Maximum Flow In Network Research Articles

A Maximum Concurrent Network Flow Based Channel Assignment Algorithm for Wireless Mesh Networks

We proposed a maximum concurrent network flow based channel assignment algorithm (MCFCA) for wireless networks. In the MCFCA algorithm, we first use the maximum concurrent network flow algorithm to compute the maximum network capacity, then we assign each link a priority according to its link throughput, finally the channel is assigned to minimize the interference between neighbor nodes in the priority order. Performance simulation shows its effectiveness in channel assignment.

On-Line Verification of Relay Protection Setting Based on Transmission Contribution Degree

In this paper, a new method that is based on the transmission contribution degree is proposed, which can effictively imprve on-line verification of relay protection setting.Actually, all protection devices of a line are treated as a whole in this method. Furthermore, the network maximum flow and complex network theory are both applied in this method, which is on the view of the structural point of the grid. The importance index of protection device in a line is determined by the transmission contribution degree. As a result, on-line verification of relay protection setting is according to the descending order of the indexes. IEEE 39-bus system is used to simulate, on the whole, the simulation and analysis of the calculation results to verify the reasonableness and correctness of the method.

Network flows modeling applied to the natural gas pipeline in Brazil

The use of natural gas during the last decades has been growing, and this trend will continue until 2030, according to the Brazilian energy plan issued by Ministry of Mines and Energy (2007a). However, the capacity of transportation is one of the important elements of the supply chain in response to the distribution market. In this context, the present study aims at identifying, in a regional and integrated way, the transportation capacity of the natural gas pipeline network. Therefore, a database and a mathematical model were developed to calculate the network maximum flow in order to enable analysis of the natural gas flow in the national network. The complex natural gas flow and the forecast of increasing demand justify the study of this issue, and the development of tools to help analyze the feasibility of implanting the decennial energy plan. The mathematical model used considers a linear programming to calculate the flows in the network. Data were collected about the operating companies, existing pipelines, handling capacity, historical flow and demand forecast. The delivery capacity in the consumer markets is also analyzed by means of economic and population index compared to the 2020 target. The results show a maximum nominal capacity of 213 MM m3 per day at reception points, and 227 MM m3 per day at delivery points. Idleness was found in the networks of the Northeast and Espírito Santo area (14% and 6.1%), and lack of capacity was found in the Southeast and South networks (11.6% and 9%), compared with the economic index of consumer centers near the networks. In comparison to the current flow, 75% of idleness was found. Idleness was identified in the networks of the Northeast and Espírito Santo areas (55% and 68%), and lack of capacity was identified in the Southeast and South networks (7% and 74%), in comparison to the 2020 target. In the analysis of the 2020 target, compared to the capacity in the metropolitan areas, lack of capacity was found in the metropolitan areas of Sao Paulo, Belo Horizonte, Fortaleza and South area (68%, 5%, 59% and 74%) and idleness was found in the areas of Vitória, Recife, Rio de Janeiro, Maceió, Aracaju, Salvador and Natal (85%, 72%, 40%, 93%, 8%, 58% and 17%).

Maximum dynamic network flow interdiction problem: New formulation and solution procedures

We consider the dynamic version of the maximum flow network interdiction problem; that is, we assume a positive number is assigned to each arc which indicates the traversal time of the flow through that arc. We also assume that an intruder uses a single resource with limited budget to interrupt the flow of a single commodity through the network within a given time limit of T. A new formulation based on the concept of Temporally Repeated Flow (TRF) is presented. The problem is then solved using Benders' decomposition. Another solution method, based on the most vital arcs in a network is also discussed. Finally, some computational results are reported.

Reduction of Maximum Flow Network Interdiction Problem: Step towards the Polynomial Time Solutions

In the present work an attempt is being made to reduce the Maximum Flow Network Interdiction Problem (MFNIP) in to the Subset Sum Problem so as to get some algorithms solvable in polynomial time. Previously developed algorithms are either applicable to some special cases of MFNIP or they do not have a constant performance guarantee. Our reduction has paved the way towards the development of fully polynomial time approximation schemes for Maximum Flow Network Interdiction Problem.

Connecting Networkwide Travel Time Reliability and the Network Fundamental Diagram of Traffic Flow

The existence of the network fundamental diagram (NFD) has been established at the urban network scale. It relates three traffic descriptors: speed, density, and flow. However, its deterministic nature does not convey the underlying variability within the network. In contrast, travel time reliability as a network performance descriptor is of growing concern to both the traveling public and traffic managers and policy makers. The objectives of this paper were to extend travel time reliability modeling from the link–path level to the network level and to connect overall network variability to NFD. Robust relationships between travel time variability and network density and flow rate were analytically derived, investigated, and validated with both simulated and real-world trajectory data. The distance-weighted standard deviation of travel time rate, as a measure of travel time variability, was found to increase monotonically with network density. A maximum network flow rate existed beyond which network travel time reliability deteriorated at a much faster pace. The results also suggest that these relationships are inherent network properties (signature) that are independent of demand level. The effects of en route information on the proposed relationships were also studied. The results showed that en route information reduced network travel time variability. The findings provide a strong connection between NFD and travel time variability, and this connection can be used further for modeling of network travel time reliability and assessment of measures intended to improve reliability of travel in a network.

Minimizing the maximum network flow: models and algorithms with resource synergy considerations

In this paper, we model and solve the network interdiction problem of minimizing the maximum flow through a network from a given source node to a terminus node, while incorporating different forms of superadditive synergy effects of the resources applied to the arcs in the network. Within this context, we examine linear, concave, and convex–concave synergy relationships, illustrate their relative effect on optimal solution characteristics, and accordingly develop and test effective solution procedures for the underlying problems. For a concave synergy relationship, which yields a convex programme, we propose an inner-linearization procedure that significantly outperforms the competitive commercial solver SBB by improving the quality of solutions found by the latter by 6.2% (within a time limit of 1800 CPU s), while saving 84.5% of the required computational effort. For general non-concave synergy relationships, we develop an outer-approximation-based heuristic that achieves solutions of objective value 0.20% better than the commercial global optimization software BARON, with a 99.3% reduction in computational effort for the subset of test problems for which BARON could identify a feasible solution within the set time limit.

The dual network theorem for static flow networks and its application for maximising the throughput flow

The paper discuses a new fundamental result in the theory of flow networks referred to as the ‘dual network theorem forstatic flow networks’. The theorem states that the maximum throughput flow in any static network is equal to the sum ofthe capacities of the edges coming out of the source, minus the total excess flow at all excess nodes, plus the maximumthroughput flow in the dual network. For very few imbalanced nodes in a flow network, determining the throughput flowin the dual network is a task significantly easier than determining the throughput flow in the original network. This createsthe basis of a very efficient algorithm for maximising the throughput flow in a network, by maximising the throughputflow in its dual network.Consequently, a new algorithm for maximising the throughput flow in a network has been proposed. For networks withvery few imbalanced nodes, in the case where only the maximum throughput flow is of interest, the proposed algorithmwill outperform any classical method for determining the maximum throughput flow.In this paper we also raise awareness of a fundamental flaw in classical algorithms for maximising the throughput flow instatic networks with directed edges. Despite the years of intensive research on static flow networks, the classicalalgorithms leave undesirable directed loops of flow in the optimised networks. These directed flow loops are associatedwith wastage of energy and resources and increased levels of congestion in the optimised networks. Consequently, analgorithm is also proposed for discovering and removing directed loops of flow in networks.

Flow Problems in Multi-Interface Networks

In heterogeneous networks, devices communicate by means of multiple wired or wireless interfaces. By switching among interfaces or by combining the available ones, each device might establish several connections. A connection may be established when the devices at its endpoints share at least one active interface. In this paper, we consider two fundamental optimization problems. In the first one (Maximum Flow in Multi-Interface Networks, MFMI), we aim to establish the maximal bandwidth that can be guaranteed between two given nodes of the input network. In the second problem (Minimum-Cost Flow in Multi-Interface Networks, MCFMI), we look for activating the cheapest set of interfaces among a network to guarantee a minimum bandwidth B of communication between two specified nodes. We show that MFMI is polynomially solvable while MCFMI is NP-hard even for a bounded number of different interfaces and bounded degree networks. Moreover, we provide polynomial approximation algorithms for MCFMI and exact algorithms for relevant subproblems. Finally, we experimentally analyze the proposed approximation algorithm, showing that in practical cases it guarantees a low approximation ratio.

Optimal data scheduling for P2P video-on-demand streaming systems

Peer-to-peer (P2P) overlay-based streaming services have became more and more attractive. However, it is still challenging to provide scalable streaming services over large-scale Internet environment beacause of the stringent quality of service requirements as well as the dynamic nature of P2P overlay network. In this study, the authors focus on the optimisation of streaming data scheduling in P2P video-on-demand (VoD) system, with the objective of minimising the server stress and maximising the playback continuity. The authors first model the data scheduling problem to the maximum network flow problem where the schedule scheme is transformed to find an optimal supplier-consumer relationship assigment among peers with minimal server strees, and then present two max-flow-based streaming data scheduling algorithms by combining the upload capacity of peers as well as the path capacity between peers. The authors prove that the computing complexing of the proposed scheduling algorithms is polynomial. The practicability of the proposal is evaluated via simulations. Simulation results indicate that the proposed scheduling scheme could distribute bandwidth load among peers well while keeping the node degree low. Simulation results also show that the novel proposal has better performance than previous work in term of the server stress and the playback continuity.

Minimize Traffic Congestion: An Application of Maximum Flow in Dynamic Networks

Minimize Traffic Congestion: An Application of Maximum Flow in Dynamic NetworksAn important characteristic of a network is its capacity to carry flow. What, given capacities on the arcs, is the maximum flow that can be sent between any two nodes? The dynamic version of the maximum flow problem on networks that generalizes the well-known static one. This basic combinatorial optimization problem has a large implementation for many practical problems. Traffic congestion is a consequence of the nature of supply and demand: capacity is time consuming and costly to build and is fixed for long time periods, demand fluctuates over time, and transport services cannot be stored to smooth imbalances between capacity and demand. In this paper, I tried to solve the traffic congestion problem i.e. Maximum flow of goods in a dynamic network with the help of a Lingo Model. The same can be generalized for the large product if the software supports the systems.

Algorithm for Minimum Cost Maximum Flow in Transportation Network

Minimum Cost Maximum Flow Problem (MCMFP) is to find the maximum flow with minimal total cost, i.e., the minimum cost maximum flow, in transportation network. In this paper, MCMFP is formulated using a bi-level programming model. As a solution method of the model, an algorithm named MCMF-A is proposed. The basic idea of the MCMF-A algorithm can be described as follows: first find a maximum flow without opposite flow in transportation network, next construct its residual network with regard to the maximum flow, then find a negative-cost cycle in the residual network by calling well-known Floyd Algorithm; if Floyd Algorithm finds that there is no negative-cost cycle in the residual network, then the maximum flow is minimum cost maximum flow, else adjust the maximum flow via the negative-cost cycle to get a new maximum flow with no opposite flow and less total transportation cost. The theory, on which the MCMF-A algorithm is based, is presented. The MCMF-A algorithm can find the optimal solution to MCMFP, and has good performance in the sense of being implemented on computer, computational time and required memory for computation. Numerical experiments demonstrate that the MCMF-A algorithm is an efficient and robust method to solve MCMFP, which can serve as an effective tool to solve other related optimization problems.

Research on the Maximum Flow of Air Traffic Network Based on Discrete Time Loss Queuing

As maximum flow could be used as a significant indicator of congestion in air traffic network, the flow model was then proposed in the study. When air traffic was influenced by emergencies, this model, adopting the discrete time loss queuing, could obtain the transition probability matrix by building conflicting factors. Then, with the loss probability of network, the theoretical maximum flow was calculated.

An Asynchronous Multithreaded Algorithm for the Maximum Network Flow Problem with Nonblocking Global Relabeling Heuristic

In this paper, we present a novel asynchronous multithreaded algorithm for the maximum network flow problem. The algorithm is based on the classical push-relabel algorithm, which is essentially sequential and requires intensive and costly lock usages to parallelize it. The novelty of the algorithm is in the removal of lock and barrier usages, thereby enabling a much more efficient multithreaded implementation. The newly designed push and relabel operations are executed completely asynchronously and each individual process/thread independently decides when to terminate itself. We further propose an asynchronous global relabeling heuristic to speed up the algorithm. We prove that our algorithm finds a maximum flow with O(\vert V\vert^2\Vert E\vert ) operations, where \vert V\vert is the number of vertices and \vert E\vert is the number of edges in the graph. We also prove the correctness of the relabeling heuristic. Extensive experiments show that our algorithm exhibits better scalability and faster execution speed than the lock-based parallel push-relabel algorithm.

Optimal Packet Scheduling in WDM Optical Switches With Output Buffer and Limited Wavelength Conversion

All-optical packet switching is a promising candidate for future high-speed switching. However, due to the absence of optical random access memory, the traditional Virtual Output Queue (VOQ) based input-queued switches are difficult to implement in the optical domain. In this paper we consider output-buffered optical packet switches. We focus on packet scheduling in an output-buffered optical packet switch with limited-range wavelength conversion, aiming at maximizing throughput and minimizing average queuing delay simultaneously. We show that this problem can be converted to a minimum cost maximum network flow problem. To cope with the high complexity of general network flow algorithms, we present an algorithm that can efficiently find an optimal schedule in O(min{NW,BW}) time, where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is the switch size, W is the number of wavelength channels per fiber and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> is the length of the longest FDL at the output of the switch. The complexity of the new algorithm asymptotically matches the lower bound of the scheduling problem. We also conduct extensive simulations to test the performance of the proposed scheduling algorithm under different traffic models.

Algoritmos de fluxo máximo em rede aplicado em gerenciamento de fluxo de tráfego aéreo

This paper presents the air traffic Flow Balancing Model (FBM) which uses network maximum flow algorithms to accomplish air traffic flow management in the flight information regions under Brazilian control responsibility . Four maximum flow algorithms were implemented and tested in this work: Edmonds-Karp, Dinic, FIFO Preflow Push and Highest Label Preflow Push. Each algorithm has its particular method to calculate the maximum flow value, that results in different air traffic flow balancing solutions. A case study comparing the results for each algorithm is presented, and the results represent different balancing options that allow the traffic flow managers to choose which one better adapts to the tactical air traffic management scenery under analysis.

Why locally-fair maximal flows in client-server networks perform well

Maximal flows reach at least a 1/2 approximation of the maximum flow in client-server networks. By adding 1 additional time round to any distributed maximal flow algorithm we show how this 1/2-approximation can be improved on bounded-degree networks. We call these modified maximal flows `locally fair' since there is a measure of fairness prescribed to each client and server in the network. Let N=(U,V,E,b) represent a client-server network with clients U, servers V, network links E, and node capacities b, where we assume that each capacity is at least one unit. Let d(u) denote the b-weighted degree of any node u?U?V, Δ=max?{d(u)|u?U} and ?=min?{d(v)|v?V}. We show that a locally-fair maximal flow f achieves an approximation to the maximum flow of $\min\{1,\frac{\varDelta^{2}-\delta}{2\varDelta^{2}-\delta\varDelta-\varDelta}$ }, and this result is sharp for any given integers ? and Δ. This results are of practical importance since local-fairness loosely models the steady-state behavior of TCP/IP and these types of degree-bounds often occur naturally (or are easy to enforce) in real client-server systems.

Applications of Maximal Network Flow Problems in Transportation and Assignment Problems

This paper presents some modifications of Ford-Fulkerson’s labeling method for solving the maximal network flow problemwith application in solving the transportation and assignment problems. The modifications involve the tree representationof the nodes labeled and the edges used them. It is shown that after each flow adjustment some of the labels canbe retained for the next labeling process. Through certain computational aspects it has been suggested that to indicatethat with theses the primal-dual approach for solving the transportation and assignment problems is improved to certainextent.

The Maximum Flow Network Interdiction Problem: Valid inequalities, integrality gaps, and approximability

We present two classes of polynomially separable valid inequalities for the Maximum Flow Network Interdiction Problem. We prove that the integrality gap of the standard integer program is not bounded by a constant, even when strengthened by our valid inequalities. Finally, we provide an approximation-factor-preserving reduction from a simpler interdiction problem.

Capacity factors of a mixed speed railway network

Fifty-four combinations of track network and speed differential are evaluated within a linear, discrete time network model that maximizes an objective function of train volume, delays, and idle train time. The results contradict accepted dispatching practice by suggesting that when introducing a priority, high-speed train onto a network, maximum network flow is attained when the priority train operates at maximum speed. In addition, increasing siding capacity at meeting points may offer a network capacity improvement comparable to partial double track.