Un modelo de difusión anisótropa para el estudio del tráfico urbano

In order to design or redesign urban transportation networks, the employment of mathematical models is very useful for predicting the effects of possible modifications of implementing. Such models allow the determination of vehicular flows and travel times for every link of the network from the knowledge of its inherent features and the corresponding traffic demand. They are based on a phenomenological law of the social collective behavior of the drivers called Wardrop principle. It is an optimization problem, in general, very demanding from the computational point of view.In order to accelerate the computation process, in this paper, a continuum model for the urban traffic is proposed. The fundamental assumption behind this theory is that the variation of network properties is small in close regions when compared with the full system. Accordingly, it is possible to use continuous functions for representing travel times or vehicular flows. Essentially, the problem is formulated as a system of non-linear anisotropic diffusion (differential) equations that can be conveniently solved by means of the finite element method. The efficiency of the proposed model is studied by means of a comparison with results obtained with the classical optimization approach. As shown, the results are similar although the computation times are significantly reduced.     

A framework for user equilibrium dynamic traffic assignment

Several analytic approaches have been developed to describe or predict traffic flows on networks with time-varying (dynamic) travel demands, flows and travel times. A key component of these models lies in modelling the flows and/or travel times on the individual links, but as this is made more realistic or accurate it tends to make the overall model less computationally tractable. To help overcome this, and for other reasons, we develop a bi-level user equilibrium (UE) framework that separates the assignment or loading of flows on the time–space network from the modelling of flows and trip times within individual links. We show that this model or framework satisfies appropriate definitions of UE satisfies a first-in-first-out (FIFO) property of road traffic, and has other desirable properties. The model can be solved by iterating between (a) a linear network-loading model that takes the lengths of time–space links as fixed (within narrow ranges), and (b) a set of link flow sub-models which update the link trip times to construct a new time–space network. This allows links to be processed sequentially or in parallel and avoids having to enumerate paths and compute path flows or travel times. We test and demonstrate the model and algorithms using example networks and find that the algorithm converges quickly and the solutions behave as expected. We show how to extend the model to handle elastic demands, multiple destinations and multiple traffic types, and traffic spillback within links and from link to link.     

A path-based double projection method for solving the asymmetric traffic network equilibrium problem

In this paper we propose a new iterative method for solving the asymmetric traffic equilibrium problem when formulated as a variational inequality whose variables are the path flows. The path formulation leads to a decomposable structure of the constraints set and allows us to obtain highly accurate solutions. The proposed method is a column generation scheme based on a variant of the Khobotov’s extragradient method for solving variational inequalities. Computational experiments have been carried out on several networks of a medium-large scale. The results obtained are promising and show the applicability of the method for solving large-scale equilibrium problems. This work has been supported by the National Research Program FIRB/RBNE01WBBBB on Large Scale Nonlinear Optimization.     

结点有约束的交通网络最短路径模型

结点有约束的网络是一类特殊的网络，如具有禁止通行限制信息的交通路网等，由于最短路径的求解是有后效性的，经典的Dijkstra算法等不能直接用来求解该问题，本文提出了一种结点有约束的交通网络最短路径建模方法，该方法所建模型为一般网络模型，可用任一传统高效的算法求其最短路径，从根本上降低了问题的复杂性，为很好地解决交通、通信等领域中的此类问题提供了有益的方法。     

高速公路行车时间估计和最优路径

行车时间估计和最优路径选择是智能交通系统中的研究热点,特别是对于车辆导航系统更具有深远的意义.首先以传统的交通流理论为基础,采用间接模型和动力学模型进行行车时间估计,通过仿真实验比较了两模型的优劣,并使用实测数据分析得到的车流量信息对动力学模型进行改进.然后使用Dijkstra算法寻找出静态状态下的最优路径,再结合前面建立的时间估计模型,给出了适用于动态随机状态下的路径寻优算法,用于解决路段行车时间期望随出发时刻动态变化的问题.最后指出了交通实时信息对解决动态随机最优路线问题的重要性,并结合卡尔曼滤波算法对路段相关的情况作了进一步讨论.     

An adjoint-based pressure correction scheme

Incompressible flows are solenoidal, i. e. the divergence of the flow field is zero. This is an algebraic constraint on the solution in time. The pressure has to be determined, so that the constraint is fulfilled. To calculate the pressure often a Poisson equation is derived, which is then solved by an iterative method. Instead of this the constraint is here formulated as an optimization problem. The objective functional is taken as the square of the norm of the divergence. A gradient based optimization is performed to calculate the pressure in every time step of the simulation. By this an alternative iterative scheme is derived. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Joint optimization traffic signal control for an urban arterial road

This paper considers the optimal traffic signal setting for an urban arterial road. By introducing the concepts of synchronization rate and non-synchronization degree, a mathematical model is constructed and an optimization problem is posed. Then, a new iterative algorithm is developed to solve this optimal traffic control signal setting problem. Convergence properties for this iterative algorithm are established. Finally, a numerical example is solved to illustrate the effectiveness of the method.     

A network traffic flow model for motorway and urban highways

The research reported in this paper develops a network-level traffic flow model (NTFM) that is applicable for both motorways and urban roads. It forecasts the traffic flow rates, queue propagation at the junctions and travel delays through the network. NTFM uses sub-models associated with all road and junction types that comprise the highway. The flow at any one part of the network is obviously very dependent on the flows at all other parts of the network. To predict the two-way traffic flow in NTFM, an iterative simulation method is executed to generate the evolution of dependent traffic flows and queues. To demonstrate the capability of the model, it is applied to a small case study network and a local Loughborough–Nottingham highway network. The results indicate that NTFM is capable of identifying the relationship between traffic flows and capturing traffic phenomena such as queue dynamics. By introducing a reduced flow rate on links of the network, the effects of strategies used to carry out roadworks can be mimicked.     

Supervisory control of hybrid systems based on model abstraction and guided search

This paper addresses the task of computing supervisory controllers by which hybrid systems with nonlinear continuous dynamics are driven into goal sets while safety specifications are met. For this class of systems, the (conservatively approximative) determination of reachable states is an important but also a computationally expensive step of the controller synthesis. This contribution proposes a technique aiming at reducing the reach set computation by using abstract models and guided search. For a discrete abstraction of the hybrid model, candidate paths are determined as possible controlled evolutions which fulfill the given specifications. A validation scheme comprising three different techniques is applied to determine whether the candidate path represents a feasible control strategy for the hybrid system. If the specification is violated, the abstract model is refined according to the validation result. The iterative application of the determination of candidate paths, the path validation and the model refinement steers the search for a control strategy such that often only a relatively small part of the reachable state space has to be explored. The synthesis procedure is illustrated for two examples.     

Iterative solution techniques for finite element applications

An iterative solver has been recently developed to solve very large systems of linear equations. The application of such a solver in commercial finite element software is not yet accepted. The purpose of the paper is to describe the new iterative solver and report on the practical application of this capability in different fields of interest.

The iterative solver uses the conjugate gradient method and employs two types of preconditioning: the traditional Jacobi and the incomplete Cholesky decomposition method. An option has been added for diagonal scaling to handle matrices whose entries greatly differ in magnitude. This paper illustrates the reduction possible in both central processor time and disk storage for problems with very large, well-conditioned matrices. Problems arising in electromagnetic analysis as well as in structural analysis have been solved with different options available in the iterative solver and compared with the standard, direct solver results. Guidelines on the use of the new solver and the status of research on even more efficient preconditioners are given.     

On the Accuracy of the MAP Inference in HMMs

In a hidden Markov model, the underlying Markov chain is usually unobserved. Often, the state path with maximum posterior probability (Viterbi path) is used as its estimate. Although having the biggest posterior probability, the Viterbi path can behave very atypically by passing states of low marginal posterior probability. To avoid such situations, the Viterbi path can be modified to bypass such states. In this article, an iterative procedure for improving the Viterbi path in such a way is proposed and studied. The iterative approach is compared with a simple batch approach where a number of states with low probability are all replaced at the same time. It can be seen that the iterative way of adjusting the Viterbi state path is more efficient and it has several advantages over the batch approach. The same iterative algorithm for improving the Viterbi path can be used when it is possible to reveal some hidden states and estimating the unobserved state sequence can be considered as an active learning task. The batch approach as well as the iterative approach are based on classification probabilities of the Viterbi path. Classification probabilities play an important role in determining a suitable value for the threshold parameter used in both algorithms. Therefore, properties of classification probabilities under different conditions on the model parameters are studied.     

综合型交通分配问题的一种模型及算法

本文针对我国城市交通状况的特点,综合分析交通网络中自行车、公交车,一般机动车三种基本方式的交通流,建立了一个综合型交通分配问题的数学模型,给出了求解它的比较实用的迭代算法,推广并改进了Sheffi等的结果.     

Traffic assignment model with fuzzy level of travel demand: An efficient algorithm based on quasi-Logit formulas

The place of fuzzy concepts in traffic assignment (TA) models has been studied in recent literature. Keeping fuzzy level of travel demand in mind, we propose a new TA model in which the travel costs of links are depended on their congestion. From the results of such fuzzy TA model, network planners are able to estimate the number of travelers on network links. By using zero–one variables, the proposed model is transformed into a crisp mixed-integer problem with respect to path-flow variables. In order to produce the Logit flows from this problem, Damberg et al. algorithm is modified. Then, the level of certainty is maximized and perceived travel delays are minimized. For a fixed certainty degree, the obtained solution, which is named the fuzzy equilibrium flow, satisfies a quasi-Logit formula similar to ordinary expression of the Logit route choice model. Eventually, we examine the quality of different path enumeration techniques in the proposed model.     

A fast non-iterative numerical algorithm to predict unsteady partial cavitation on hydrofoils

A new algorithm to predict partial sheet cavity behavior on hydrofoils is proposed. The proposed algorithm models the unsteady partial cavitation using Boundary Element Method (BEM). In the proposed method the spatial iterative scheme is removed by means of a new approach determining the instantaneous cavity length. This iterative scheme is required in conventional algorithms to obtain the cavity length at each time step. Performance of the new algorithm for various unsteady cavitating flows with different reduced frequencies, cavitation numbers, hydrofoil geometries and inflow conditions are investigated. Comparison between the obtained results using the proposed method and those of conventional ones indicates that the present algorithm works well with sufficient accuracy. Moreover, it is shown that the proposed method is computationally more efficient than the conventional one for unsteady sheet cavitation analysis on hydrofoils.     

An accurate solution procedure for fluid flow with natural convection

We consider the Boussinesq model of buoyancy driven fluid flows. This nonlinear system is solved numerically using a two level finite element method. On the first level, a nonlinear system is solved on a very coarse mesh. Thereafter, a linear system is solved on a fine mesh.

In a standard approach, one might obtain the numerical solution from a discretization of the original, nonlinear system using the same fine mesh.

Both solutions are of equal order of accuracy if the mesh widths are properly balanced. Therefore the two level method is very efficient.     

Unique solvability of the periodic Cauchy problem for wave-hierarchy problems with dissipation

Wave-hierarchy problems appear in a variety of applications such as traffic flows, roll waves down an open inclined channel and multiphase flows. Usually, these are described by the compressible Navier-Stokes equations with specific non-linearities; in a fluidized bed model they contain an additional pressure gradient term and are supplemented by an elliptic equation for this unknown pressure. These equations admit solutions periodic in space as well as in time, i.e. periodic travelling waves. Therefore, the corresponding initial value problem with periodic boundary conditions is solved locally in time in appropriate Sobolev spaces. Some remarks are made concerning global solutions, the occurrence of clusters or voids and the bifurcation of time periodic solutions, respectively.     

Performance analysis of CONWIP systems with batch size constraints

Multi-product manufacturing systems operating under CONWIP control are often modeled as closed queuing networks with synchronization stations. Performance analysis of these systems can be challenging, especially when batch size constraints are explicitly considered. This research develops a new approach for evaluating the performance of these systems based on parametric characterizations and traffic process approximations. The approach explicitly models the effect of batch size constraints on the departure process and waiting times at the different stations in the network to derive new characterization equations. These equations are used to derive a set of linking equations that is solved using an iterative algorithm to obtain estimates of network performance. Numerical studies indicate that the proposed method is yields fairly accurate performance estimates and can be useful in evaluating tradeoffs that guide managerial decisions.     

A branch and bound method for the job-shop problem with sequence-dependent setup times

This paper deals with the job-shop scheduling problem with sequence-dependent setup times. We propose a new method to solve the makespan minimization problem to optimality. The method is based on iterative solving via branch and bound decisional versions of the problem. At each node of the branch and bound tree, constraint propagation algorithms adapted to setup times are performed for domain filtering and feasibility check. Relaxations based on the traveling salesman problem with time windows are also solved to perform additional pruning. The traveling salesman problem is formulated as an elementary shortest path problem with resource constraints and solved through dynamic programming. This method allows to close previously unsolved benchmark instances of the literature and also provides new lower and upper bounds.     

A simplicial decomposition algorithm for solving the variational inequality formulation of the general traffic assignment problem for large scale networks

Summary The class of simplicial decomposition methods has been shown to constitute efficient tools for the solution of the variational inequality formulation of the general traffic assignment problem. This paper presents a particular implementation of such an algorithm, with emphasis on its ability to solve large scale problems efficiently. The convergence of the algorithm is monitored by the primal gap function, which arises naturally in simplicial decomposition schemes. The gap function also serves as an instrument for maintaining a reasonable subproblem size, through its use in column dropping criteria. The small dimension and special structure of the subproblems also allows for the use of very efficient algorithms; several algorithms in the class of linearization methods are presented. When restricting the number of retained extremal flows in a simplicial decomposition scheme, the number of major iterations tends to increase. For large networks the shortest path calculations, leading to new extremal flow generation, require a large amount of the total computation time. A special study is therefore made in order to choose the most efficient extremal flow generation technique. Computational results on symmetric problems are presented for networks of some large cities, and on asymmetric problems for some of the networks used in the literature. Computational results for bimodal models of some large cities leading to asymmetric problems are also discussed.     

道路维修施工路段交通分流信控优化模型

针对道路维修施工期间常采用的部分路面封闭施工且利用辅路进行分流的情形,探讨了交通分流信控优化模型。借助交通流波动理论,分析了施工路段及其前后车流拥挤排队及疏散特征和规律,分析了对车流进行控制需满足的约束,并分析了车流的延误计算公式。以总的车辆行驶时间最小化目标,原路径及分流路径的绿时分配及信号周期为优化参数,考虑交通分流控制的各种约束,建立了道路施工路段交通分流信控优化模型。分析了该模型属于非凸问题,因此提出了一种近似求解最优解的办法。通过一个示例对模型和求解算法进行了验证,并对一些规律性结果进行了分析。