair if /spl alpha/ is large and efficient if aggregate throughput is large. All examples in the literature suggest that a fair allocation is necessarily inefficient. We characterize exactly the tradeoff between fairness and throughput in general networks. The characterization allows us both to produce the first counter-example and trivially explain all the previous supporting examples. Surprisingly, our counter-example has the property that a fairer allocation is always more efficient. In particular it implies that maxmin fairness can achieve a higher throughput than proportional fairness. Intuitively, we might expect that increasing link capacities always raises aggregate throughput. We show that not only can throughput be reduced when some link increases its capacity, more strikingly, it can also be reduced when all links increase their capacities by the same amount. If all links increase their capacities proportionally, however, throughput will indeed increase. These examples demonstrate the intricate interactions among sources in a network setting that are missing in a single-link topology.

It has been analytically proved that both MaxNet and SumNet can achieve max-min fair allocation in static networks. In SumNet networks, such as the TCP algorithm of the current Internet, the source rate is controlled by congestion signal which is the sum of signals from all of the congested links along the path from the source to the destination. In MaxNet networks, only the most congested link generates the control signal to dictate the source rate. This paper investigates the practical aspects of both schemes, specifically, the convergence speed and fairness tracking capability under transient network conditions. We have shown that the stability of SumNet's max-min fairness heavily depends on the network load. Within the stable ranges of operating points, SumNet's max-min fair allocation is obtained at the cost of response speed. An enhanced approach is proposed to improve the stability of SumNet to meet the max-min fairness criterion. We have shown both analytically and by simulation that under stable conditions, Maxnet has faster convergence speed and better fairness tracking capability than SumNet in a highly volatile environment.

Heterogeneous network (HetNet) is a promising solution to meeting the unprecedented demand for higher data rate in the next generation mobile networks. Compared with the traditional single-layer cellular networks, the resource management (e.g., user association and power control problems) is more challenging in the multi-tier HetNets. In addition, due to the new application scenarios and battery-limited nature of the user equipment (UE), improving energy efficiency (EE) of individual while ensuring EE fairness among UEs is one of the key design issues in the uplink HetNets. In this paper, by considering the fairness for EE, joint user association and power control problems are studied in the uplink multiple input multiple output (MIMO) enabled HetNets. Under the quality of service (QoS) and transmit power constraints of UE, two kinds of fairness, namely, proportional fairness and max-min fairness, are investigated. The optimization problems of maximizing the EE are formulated by considering the fairness among UEs. Considering the non-convex characteristic of the problem, the formulated problem is divided into two subproblems, i.e., user association and power control subproblems, then an iterative algorithm is proposed to achieve the fair EE resource allocation for each fairness criterion until convergence. For the proportional fairness problem, the dual decomposition and Newton methods are applied. Then, by using successive convex approximation (SCA) and dual decomposition, the problem of max-min fairness is solved. Through both theoretical analysis and simulations, the convergence and the effectiveness of the proposed algorithms are proved and evaluated. Simulation results show that the proposed algorithms can significantly improve the average EE of users.

Fairness in Routing and Load Balancing

Max-min fairness is widely used in various areas of networking. In every case where it is used, there is a proof of existence and one or several algorithms for computing the max-min fair allocation; in most, but not all cases, they are based on the notion of bottlenecks. In spite of this wide applicability, there are still examples, arising in the context of wireless or peer-to-peer networks, where the existing theories do not seem to apply directly. In this paper, we give a unifying treatment of max-min fairness, which encompasses all existing results in a simplifying framework, and extend its applicability to new examples. First, we observe that the existence of max-min fairness is actually a geometric property of the set of feasible allocations (uniqueness always holds). There exist sets on which max-min fairness does not exist, and we describe a large class of sets on which a max-min fair allocation does exist. This class contains, but is not limited to the compact, convex sets of RN. Second, we give a general purpose centralized algorithm, called Max-min Programming, for computing the max-min fair allocation in all cases where it exists (whether the set of feasible allocations is in our class or not). Its complexity is of the order of N linear programming steps in RN, in the case where the feasible set is defined by linear constraints. We show that, if the set of feasible allocations has the free-disposal property, then Max-min Programming reduces to a simpler algorithm, called Water Filling, whose complexity is much lower. Free disposal corresponds to the cases where a bottleneck argument can be made, and Water Filling is the general form of all previously known centralized algorithms for such cases. Our derivations are based on the relation between max-min fairness and leximin ordering. All our results apply mutatis mutandis to min-max fairness. Our results apply to weighted, unweighted and util-max-min and min-max fairness. Distributed algorithms for the computation of max-min fair allocations are outside the scope of this paper.

This paper addresses first the problem of max-min fair (MMF) link transmissions in wireless sensor networks (WSNs) and in a second stage studies the joint link scheduling and transmission power assignment problem. Given a set of concurrently transmitting links, the MMF link transmission problem looks for transmission powers of nodes such that the signal-to-interference and noise ratio (SINR) values of active links satisfy max-min fairness property. By guaranteeing a “fair” transmission medium (in terms of SINR), other network requirements may be directly affected, such as the schedule length, the throughput (number of concurrent links in a time slot), and energy savings. Hence, the whole problem seeks to find a feasible schedule and a power assignment scheme such that the schedule length is minimized and the concurrent transmissions have a fair quality in terms of SINR. The focus of this study falls on the transmission power control strategy, which ensures that every node that is transmitting in the network chooses a transmission power that will minimally affect the other concurrent transmissions and, even more, achieves MMF SINR values of concurrent link transmissions. We show that this strategy may have an impact on reducing the network time schedule.

We study the problem of fair allocation of items / goods / resources to m agents. The problem appears in two broad variants: (a) fair allocation of a divisible item wherein one item is to be divided amongst m agents; the problem is popularly known as cake-cutting problem, (b) fair allocation of indivisible items wherein n indivisible or non-shareable items are to be allocated amongst m agents. Further, the item/items can be homogeneous or heterogeneous. Both the variants have several real-time applications such as land-division amongst heirs is an example of allocation of a divisible item, whereas in divorce settlement, division of assets such as house, car, artifacts, etc. is an example of allocation of indivisible items. There are many notions of fairness and social welfare that are important and have been studied: envy-freeness, proportionality, Pareto optimality, maximin share guarantee, Borda maximin share guarantee, utilitarian social welfare, egalitarian social welfare and Nash social welfare. In this chapter, we discuss about the fair-allocation problem and their related results.

We consider the problem of fair allocation of the cost of a transmission system among load and generation entities using the marginal participation approach. We show that a cost-causal approach involving capacity-based line cost rate and a min-max fair economic slack bus selection for price-taking entities leads to a rigorously fair and more accurate implementation of marginal participation method. In the existing methods the counter-flows are masked, which is a compromise with fairness and linearity. However, if the counter-flows are incentivized then it can lead to pay-offs to some entities. The proposed approach solves the problem of pay-offs without masking the counter-flows. This is achieved by separation of the total transmission services cost into usage, reliability and residual capacity components. The allocation of the first two components is based on the min-max fairness policy, and the residual capacity costs are allocated on a pro-rata basis. Simulation results on multiple IEEE test systems, Indian utility power systems and extensive comparative evaluations for the contemporary methods demonstrate the claims made.

In modern data intensive computing, it is increasingly common for jobs to be executed in a distributed fashion across multiple machine clusters or datacenters to take advantage of data locality. This paper studies fair resource allocation among jobs requiring distributed execution. We extend conventional max-min fairness for resource allocation in a single machine or machine cluster to distributed job execution over multiple sites and define Aggregate Max-min Fairness (AMF) which requires the aggregate resource allocation across all sites to be max-min fair. We show that AMF satisfies the properties of Pareto efficiency, envy-freeness and strategy-proofness, but it does not necessarily satisfy the sharing incentive property. We propose an enhanced version of AMF to guarantee the sharing incentive property. We present algorithms to compute AMF allocations and propose an add-on to optimize the job completion times under AMF. Experimental results show that compared with a baseline which simply requires the resource allocation at each site to be max-min fair, AMF performs significantly better in balancing resource allocation and in job completion time, particularly when the workload distribution of jobs among sites is highly skewed.

We study bandwidth allocation at base stations of a wireless network as a non-cooperative game between different wireless users. A user demands bandwidth from the base stations it has access to by submitting bids. Once the bidding process is complete, a base station distributes its bandwidth to the users in proportion to their bids. Users are assumed to be budget constrained and price anticipating, and split their wealth across base stations so as to maximize their individual bandwidths. In this paper, we study the properties of Nash Equilibrium (NE) for this bandwidth allocation game. For the special case where each user can access all base stations, we argue that there exists a unique NE, at which the bandwidth obtained by any user is proportional to its wealth. For a more general scenario where a user may be able to access only a subset of all base stations, we compare the NE of the game to the max-min fair bandwidth allocation. We show that although the NE may not be max-min fair in general, the bandwidth allocation at NE becomes arbitrarily close to max-min fair allocation as the number of users is increased, while keeping the number of base stations fixed.

Fairness comparison of FAST TCP and TCP Reno