Min Fairness Research Articles

Linear transceiver design for a MIMO interfering broadcast channel achieving max–min fairness

We consider the problem of linear transceiver design to achieve max–min fairness in a downlink MIMO multicell network. This problem can be formulated as maximizing the minimum rate among all the users in an interfering broadcast channel (IBC). In this paper we show that when the number of antennas is at least two at each of the transmitters and the receivers, the min rate maximization problem is NP-hard in the number of users. Moreover, we develop a low-complexity algorithm for this problem by iteratively solving a sequence of convex subproblems. We theoretically establish the global convergence of the proposed algorithm to the set of stationary points, which may be suboptimal due to the non-convexity of the original minimum rate maximization problem. Numerical simulations show that this algorithm is efficient in achieving fairness among all the users.

A novel approach for the performance bound of QoS-aware data networks under greedy CAC policy

The performance of QoS-aware data networks is measured in terms of acceptance probability of traffic demands requiring an amount of end-to-end bandwidth, which is determined by the Call Admission Control (CAC) policy and the QoS routing algorithm. In this paper, we characterize the theoretical upper bound on the network performance under the greedy CAC policy. Whereas similar problems have been studied in teletraffic networks, the existing approaches consider a specific routing algorithm and obtain its performance. They cannot be used to find performance bound in data networks using complex dynamic QoS routing algorithms. We obtain the bound through modeling the network as a multidimensional Markov chain, which does not depend on a particular routing algorithm. Since this model is computational intensive, the greediest online routing algorithm is developed to estimate the performance bound with lower computational complexity through simulation. In single rate traffic condition, we show that resources allocated by this algorithm for each traffic class is approximately weighted max–min fair. Using this observation, we develop a novel technique to estimate the bound in which an individual loss system is considered per traffic class. Simulation results show that the technique provides an accurate estimation of the bound in a wide range of traffic and network parameter settings.

Cross‐layer optimization for fair end‐to‐end rate allocation in WMNs with MIMO links

ABSTRACTMultiple‐input multiple‐output (MIMO) technology can bring substantial throughput improvement in wireless mesh networks (WMNs) via a combination of interference suppression and spatial multiplexing. In this paper, we investigate a cross‐layer design problem in MIMO‐based WMNs, which involves end‐to‐end rate allocation, routing, and stream control scheduling. Scheduling is addressed by using a set of transmission configurations (TCs), and a greedy heuristic algorithm is proposed to identify a good subset of all possible TCs. We define three optimization problems to find the maximum throughput, max–min fair and proportional fair rate allocation solutions. We propose a cross‐layer scheme to solve these problems. We also discuss how the proposed cross‐layer scheme can be implemented on the basis of the IEEE 802.16 mesh mode. Simulation results show that the performance of the proposed schemes with the heuristic algorithm is close to the optimal. The computational complexity of obtaining the solution using the proposed heuristic algorithm is substantially less than that of finding the optimal solution. Copyright © 2012 John Wiley & Sons, Ltd.

Resource sharing in LTE‐Advanced relay networks: uplink system performance analysis

ABSTRACTRelay‐enhanced networks are expected to fulfil the demanding coverage and capacity requirements in a cost‐efficient way. Type 1 inband relaying has been standardised as an integral part of the Third Generation Partnership Project (3GPP) Long‐Term Evolution Release 10 and beyond (LTE‐Advanced). This type of relay nodes (RNs) supports a relaying mode where the RN to donor evolved node B (donor eNB, DeNB) link (relay link, a.k.a. backhaul link) transmission is time‐division multiplexed with the RN‐served user equipments (RUEs) to RN link (access link) transmission, whereas macrocell‐served user equipments (MUEs) share the same resources with the RNs at DeNB. Hence, system performance depends strongly on the resource sharing strategy among and within the links. Further, the set of subframes assigned for the relay link transmission is semi‐statically configured and thus a dynamic reconfiguration to adapt to fast‐changing system conditions (e.g. RN cell load) is not viable. Besides, in order to fully exploit the benefits of relaying, the inter‐cell interference, which is increased because of the presence of RNs, should be limited via a proper power control (PC) scheme on each link. Therefore, an optimisation of both the resource sharing and PC strategy is required to enhance the overall performance of relay networks. In order to tackle these issues, we employ a statistic‐based over‐provisioned backhaul subframe allocation to be utilised for flexible co‐scheduling of RNs and MUEs at the DeNB. In addition, we propose a combination of RN scheduling based on the number of RUEs and user throughput throttling achieving max–min fairness. Performance analysis of various resource sharing techniques along with PC optimisation is then carried out within the LTE‐Advanced uplink framework in urban and suburban scenarios. Comprehensive results show that the proposed schemes achieve significant throughput gains and high system fairness with substantially increased flexibility in resource allocation. Copyright © 2012 John Wiley & Sons, Ltd.

Proportional fairness in MAC layer channel access of IEEE 802.11s EDCA based wireless mesh networks

Fairness provisioning in IEEE 802.11s EDCA based Wireless Mesh Networks (WMNs) is a very challenging task due to relayed traffic and traffic load variation among mesh routers. Because of bursty traffic in general purpose community wireless mesh networks, proportional fairness is more suited than max–min fairness, where mesh routers and clients should get channel access proportional to their traffic load. However, proportional fairness is hard to achieve by solving optimization function because of non-linearity and non-concave property of the objective function. In this paper, a probabilistic approach is proposed to provide proportional fairness without solving global non-linear and non-concave optimization. Every mesh node use a load estimation strategy to estimate total traffic load that it needs to forward. The required channel share of a mesh node should be proportional to its traffic load, whereas, the total normalized channel share for all the contending mesh nodes should be kept less than unity to satisfy the clique constraint. The network architecture and contention property in WMN are explored to deduce the required channel share of mesh nodes. A probabilistic approach is used to tune the contention window based on the difference between actual channel share and required channel share, so that the node with more traffic load gets more channel share. A discrete time Markov Chain based modeling is used to deduce the overall network throughput for the proposed scheme. Simulation result shows that the proposed scheme works better than the standard IEEE 802.11s based EDCA MAC in terms of fairness and throughput.

Joint power and rate allocation in CDMA-based underlay cognitive radio networks for a mixture of streaming and elastic traffic

This article investigates the issue of radio resource allocation strategies for cognitive networks based on the underlay approach, while adhering to the interference constraint on the primary user. Joint rate and power allocation problem is considered for secondary users (SUs) with homogeneous and heterogenous traffic subject to the QoS and interference threshold constraints. Two well-known fairness approaches [max–min and proportional fairness (PF)] are compared for the proposed optimization problem. Three scenarios are considered. The first scenario corresponds to elastic traffic in which all the SUs are elastic users. In the second, it is assumed that all the SUs are streaming users. Considering the proportional and max min fairness, it is observed that for both fairness criterion the streaming users achieving higher throughput and fairness, compared with the elastic users due to the fact that for streaming users, stringent transmission rate guarantees are necessary to ensure real-time communication. Moreover, considering the requirements of future wireless networks, a cross-layer resource-allocation is proposed for heterogeneous traffic in the third scenario. A combination of streaming traffic (which requires a maximum guaranteed average delay) and elastic traffic (with flexible rate requirements) is investigated. The optimization problem allocates the available resources to the streaming users such that the delay constraints of the streaming users are satisfied. Through extensive simulations, the effect of streaming traffic, Interference threshold, minimum processing gain, imperfect channel state information and signal-to-interference-noise ratio constraint on the total throughput of elastic users are investigated. Simulation results demonstrate that in all scenarios PF outperforms max min fairness. Furthermore, it is shown that increasing the number of streaming traffic results in lower throughput of elastic users for both PF and max min fairness.

Max Min Fair Scheduling Algorithm using In Grid Scheduling with Load Balancing

This paper shows the importance of fair scheduling in grid environment such that all the tasks get equal amount of time for their execution such that it will not lead to starvation. The load balancing of the available resources in the computational grid is another important factor. This paper considers uniform load to be given to the resources. In order to achieve this, load balancing is applied after scheduling the jobs. It also considers the Execution Cost and Bandwidth Cost for the algorithms used here because in a grid environment, the resources are geographically distributed. The implementation of this approach the proposed algorithm reaches optimal solution and minimizes the make span as well as the execution cost and bandwidth cost..

Design a novel fairness model in WiMAX mesh networks

WiMAX mesh is acting as a promising alternative to construct high speed and wide range multi-hop wireless access network; however the resource scheduling with respect to user fairness and system efficiency in such networks is still remained unspecified. To perform the global fair bandwidth allocation for all competing traffic flows, we design a new fairness model called multihop max–min fair (MMF) to be applied in WiMAX mesh network. The MMF fairness is firstly designed based on the homogenous scenario where every link holds the same transmission capacity; then it is extended to the heterogeneous scenario where different links have different transmission capacity. As for the scheduling for all those competing traffic flows over the mesh network, we first get the global fair share of scheduling opportunities for each flow according to the MMF principle, then determine the resource allocation for each flow and each traffic link. The relevant resource scheduling algorithm is given with an analysis on various performance metrics as well. The simulation results validate the superiority of our proposed scheme compared with the existing schemes.

Max–min fairness aware joint power, subcarrier allocation and relay assignment in multicast cognitive radio

The authors presented low-complexity schemes for jointly deciding subcarrier assignment, power allocation and relay assignment (JSPARA) for multiuser non-regenerative relaying in a multigroup, multicast cognitive radio system (MMCRS). The authors considered two different optimisation problems. In one optimisation problem, the authors studied the problem of maximising the sum-rate of an MMCRS. In another optimisation problem, the authors considered the problem of maximising the rate of the worst multicast group of users. And also the authors proposed low-complexity iterative algorithms for JSPARA. The proposed algorithms have low-computational complexity, and their effectiveness is verified through simulation results.

Load-balanced three-stage switch

A load-balanced two-stage switch is scalable and can provide close to 100% throughput. Its major problem is that packets can be mis-sequenced when they arrive at outputs. In a recent work, the packet mis-sequencing problem is elegantly solved by a feedback-based switch architecture. In this paper, we extend the feedback-based switch from two-stage to three-stage for further cutting down average packet delay while still ensuring in-order packet delivery and close to 100% throughput. The basic idea is to use the third stage switch to map heavy flows to experience less middle-stage delays. To identity heavy flows, an adaptive traffic estimation algorithm is proposed. To ensure max–min fairness in bandwidth allocation under any inadmissible traffic pattern, an efficient fair scheduler is devised.

Optimal Max–Min Fair Resource Allocation in Multihop Relay-Enhanced WiMAX Networks

In this paper, an optimal resource allocation scheme is proposed for WiMAX networks that are enhanced with nontransparent relay stations (RSs). We first focus on two-hop relaying networks, because this scenario has the largest throughput gain. Furthermore, several researchers have proposed different resource allocation schemes in two-hop relaying networks, and thus, we can compare the performance of our proposed scheme with the following two well-known schemes in terms of cell throughput, outage rate, and computational time: 1) orthogonal and 2) overlapped . We then explore an extension of the proposed scheme to a general multihop relaying scenario by taking into account spatial reuse in both the access and relay zone periods. The numerical results show that the highest cell throughput can be achieved by the proposed optimal scheme while maintaining the fairness and lower outage performance of the orthogonal scheme at a higher computational cost. Moreover, the cell throughput degradation from increasing the number of hops from two to three hops, under the proposed optimal scheduling scheme, is only 12% and 19% when six and nine RSs are deployed, respectively.

On the performance and fairness of dynamic channel allocation in wireless mesh networks

SUMMARYChannel assignment in multichannel multiradio wireless mesh networks is a powerful resource management tool to exploit available multiple channels. Channels can be allocated either statically on the basis of long‐term steady state behavior of traffic or dynamically according to actual traffic demands. It is a common belief that dynamic schemes provide better performance; however, these two broad classes of channel allocation schemes have not been compared in detail. In this paper, we quantify the achievable performance gain and fairness improvement through an optimal dynamic channel allocation scheme. We develop optimal algorithms for a dynamic and three static schemes using mixed integer linear programming and compare them in the context of QoS provisioning, where network performance is measured in terms of acceptance rate of QoS sensitive traffic demands.Our extensive simulations show that static schemes should optimize channel allocation for long‐term traffic pattern and maintain max–min fairness to achieve acceptable performances. Although the dynamic and max–min fair static schemes accomplish the same fairness, the dynamic channel allocation outperforms the static scheme about 10% in most cases. In heavily overloaded regimes, especially when network resources are scarce, both have comparable performances, and the max–min fair scheme is preferred because it incurs less overhead. Copyright © 2011 John Wiley & Sons, Ltd.

On max–min fair flow optimization in wireless mesh networks

The paper is devoted to modeling wireless mesh networks (WMN) through mixed-integer programming (MIP) formulations that allow to precisely characterize the link data rate capacity and transmission scheduling using the notion of time slots. Such MIP models are formulated for several cases of the modulation and coding schemes (MCS) assignment. We present a general way of solving the max–min fairness (MMF) traffic objective for WMN using the formulated capacity models. Thus the paper combines WMN radio link modeling with a non-standard way of dealing with uncertain traffic, a combination that has not, to our knowledge, been treated so far by exact optimization models. We discuss several ways, including a method based on the so called compatible or independent sets, of solving the arising MIP problems. We also present an extensive numerical study that illustrates the running time efficiency of different solution approaches, and the influence of the MCS selection options and the number of time slots on traffic performance of a WMN. Exact joint optimization modeling of the WMN capacity and the MMF traffic objectives forms the main contribution of the paper.

Joint time-frequency-power resource allocation for low-medium-altitude platforms-based WiMAX networks

Low-medium-altitude platforms (LMAPs) are being actively researched and developed as a key solution to improve the performance and services of emergency communications. In order to provide higher capacity, throughput and quality of service guarantee to territorial users in emergency scenarios, a LMAP-based WiMAX system, AirWiMAX, is presented in this paper. Firstly, a hierarchical AirWiMAX topology is presented. Secondly, a joint radio resource allocation is carried out simultaneously at the time, frequency and power domain for the AirWiMAX downlink. This problem is modelled as a cooperative game in which a fairness criterion is enforced. Simulation results show that compared to the other two typical resource allocation algorithms, that is, the max-rate algorithm and the max–min fairness algorithm, the proposed algorithm achieves a good trade-off between the overall system throughput and the fairness.

On the optimality of max–min fairness in resource allocation

In this work, a basic resource allocation (RA) problem is considered, where a fixed capacity must be shared among a set of users. The RA task can be formulated as an optimization problem, with a set of simple constraints and an objective function to be minimized. A fundamental relation between the RA optimization problem and the notion of max–min fairness is established. A sufficient condition on the objective function that ensures the optimal solution is max–min fairness is provided. Notably, some important objective functions like least squares and maximum entropy fall in this case. Finally, an application of max–min fairness for overload protection in 3G networks is considered.

Stabilization of max–min fair networks without per-flow state

Let a flow be a sequence of packets that are sent from a source computer to a destination computer. In this paper, we consider the fair allocation of bandwidth to each flow in a computer network. We focus on max–min fairness, which assigns to each flow the largest possible bandwidth that avoids affecting other flows. What distinguishes our approach is that routers only maintain a constant amount of state, i.e., no per-flow state is maintained. This is consistent with trends in the Internet (such as the proposed Differentiated Services Internet architecture). In addition, to provide a high degree of fault-tolerance, we ensure our approach is self-stabilizing, that is, it returns to a normal operating state after a finite sequence of faults.

Distributed WFQ scheduling converging to weighted max–min fairness

This paper studies the fairness properties of distributed WFQ scheduling in buffered crossbars. Using a fluid model, we prove that these networks converge to ideal weighted max–min fair allocation. We simulate the cell-based system, and observe how close real rates come to the theoretical WMM fair: with buffer sizes of 2–5 cells per crosspoint, the average rate discrepancy is below 1%; the worst-case discrepancy falls below 4% with 4- to 8-cell buffers. We also study the transient phenomena when some flows come and go. We find that, after a change in a flow’s state, rate changes visit flows along non-circular paths, stabilizing them to their new fair rates; interestingly, some flows can affect all other active flows in the crossbar. Regarding the factors that influence the stabilization delay, although larger buffers yield more accurate convergence, they increase stabilization delay. Larger networks may also take more time to stabilize. Finally, convergence speeds up as the difference between the present rates and the WMM fair rates increases. Transient behavior simulations verify these results. Although we deal with data crossbar networks only, our analysis reveals complicated, “multi-hop” interactions among the flows in the crossbar, similar to those that can appear in arbitrary, point-to-point networks with distributed WFQ schedulers and backpressure mechanisms, such as the scheduling sub-system of a multi-stage switching fabric.

TrainNet: A transport system for delivering non real-time data

This paper proposes TrainNet, a vehicular network that uses trains to transport latency insensitive data. TrainNet augments a railway network by equipping stations and trains with mass storage devices; e.g., a rack of portable hard disks. TrainNet has two applications. First, it provides a low cost, very high bandwidth link that can be used to deliver nonreal-time data. In particular, network operators can use TrainNet to meet the high bandwidth requirement associated with Video on Demand (VoD) services. Moreover, TrainNet is able to meet this requirement easily because its links are scalable, meaning their capacity can be increased inexpensively due to the continual fall of hard disk price. Secondly, TrainNet provides an alternative, economically viable, broadband solution to any regions that are reachable via a railway. Therefore, using TrainNet, any communities closed to a train station will be able to gain access to bandwidth intensive digital contents such as music, video, television programs, and movies cheaply. A key problem in TrainNet is resource scheduling. This problem arises because hard disks have finite capacity, and only a fixed number of hard disks can be loaded and unloaded at each station. To this end, this paper proposes three max–min scheduling algorithms, namely local max–min fair (LMMF), global max–min fair (GMMF) and weighted global max–min fair (WGMMF), to ensure the space on hard disks are divided fairly amongst competing stations. To study these algorithms, a simulator is constructed using the DESMO-J framework to investigate the behavior of these max–min schedulers in scenarios with realistic traffic patterns. Results show that while LMMF is the fairest algorithm, it results in data loss and has the longest mean delay, the lowest average throughput, and the lowest hard disk utilization. Furthermore, according to Jain’s fairness index, WGMMF is the least fair algorithm. Despite that, it avoids data loss as is the case with GMMF, and achieves the best performance in terms of mean delay, averaged throughput, and hard disk utilization.

Scalable max–min fairness in wireless ad hoc networks

Our previous work proposes a macro model to perform flow and access control in wireless ad hoc networks. In this paper, we demonstrate specifically how to apply the model to achieve max–min fair rate allocation. Our proposed scheme is simple and scalable when comparing to other techniques in the literature. Moreover, it has the ability to provide stability in mobile environment. Simulation results show that our new method provides a good max–min fair flow assignment, and with that assignment, quality of service guarantees can be achieved for real-time applications.

An efficient bandwidth allocation algorithm for real-time VBR stream transmission under IEEE 802.16 wireless networks

This paper investigates variable rate control strategies for real-time multimedia variable bit rate (VBR) services over IEEE 802.16 broadband wireless networks. A data rate control mechanism is derived for the case where the uplink channel provides real-time services and the traffic rate parameter remains constant. This paper shows that the common queuing scheduling algorithms have some bandwidth allocation fairness problems for the real-time polling service (rtPS) in the MAC layer. In other words, the use of a VBR for the rtPS by a WiMAX system results in additional access latency jitter and bandwidth allocation disorder in the transmitted multimedia streams during the regular time interval polling of subscribe stations (SSs) for the contention bandwidth request period. However, the proposed scheduling algorithm solves these SSs contending with bandwidth resource allocation problems based on an extended rtPS (ertPS) of quality-of-service (QoS) pre-programming for a ranging response non-contention polling period. The adopted bandwidth allocation of max–min fairness queue scheduling uses a time constraint condition to transmit real-time multimedia VBR streaming in an IEEE 802.16 broadband wireless environment. In addition, we use the ns-2 simulation tool to compare the capacity of multimedia VBR stream and show that the proposed ertPS scheduling algorithm outperforms other rtPS scheduling algorithms.