求解用户平衡与系统最优模型的新算法

近些年,国内外许多学者针对交通规划提出了诸如用户平衡(UE)、系统最优(SO)等模型,但由于交通网络的复杂性,这些模型的求解相对困难,考虑到在一般的UE、S0模型中,其约束条件为线性约束与非负约束,给出一种求解交通规划模型的新算法,算法不需使用任何线搜索,只要通过求解一个简单的二次规划问题得到下降方向即可,最后,将该算法应用到简单的交通网络中,并通过与相继平均法(MSA)进行比较,验证了该算法的收敛速度较快。     

Chaos in a dynamic model of urban transportation network flow based on user equilibrium states

In this study, we investigate the dynamical behavior of network traffic flow. We first build a two-stage mathematical model to analyze the complex behavior of network flow, a dynamical model, which is based on the dynamical gravity model proposed by Dendrinos and Sonis [Dendrinos DS, Sonis M. Chaos and social-spatial dynamic. Berlin: Springer-Verlag; 1990] is used to estimate the number of trips. Considering the fact that the Origin–Destination (O–D) trip cost in the traffic network is hard to express as a functional form, in the second stage, the user equilibrium network assignment model was used to estimate the trip cost, which is the minimum cost of used path when user equilibrium (UE) conditions are satisfied. It is important to use UE to estimate the O–D cost, since a connection is built among link flow, path flow, and O–D flow. The dynamical model describes the variations of O–D flows over discrete time periods, such as each day and each week. It is shown that even in a system with dimensions equal to two, chaos phenomenon still exists. A “Chaos Propagation” phenomenon is found in the given model.     

Day-to-day evolution of the traffic network with Advanced Traveler Information System

Since the notion of user equilibrium (UE) was proposed by Wardrop [13], it has become a cornerstone for traffic assignment analysis. But, it is not sufficient to only ask whether equilibrium exists or not; it is equally important to ask whether and how the system can achieve equilibrium. Meanwhile, stability is an important performance in the sense that if equilibrium is unsustainable, both the equilibrium and the trajectory are sensitive to disturbances, even a small perturbation will result in the system evolution away from the equilibrium point. These incentive a growing interest in day-to-day dynamics. In this paper, we develop a dynamical system with Advanced Traveler Information System (ATIS) and study the stability of the network with ATIS. A simple network is used to simulate the model, and the results show that there exist periodic attractors in the traffic network in some cases (for example, the market penetration level of ATIS is 0.25 and traffic demand is 2 unit). It is found that the logit parameter of the dynamical model and the traffic demand can also affect the stability of the traffic network. More periodic attractors appear in the system when the traffic demand is large and the low logit parameter can delay the appearance of periodic attractors. By simulation, it can be concluded that if the range of the periodic attractors’ domain of the simple network is known, the road pricing based on the range of the attraction domain is effective to alleviate the instability of the system.     

An N-path user equilibrium for transportation networks

The traditional trip-based approach to transportation modeling has been employed for the past decade. The last step of the trip-based modeling approach is traffic assignment, which has been typically formulated as a user equilibrium (UE) problem. In the conventional perspective, the definition of UE traffic assignment is the condition that no road user can unilaterally change routes to reduce their travel time. An equivalent definition is that the travel times of all the used paths between any given origin–destination pair are equal and less than those of the unused paths. The underlying assumption of the UE definition is that road users have full information on the available transportation paths and can potentially use any path if the currently used path is overly congested. However, a more practical scenario is that each road user has a limited path set within which she/he can choose routes from. In this new scenario, we call the resulting user equilibrium an N-path user equilibrium (NPUE), in which each road user has only N paths to select from when making route choices in the network. We introduce a new formulation of the NPUE and derive optimality conditions based on this formulation. Different from traditional modeling framework, the constraints of the proposed model are of linear form, which makes it possible to solve the problem with conventional convex programming techniques. We also show that the traditional UE is a special case of an NPUE and prove the uniqueness of the resulting flow pattern of the NPUE. To efficiently solve this problem, we devise path-based and link-based solution algorithms. The proposed solution algorithms are empirically applied to networks of various sizes to examine the impact of constrained user path sets. Numerical results demonstrate that NPUE results can differ significantly from UE results depending on the number of paths available to road users. In addition, we observed an interesting phenomenon, where increasing the number of paths available to road users can sometimes decrease the overall system performance due to their selfish routing behaviors. This paradox demonstrates that network information should be provided with caution, as such information can do more harm than good in certain transportation systems.     

Modeling demand management strategies for evacuations

Evacuations are massive operations that create heavy travel demand on road networks some of which are experiencing major congestions even with regular traffic demand. Congestion in traffic networks during evacuations, can be eased either by supply or demand management actions. This study focuses on modeling demand management strategies of optimal departure time, optimal destination choice and optimal zone evacuation scheduling (also known as staggered evacuation) under a given fixed evacuation time assumption. The analytical models are developed for a system optimal dynamic traffic assignment problem, so that their characteristics can be studied to produce insights to be used for large-scale solution algorithms. While the first two strategies were represented in a linear programming (LP) model, evacuation zone scheduling problem inevitable included integers and resulted in a mixed integer LP (MILP) one. The dual of the LP produced an optimal assignment principle, and the nature of the MILP formulations revealed clues about more efficient heuristics. The discussed properties of the models are also supported via numerical results from a hypothetical network example.     

Using fuzzy integral for evaluating subjectively perceived travel costs in a traffic assignment model

A good traffic assignment model can be a powerful tool to describe the characteristics of traffic behavior in a road network. The traffic assignment results often play an important role in transportation planning, e.g., an optimal and economical network design. Many traditional traffic assignment models rely heavily on the travel cost function established by Wardrop’s principles; however, the Wardrop’s travel cost function has been proven to be weak for explaining the uncertainty and interactivity of traffic among links. This study tries to construct a traffic assignment model that is different from Wardrop’s in many aspects. First, it considers the cross-effect among the links. Second, a fuzzy travel cost function is established based on the possibility concept instead of precise calculation of traffic volumes. Third, the techniques of fuzzy measure and fuzzy integral are applied to calculate the subjectively perceived travel costs during traffic assignment. Furthermore, in order to validate our model, a detailed network with 22 nodes and 36 links is used to illustrate it. Study results show that our model explains more interactivity and uncertainty of traffic among links when compared with the traditional model of Wardrop’s.     

多用户类多准则交通分配的势博弈与拥挤定价

交通管理者在解决路网拥挤问题时,并不知道出行者的出行效用,同时管理者难以对出行者的路径选择行为做出准确的观测.运用势博弈理论分析多用户类多准则交通行为的演化过程,得到了固定需求和弹性需求情形下的可容许动态(一种刻画出行者通过转换路径增加当前效用的近似调整行为的演化动态),证明当路段时间函数和逆需求函数为严格单调、连续、可微时,所对应的交通分配是势博弈问题的惟一Nash均衡点.进一步研究了固定需求下的可变拥挤道路收费问题,得到了在当前系统状态下实现系统最优交通分配的拥挤收费水平.     

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.     

Bounding the inefficiency of logit-based stochastic user equilibrium

Bounding the inefficiency of selfish routing has become an emerging research subject. A central result obtained in the literature is that the inefficiency of deterministic User Equilibrium (UE) is bounded and the bound is independent of network topology. This paper makes a contribution to the literature by bounding the inefficiency of the logit-based Stochastic User Equilibrium (SUE). In a stochastic environment there are two different definitions of system optimization: one is the traditional System Optimum (SO) which minimizes the total actual system travel time, and the other is the Stochastic System Optimum (SSO) which minimizes the total perceived travel time of all users. Thus there are two ways to define the inefficiency of SUE, i.e. to compare SUE with SO in terms of total actual system travel time, or to compare SUE with SSO in terms of total perceived travel time. We establish upper bounds on the inefficiency of SUE in both situations.     

Handling uncertainty in route choice models: From probabilistic to possibilistic approaches

In order to design effective advanced traffic information systems (ATIS) suitable mathematical models have to be defined to simulate the effects of information on users route choice behaviour and then to incorporate it into traffic assignment models to estimate how traffic demand loads the roads network.To face this problem it is necessary to deal with uncertainty that plays a crucial role in the users decision-making processes.To this purpose this paper first analyses how uncertainty affects users’ route choice process and how traffic assignment models may take it into account.In literature route choice behaviour modelling is widely solved within the random utility theory framework but, we show in this paper that such an approach only considers one type of uncertainty. More precisely, the consideration of randomness of traffic by drivers is, for example, hardly ever represented in classical models in spite of its importance in the management of information by drivers.Starting from the presented analysis a new route choice model is also proposed to represent explicitly the uncertainty lying in users’ route choice behaviour. It is based on recent developments in possibility theory which is an alternate way to probability theory in order to represent or measure uncertainty.     

Application of a simulation-based dynamic traffic assignment model

The evaluation of on-line intelligent transportation system (ITS) measures, such as adaptive route-guidance and traffic management systems, depends heavily on the use of faster than real time traffic simulation models. Off-line applications, such as the testing of ITS strategies and planning studies, are also best served by fast-running traffic models due to the repetitive or iterative nature of such investigations. This paper describes a simulation-based, iterative dynamic equilibrium traffic assignment model. The determination of time-dependent path flows is modeled as a master problem that is solved using the method of successive averages (MSA). The determination of path travel times for a given set of path flows is the network-loading sub-problem, which is solved using the space-time queuing approach of Mahut. This loading method has been shown to provide reasonably accurate results with very little computational effort. The model was applied to the Stockholm road network, which consists of 2100 links, 1191 nodes, 228 zones, representing and 4964 turns. The results show that this model is applicable to medium-size networks with a very reasonable computation time.     

Integrating link-based discrete credit charging scheme into discrete network design problem

In this paper, we present an optimization model for integrating link-based discrete credit charging scheme into the discrete network design problem, to improve the transport performance from the perspectives of both transport network planning and travel demand management. The proposed model is a mixed-integer nonlinear bilevel programming problem, which includes an upper level problem for the transport authority and a lower level problem for the network users. The lower level sub-model is the traffic network user equilibrium (UE) formulation for a given network design strategy determined by the upper level problem. The network user at the lower level tries to minimize his/her own generalized travel cost (including both the travel time and the value of the credit charged for using the link) by choosing his/her route. While the transport authority at the upper level tries to find the optimal number of lanes and credit charging level with their locations to minimize the total system travel time (or maximize the transportation system performance). A genetic algorithm is used to solve the proposed mixed-integer nonlinear bilevel programming problem. Numerical experiments show the efficiency of the proposed model for traffic congestion mitigation, reveal that interaction effects across the tradable credit scheme and the discrete network design problem which amplify their individual effects. Moreover, the integrated model can achieve better performance than the sequential decision problems.     

Modelling dynamic network loading ontransportation networks through a continuous

The efforts spent by researchers in the last few years in traffic modelling have been focused on the modelization of dynamic behaviour of the several components making up a transportation system.In the field of traffic assignment, a large number of models and procedures have been proposed in order to perform Dynamic Network Loading (DNL), that is the reproduction of within-day variable link performances once a corresponding Origin/Destination (O/D) demand and users' choice model has been given. These models can be used both to evaluate traffic flows and, what is more relevant, to simulate the effects of regulation strategies on users' behaviour.

In this paper, after a brief review of the state of the art in this field, a continuous dynamic network loading model is proposed; it removes some of the drawbacks of other packet approach models proposed in literature and explicitly allows the en-route modification of the followed path. An algorithmic development of the model and a set of applications on text networks are also proposed.     

User equilibrium traffic network assignment with stochastic travel times and late arrival penalty

The classical Wardrop User Equilibrium (UE) assignment model assumes traveller choices are based on fixed, known travel times, yet these times are known to be rather variable between trips, both within and between days; typically, then, only mean travel times are represented. Classical Stochastic User Equilibrium (SUE) methods allow the mean travel times to be differentially perceived across the population, yet in a conventional application neither the UE or SUE approach recognises the travel times to be inherently variable. That is to say, there is no recognition that drivers risk arriving late at their destinations, and that this risk may vary across different paths of the network and according to the arrival time flexibility of the traveller. Recent work on incorporating risky elements into the choice process is seen either to neglect the link to the arrival constraints of the traveller, or to apply only to restricted problems with parallel alternatives and inflexible travel time distributions. In the paper, an alternative approach is described based on the ‘schedule delay’ paradigm, penalising late arrival under fixed departure times. The approach allows flexible travel time densities, which can be fitted to actual surveillance data, to be incorporated. A generalised formulation of UE is proposed, termed a Late Arrival Penalised UE (LAPUE). Conditions for the existence and uniqueness of LAPUE solutions are considered, as well as methods for their computation. Two specific travel time models are then considered, one based on multivariate Normal arc travel times, and an extended model to represent arc incidents, based on mixture distributions of multivariate Normals. Several illustrative examples are used to examine the sensitivity of LAPUE solutions to various input parameters, and in particular its comparison with UE predictions. Finally, paths for further research are discussed, including the extension of the model to include elements such as distributed arrival time constraints and penalties.     

Location-allocation models for traffic police patrol vehicles on an interurban network

This research investigates the traffic police routine patrol vehicle (RPV) assignment problem on an interurban road network through a series of integer linear programs. The traffic police RPV’s main task, like other emergency services, is to handle calls-for-service. Emergency services allocation models are generally based on the shortest path algorithm however, the traffic police RPV also handles other roles, namely patrolling to create a presence that acts as a deterrence, and issuing tickets to offenders. The RPVs need to be located dynamically on both hazardous sections and on roads with heavy traffic in order to increase their presence and conspicuousness, in an attempt to prevent or reduce traffic offences, road accidents and traffic congestion. Due to the importance of the traffic patrol vehicle’s location with regard to their additional roles, allocation of the RPVs adheres to an exogenous, legal, time-to-arrival constraint. We develop location-allocation models and apply them to a case study of the road network in northern Israel. The results of the four models are compared to each other and in relation to the current chosen locations. The multiple formulations provide alternatives that jointly account for road safety and policing objectives which aid decision-makers in the selection of their preferred RPV assignments. The results of the models present a location-allocation configuration per RPV per shift with full call-for-service coverage whilst maximizing police presence and conspicuousness as a proxy for road safety.     

ATIS和道路收费下的混合随机用户均衡的效率损失

在ATIS作用下的交通网络中,用户在交通信息的接受程度上是异质的;考虑到装有ATIS的用户并不总是遵循ATIS的建议,因此,引入信息遵从率这一参数,将所有用户分为三类:安装并遵从信息、安装但不遵从信息和不安装的用户;均按照随机用户均衡的方式进行择路,但对出行时间有不同的感知。同时考虑存在道路收费的情形下,用户在时间价值上是异质的。综合考虑交通信息与道路收费的影响,基于用户两方面的异质性,对其进行合理分类,构建了多用户多准则的混合随机均衡模型及其等价的变分不等式;当收费不作为系统总成本的一部分时,建立了时间准则与费用准则下的系统最优模型;在此基础之上,分别研究了两种准则下混合均衡相对于系统最优的效率损失,给出了效率损失上界,并进一步分析了效率损失上界与各参数间的关系;交通管理者可以从道路收费策略的实施、信息诱导系统的完善等角度进行路网的改造和优化设计。     

A modified Physarum-inspired model for the user equilibrium traffic assignment problem

The user equilibrium traffic assignment principle is very important in the traffic assignment problem. Mathematical programming models are designed to solve the user equilibrium problem in traditional algorithms. Recently, the Physarum shows the ability to address the user equilibrium and system optimization traffic assignment problems. However, the Physarum model are not efficient in real traffic networks with two-way traffic characteristics and multiple origin–destination pairs. In this article, a modified Physarum-inspired model for the user equilibrium problem is proposed. By decomposing traffic flux based on origin nodes, the traffic flux from different origin–destination pairs can be distinguished in the proposed model. The Physarum can obtain the equilibrium traffic flux when no shorter path can be discovered between each origin–destination pair. Finally, numerical examples demonstrate the rationality and convergence properties of the proposed model.     

An anisotropic continuum model for traffic assignment in mixed transportation networks

This work deals with a two-dimensional continuum model for the problem of congested traffic assignment in an urban transportation system consisting of a set of freeways superimposed over a dense street network. The formulation leads to a system of non-linear differential equations whose unknowns are given by the travel times from arbitrary points of the network to the corresponding destinations. The governing equations are appropriately solved by means of the Finite Element Method. Then, traffic flow on every link of the network can be obtained. Numerical examples are given in order to demonstrate the efficiency of the developed model.     

An efficient algorithm for computing traffic equilibria using TRANSYT model

Computing traffic equilibria with signal settings using TRANSYT model for an area traffic control road system is considered in this paper. Following Wardrop’s first principle, this problem can be formulated as a variational inequality problem. In this paper, we propose a novel algorithm to efficiently solve this equilibrium traffic assignment with global convergence. Numerical calculations are conducted on a grid-size road network. As it shows, the proposed method achieved greater savings in computational overheads than did those conventional methods for solving traffic equilibria when signal settings are particularly taken into account.     

Optimal egress time calculation and path generation for large evacuation networks

Finding the optimal clearance time and deciding the path and schedule of evacuation for large networks have traditionally been computationally intensive. In this paper, we propose a new method for finding the solution for this dynamic network flow problem with considerably lower computation time. Using a three phase solution method, we provide solutions for required clearance time for complete evacuation, minimum number of evacuation paths required for evacuation in least possible time and the starting schedules on those paths. First, a lower bound on the clearance time is calculated using minimum cost dynamic network flow model on a modified network graph representing the transportation network. Next, a solution pool of feasible paths between all O-D pairs is generated. Using the input from the first two models, a flow assignment model is developed to select the best paths from the pool and assign flow and decide schedule for evacuation with lowest clearance time possible. All the proposed models are mixed integer linear programing models and formulation is done for System Optimum (SO) scenario where the emphasis is on complete network evacuation in minimum possible clearance time without any preset priority. We demonstrate that the model can handle large size networks with low computation time. A numerical example illustrates the applicability and effectiveness of the proposed approach for evacuation.