MaxNet: an efficient Max-Mi fair allocation scheme

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.

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.

Fairness comparison of FAST TCP and TCP Reno

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.

The OFEX (Optimal and Fully EXplicit) rate controller is able to provide not only the optimal bandwidth allocation but also the fully explicit congestion signal to sources. It exercises link-wise proportional fairness and network-wise max-min fairness, which enables the controller to feed the congestion signal back from the most congested link, instead of using the networkwise proportional fairness which feeds back the congestion signal summed along a flow path. As a result, the OFEX controller overcomes the drawbacks of the relatively explicit controllers that 1) bias the multi-bottlenecked users in terms of their source sending rate and convergence speed, 2) are not adaptable to varying link bandwidth and 3) can potentially incur large queue size upon congestion. In this paper, we first prove that the OFEX controller can converge to its equilibrium at least as fast as a geometric series in a link. Then we analyze the system stability with time delay in a single bottleneck network and show that the OFEX controller can achieve local stability under certain conditions. Besides, the robustness analysis of the OFEX controller shows how the dynamics of link bandwidth may affect the revenue of a link. Finally, with the OPNET modeler, we evaluate the performances of the OFEX controller and verify its effectiveness.

Max-min fair allocation for resources with hybrid divisibilities

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.

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

Document transfer in the Internet is regulated by distributed packet-based congestion control mechanisms, usually relying on TCP. By dividing a document into packets, parts of one file reside at different nodes along the transmission path. The "instantaneous transfer rate" of the entire document can be thought of as being equal to the minimum transfer rate along the entire path. Bandwidth-sharing networks as considered by Massoulié & Roberts [2] provide a natural modeling framework for the dynamic flow-level interaction among document transfers. The class α-fair policies for such networks, as introduced by Mo & Walrand [3], captures a wide range of distributed allocation mechanisms such as TCP, the proportional fair allocation and the max-min fair allocation.

Fairness in Routing and Load Balancing

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.

Resource allocation problems are concerned with the allocation of limited resources among competing activities so as to achieve the best overall performances of the system but providing fair treatment of all the competitors. Telecommunication networks are facing the increasing demand for Internet services. Therefore, a problem of network dimensioning with elastic traffic arises which requires to allocate bandwidth to maximize service flows with fair treatment of all the services. In such applications, the so-called max-min fairness (MMF) solution concept is widely used to formulate the resource allocation scheme. This guarantees the fairness but may lead to significant losses in the overall throughput of the network. In this paper we show how multiple criteria optimization concepts can be used to generate various fair resource allocation schemes. The solution concepts are tested on the network dimensioning problem and their abilities to model various preferences are demonstrated.

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.

Cogging effect minimization in PMSM position servo system using dual high-order periodic adaptive learning compensation

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.