A Unified Framework for Max-Min and Min-Max Fairness With Applications

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.

Fairness comparison of FAST TCP and TCP Reno

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.

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 in Routing and Load Balancing

We consider a centralized spectrum server that coordinates the transmissions of a group of links sharing a common spectrum. Links employ on-off modulation with fixed transmit power when active. In the on state, a link obtains a data rate determined by the signal-to-interference ratio on the link. By knowing the link gains in the network, the spectrum server finds an optimal schedule that maximizes the average sum rate subject to a minimum average rate constraint for each link. Using a graph theoretic model for the network and a linear programming formulation, the resulting schedules are a collection of transmission modes (sets of active links) that are time shared in a fashion that is reminiscent of spatial reuse patterns in cellular networks. In the special case when there is no minimum rate constraint, the optimal schedule results in a fixed dominant mode with highest sum rate being operated all the time. In order to offset the inherent unfairness in the above solution, we introduce a minimum rate constraint and characterize the resulting loss in sum rate when compared to the case when there is no minimum rate constraint. We also investigate alternate fairness criteria by designing scheduling algorithms that achieve max-min fairness and proportional fairness. It is shown that the max-min fair rate allocation maximizes the minimum common rate among the links. Simulation results are presented and future work is described

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.

Max-min fair allocation for resources with hybrid divisibilities

The existence of equilibrium in production economies has been shown assuming, among other things, that the set of attainable allocations is compact. Even though this is a very reasonable property, it has been introduced as an axiom rather than as a consequence of some primitive assumptions on production and consumption sets. We deal with this point here, analyzing in detail conditions under which the aggregate consumption and production sets are closed, and the set of feasible allocations is compact.

We show that a finite, competitive economy isimmune to sunspots if (i) preferences are strictly convex, (ii) the set of feasible allocations is convex, and (iii) the contingent-claims market is perfect. The conditions (i)–(ii) cover some, but not all, economies with nonconvex technologies. Based on an indivisible-good example, we show that even economies with strictly convex preferences and full insurance arenot in general immune from sunspots. We also show that (1) the sufficient conditions (i)–(iii) are not necessary for sunspot immunity and (2)ex-ante efficiency is not necessary for immunity from sunspots.

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 of fair and feasible allocation of user throughputs in capacitated networks is investigated. The main contribution of the paper is an extension of network fairness, and in particular, max-min fairness from the traditional fixed- path model to a more versatile, routing-independent model. We show that the set of throughput configurations realizable in a capacitated network makes up a polyhedron, which gives rise to a max-min fair allocation completely analogous to the conventional case.

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.

Often one would like to allocate shared resources in a fair way. A common and well studied notion of fairness is Max-Min Fairness, where we first maximize the smallest allocation, and subject to that the second smallest, and so on. We consider a networking application where multiple commodities compete over the capacity of a network. In our setting each commodity has multiple possible paths to route its demand (for example, a network using MPLS tunneling). In this setting, the only known way of finding a max-min fair allocation requires an iterative solution of multiple linear programs. Such an approach, although polynomial time, scales badly with the size of the network, the number of demands, and the number of paths. More importantly, a network operator has limited control and understanding of the inner working of the algorithm. Finally, this approach is inherently centralized and cannot be implemented via a distributed protocol. In this paper we introduce Upward Max-Min Fairness, a novel relaxation of Max-Min Fairness and present a family of simple dynamics that converge to it. These dynamics can be implemented in a distributed manner. Moreover, we present an efficient combinatorial algorithm for finding an upward max-min fair allocation, which is a natural extension of the well known Water Filling Algorithm for a multiple path setting. We test the expected behavior of this new algorithm and show that on realistic networks upward max-min fair allocations are comparable to the max-min fair allocations both in fairness and in network utilization.

Resource allocation strategy selection in 5G networks is a MADM (Multi-Attribute Decision-Making) problem, which all the methods defined so far or those used to solve it have neglected the negative aspects of attributes. This can result in the occurrence of information loss and it would be difficult to come to the right decision. Thus, in this paper, we present a MADM technique that can be used to take the negative aspects of attributes into account. This goal will be achieved by the method based on bipolar fuzzy sets (BFS) and tangent trigonometric aggregation operators (AOs). For this, in this article, firstly, we devise the concept of tangent trigonometric bipolar fuzzy number (TT-BFN) and linked algebraic operators. Then, we deduce tangent trigonometric bipolar fuzzy weighted averaging (TT-BFWA), tangent trigonometric bipolar fuzzy ordered weighted averaging (TT-BFOWA), tangent trigonometric bipolar fuzzy weighted geometric (TT-BFWG), and tangent trigonometric bipolar fuzzy ordered weighted geometric (TT-BFOWG) operators. We also devised the related results of these operators that is idempotency, monotonicity, and boundedness. Further in this manuscript, we investigate a case study “Selection of resource allocation strategy for 5G network” by considering artificial data and employing the invented MADM approach in the environment of BFS and get that “Max-Min Fairness Allocation” is the finest resource allocation strategy in 5G network. Finally, we compare our deduced theory with a few current ones to reveal supremacy and dominance.