Link Travel Times II: Properties Derived from Traffic-Flow Models

We investigate the properties of travel times when the latter are derived from traffic-flow models. In particular we consider exit-flow models, which have been used to model time-varying flows on road networks, in dynamic traffic assignment (DTA). But we here define the class more widely to include, for example, models based on finite difference approximations to the LWR (Lighthill, Whitham and Richards) model of traffic flow, and large step versions of these. For the derived travel times we investigate the properties of existence, uniqueness, continuity, first-in-first-out (FIFO), causality and time-flow consistency (or intertemporal consistency). We assume a single traffic type and assume that time may be treated as continuous or as discrete, and for each case we obtain conditions under which the above properties are satisfied, and interrelations among the properties. For example, we find that FIFO is easily satisfied, but not strict causality, and find that if we redefine travel time to ensure strict causality then we lose time-flow consistency, and that neither of these conditions is strictly necessary or sufficient for FIFO. All of the models can be viewed as an approximation to a model that is continuous in time and space (the LWR model), and it seems that any loss of desirable properties is the price we pay for using such approximations. We also extend the exit-flow models and results to allow inhomogeneity over time (link capacity or other parameters changing over time), and show that FIFO is still ensured if the exit-flow function is defined appropriately.     

Dynamic Traffic Assignment with More Flexible Modelling within Links

Traffic network models tend to become very large even for medium-size static assignment problems. Adding a time dimension, together with time-varying flows and travel times within links and queues, greatly increases the scale and complexity of the problem. In view of this, to retain tractability in dynamic traffic assignment (DTA) formulations, especially in mathematical programming formulations, additional assumptions are normally introduced. In particular, the time varying flows and travel times within links are formulated as so-called whole-link models. We consider the most commonly used of these whole-link models and some of their limitations.In current whole-link travel-time models, a vehicle's travel time on a link is treated as a function only of the number of vehicles on the link at the moment the vehicle enters. We first relax this by letting a vehicle's travel time depend on the inflow rate when it enters and the outflow rate when it exits. We further relax the dynamic assignment formulation by stating it as a bi-level program, consisting of a network model and a set of link travel time sub-models, one for each link. The former (the network model) takes the link travel times as bounded and assigns flows to links and routes. The latter (the set of link models) does the reverse, that is, takes link inflows as given and finds bounds on link travel times. We solve this combined model by iterating between the network model and link sub-models until a consistent solution is found. This decomposition allows a much wider range of link flow or travel time models to be used. In particular, the link travel time models need not be whole-link models and can be detailed models of flow, speed and density varying along the link. In our numerical examples, algorithms designed to solve this bi-level program converged quickly, but much remains to be done in exploring this approach further. The algorithms for solving the bi-level formulation may be interpreted as traveller learning behaviour, hence as a day-to-day traffic dynamics. Thus, even though in our experiments the algorithms always converged, their behaviour is still of interest even if they cycled rather than converged. Directions for further research are noted. The bi-level model can be extended to handle issues and features similar to those addressed by other DTA models.     

A Dynamic Travel Time Model for Spillback

In this paper we introduce travel time models that incorporate spillback and bottleneck phenomena. In particular, we study a model for determining the link travel times for drivers entering a link as well as drivers already in the link but whose travel times are affected by a significant change in traffic conditions (e.g. spillback or bottleneck phenomena). To achieve this goal, we extend the fluid dynamics travel time models proposed by Perakis (1997)and subsequently by Kachani (2002), and Kachani and Perakis (2001), to also incorporate such phenomena. These models utilize fluid dynamics laws for compressible flow to capture a variety of flow patterns such as the formation and dissipation of queues, drivers’ response to upstream congestion or decongestion and drivers’ reaction time. We propose variants of these models that explicitly account for spillback and bottleneck phenomena. Our investigation considers both separable and non-separable velocity functions.     

The CONTRAM Dynamic Traffic Assignment Model

CONTRAM is a computer model of time-varying traffic in road networks, which takes as input the network definition and time-varying demand for travel between a set of origin and destination zones, and outputs the resulting network flows, routes and travel times. It combines a macroscopic time-sliced traffic model with disaggregate dynamic assignment of traffic, so is intermediate between macroscopic equilibrium and microscopic models. The paper details the methods used, including time-dependent queuing which plays a central role, and the treatment of network definition, user classes, road capacities, signals and coordination, vehicle emissions, Intelligent Transport Systems and research lines.     

Comparison of Methods for Path Flow Reassignment for Dynamic User Equilibrium

Models to describe or predict of time-varying traffic flows and travel times on road networks are usually referred to as dynamic traffic assignment (DTA) models or dynamic user equilibrium (DUE) models. The most common form of algorithms for DUE consists of iterating between two components namely dynamic network loading (DNL) and path inflow reassignment or route choice. The DNL components in these algorithms have been investigated in many papers but in comparison the path inflow reassignment component has been relatively neglected. In view of that, we investigate various methods for path inflow reassignment that have been used in the literature. We compare them numerically by embedding them in a DUE algorithm and applying the algorithm to solve DUE problems for various simple network scenarios. We find that the choice of inflow reassignment method makes a huge difference to the speed of convergence of the algorithms and, in particular, find that ??travel time responsive?? reassignment methods converge much faster than the other methods. We also investigate how speed of convergence is affected by the extent of congestion on the network, by higher demand or lower capacity. There appears to be much scope for further improving path inflow reassignment methods.     

The pseudo-self-similar traffic model: application and validation

Since the early 1990s, a variety of studies have shown that network traffic, both for local- and wide-area networks, has self-similar properties. This led to new approaches in network traffic modelling because most traditional traffic approaches result in the underestimation of performance measures of interest. Instead of developing completely new traffic models, a number of researchers have proposed to adapt traditional traffic modelling approaches to incorporate aspects of self-similarity. The motivation for doing so is the hope to be able to reuse techniques and tools that have been developed in the past and with which experience has been gained. One such approach is the so-called pseudo-self-similar traffic (PSST) model. This model is appealing, as it is easy to understand and easily embedded in Markovian performance evaluation studies.

In applying this model in a number of cases, we have perceived various problems which we initially thought were particular to these specific cases. However, we recently have been able to show that these problems are fundamental to the PSST model.

In this paper we review the PSST model, validate it experimentally and discuss its shortcomings. As far as we know, this is the first paper that discusses these shortcomings formally. We also report on ongoing work to overcome some of these problems.     

利用ActionScript3.0技术构建虚拟交通系统

该文介绍了如何利用Flash CS3.0中的ActionScript3.0技术构建一种全新的虚拟交通系统,从而为人们提供更多的出行参照信息,以解决传统电子地图的一些弊端,并且具有一定程度上的实用性和可移植性。人们可以通过该虚拟交通系统获得更加直观的道路信息,从而可以更加方便准确的找到自己想要到达的地方。     

基于换乘次数最少的公交网络最优路径模型研究

结合乘客出行心理分析,提出以换乘次数最少为目标的公交乘车模型。在公交网络建模方面,综合考虑公交站点空间关系,提出空间数据到拓扑模型再到搜索模型的公交网络双层建模方案。通过搜索模型的建立,将最小换乘次数问题转化为两点间的最短路径问题进行求解。在搜索算法的设计上,首先提出改造的边权为1的Dijktra算法,以此为基础设计前驱节点算法。并以前驱节点算法为前提,设计所有最短路径算法,能够高效地求解两点间的所有换乘次数最小的乘车方案。最后,以大连市公交数据为例,验证了建模方案和算法的可行性。     

Stochastic User Equilibrium Traffic Assignment with Turn-delays in Intersections

Turn-delays in intersections contribute significantly to travel times and thus route choices in urban networks. However, turns are difficult to handle in traffic assignment models due to the asymmetric Jacobian in the cost functions. The paper describes a model where turn delays have been included in the solution algorithm of Stochastic User Equilibrium (SUE) traffic assignment. When the Jacobian is symmetric, SUE minimises the road users' 'perceived travel resistances'. This is a probit-model where the links cost-functions of the links are traffic dependent. Hereby, overlapping routes are handled in a consistent way. However, no theoretical proof of convergence has been given if the Jacobian is asymmetric, although convergence can be shown probable for model data representing realistic road-networks. However, according to the authors knowledge SUE with intersection delays have not been tested earlier on a full-scale network. Therefore, an essential part of the paper presents practical tests of convergence. Both geometric delays and delays caused by other turns are considered for each turn. Signalised and non-signalised intersections are handled in different ways, as are roundabouts. In signalised intersections a separate model handles queues longer than one green-period. Green-waves can also be taken into consideration. The model has been tested on a large-scale network for Copenhagen with good results. To make it possible to establish the comprehensive data, a GIS-based 'expert system' was implemented (see Nielsen, O.A., Frederiksen, R. D. and Simonsen, N. (1997). Using expert system rules to establish data on intersections and turns in road networks. International Transactions in Operational Research , 5 , 513–529.     

基于城市交通信息网格的个性化出行服务研究

智能城市交通系统由于缺少对个性化出行需求统一的认识，以及在实时路况信息计算、信息共享等方面能力上的不足。尚不能提供大规模的个性化出行服务。在调研的基础上，首先给出了一个统一的个性化出行需求定义，然后设计了一个基于城市交通信息网格的个性化出行服务系统，重点探讨了其中的个性化出行需求定制、个性化出行导航和个性化出行服务实现的关键技术。基于交通信息网格的个性化出行系统研究是提高城市交通出行效率并进而缓解交通压力的有效手段。     

A Simple Traffic Analysis Procedure

This paper presents a simple approximate procedure for traffic analysis that can be described geometrically without calculus. The procedure, which is graphically intuitive, operates directly on piecewise linear approximations of the N-curves of cumulative vehicle count. Because the N-curves are both readily observable and of direct interest for evaluation purposes (e.g., they yield the total vehicle-hours and vehicle-miles of travel in a time interval, and the vehicular accumulation as a function of time) the predictions made with this method should be practical and easy to test.Queued traffic is treated first. Predictions of cumulative counts for this traffic regime are based on three mild assumptions stating the relationship between the linearized input and output curves of vehicle count. These assumptions are a simple twist on those of the kinematic wave (KW) model of Lighthill and Whitham [7] and Richards [11]; thus, the part of the proposed procedure that deals with queued traffic is just an efficient way of solving the KW model based on readily observable data. The method is somewhat more complicated but also more general than that in Newell [10]. The paper shows that the particular way in which the data are linearized prior to the procedure is not important provided one works within certain tolerances, and that errors in the model parameters also have a limited effect. These results can help discriminate between model errors and calculation errors in a validation effort.The second part of the paper examines traffic streams that include queued and unqueued traffic, as well as bottlenecks. Here, unqueued traffic is allowed to obey any reasonable model, e.g., as could be the result of a simulation with multiple vehicle classes, drivers that wish to travel at different speeds and certain rules for passing. The unqueued model, however, cannot include vehicle classes with speeds lower than the maximum possible in queued traffic. The bottlenecks are assumed to have a well-defined capacity and always to allow the maximum possible flow consistent with: (i) the availability of upstream traffic, (ii) the presence of a downstream queue and (iii) the capacity. The capacity can be time-dependent and endogenous. The paper presents the theory, some examples and a computational framework.     

信号控制下的动态路段行程时间模型

通过对车辆在路段上所处的状态不同,将路段行程时间划分成多个组成部分,并分别研究各部分的计算模型,提出一种新的动态路段行程时间模型。这种新的模型计算简单,能够适用于实际交通网络中对动态路段行程时间进行预测计算。通过算例的分析表明,在信号灯的控制下,车辆的动态行程时间是一个间断函数,其不仅仅与路段流量有关,还与该车辆进入路段的时刻以及控制信号设置有很大关系。      

Optimization of robust area traffic control with equilibrium flow under demand uncertainty

For area traffic control road network under realization of uncertain travel demand, a robust signal setting is investigated in this paper. Due to certain hierarchy in a decision-making order, a min–max bilevel program is proposed. A new solution method is presented to determine a Nash–Stackelberg solution where a proposed signal setting is found for area traffic control under demand uncertainty. In order to investigate the robustness of the proposed signal settings, numerical computations are performed for various initial data sets in a medium-sized example road network. Good computational results indicated that the proposed signal settings can successfully reduce a worst-case travel cost substantially while incurring a relatively slight loss of optimality with respect to the optimal deterministic solutions for nominal travel demands. Particularly, our computation results showed that the proposed signal settings become even attractive as demand growth increases under a worst-case realization taken by uncertain travel demands.     

Combined Activity/Travel Choice Models: Time-Dependent and Dynamic Versions

To fully understand and predict travel demand and traffic flow, it is necessary to investigate what drives people to travel. The analysis should examine why, where and when various activities are engaged in, and how activity engagement is related to the spatial and institutional organization of an urban area. In view of this, two combined activity/travel choice models are presented in this paper. The first one is a time-dependent (quasi-dynamic) model for long-term transport planning such as travel demand forecasting, while the other one is a dynamic model for short-term traffic management such as instantaneous flow analysis. The time-dependent model is formulated as a mathematical programming problem for modeling the multinomial logit activity/destination choice and the user equilibrium route choice behavior. It can further be converted to a variational inequality problem. On the other hand, the dynamic model is aimed to find a solution for equilibrium activity location, travel route and departure time choices in queuing networks with multiple commuter classes. It is formulated as a discrete-time, finite-dimensional variational inequality and then converted to an equivalent zero-extreme value minimization problem. Solution algorithms are proposed for these two models and numerical example is presented for the latter. It is shown that the proposed modeling approaches, either based on time-dependent or dynamic traffic assignment principles, provide powerful tools to a wide variety of activity/travel choice problems in dynamic domain.     

Cellular Automata Simulations of Traffic: A Model for the City of Geneva

This paper proposes a micro-simulation based on a simple cellular automata model to analyze and describe the traffic of cars in the city of Geneva. We consider a road network containing the most important roads in the city center and its suburbs. As many as 1066 street junctions are considered, for a total network length of about 4000 km. Our simulation reproduces the rush hour period, based on real data involving around 85000 vehicles. The main properties we study concern the average travel time and its fluctuation of various routes, as a function of the departure time. Finally we briefly discuss the computer implementation of our model and its performance on a parallel computer.     

Red Swarm: Reducing travel times in smart cities by using bio-inspired algorithms

This article presents an innovative approach to solve one of the most relevant problems related to smart mobility: the reduction of vehicles’ travel time. Our original approach, called Red Swarm, suggests a potentially customized route to each vehicle by using several spots located at traffic lights in order to avoid traffic jams by using V2I communications. That is quite different from other existing proposals, as it deals with real maps and actual streets, as well as several road traffic distributions. We propose an evolutionary algorithm (later efficiently parallelized) to optimize our case studies which have been imported from OpenStreetMap into SUMO as they belong to a real city. We have also developed a Rerouting Algorithm which accesses the configuration of the Red Swarm and communicates the route chosen to vehicles, using the spots (via WiFi link). Moreover, we have developed three competing algorithms in order to compare their results to those of Red Swarm and have observed that Red Swarm not only achieved the best results, but also outperformed the experts’ solutions in a total of 60 scenarios tested, with up to 19% shorter travel times.     

基于计算实验的城市道路行程时间预测与建模

城市道路行程时间预测对于提高交通管控效果具有重要意义. 本文综合应用平行系统、集散波、误差反馈修正、多模型自适应控制及模型库动态优 化策略等方法与技术对间断流行程时间预测问题进行了研究. 首先,介绍了平行系统理论的基本原理及计算实验的基本方法; 然后,给出了基于平行系统理论的路段行程时间的预测模型, 设计了基于集散波的行程时间计算实验方法, 提出了多模型自适应行程时间预测并给出了模型动态优化策略. 最后,通过实验证明了本方法的有效性. 结果表明, 本文方法预测精度较高, 且能够对行程时间预测值进行持续优化, 可为后续的间断流行程时间预测研究提供借鉴.     

Determining optimal sensor locations in freeway using genetic algorithm-based optimization

Travel time is the most intuitive measure of effectiveness for road users and transportation agency operators. However, travel times derived from speed data measured at fixed point sensors often varies from actual travel time. This is, in part, due to the intentional positioning of sensors to avoid lane changing and/or to inadequate numbers of sensors capturing the dynamic characteristics inherent in freeway traffic flow. This paper presents an approach that optimizes the location of sensors in a freeway to support more accurate estimations of travel times than those obtained from conventionally deployed fixed point sensors. Evaluation results, under varying traffic conditions, including incidents, showed that the proposed approach produced average travel time estimation errors within 10% and performed much better than the conventional approach. Thus, the proposed approach provides a promising tool to support re-positioning of the existing non-intrusive point sensors (e.g., video sensors) or deployment of new sets of point sensors for improving travel time estimation.     

Efficient Discretisation for Link Travel Time Models

In the literature, two different models have been used to compute link travel times in dynamic traffic assignment (DTA), and elsewhere we investigated how these are affected by discretising the link length. Here we consider discretising time as well as space (the link length). We vary the discretising of time with spatial discretisation held fixed, and vice versa, and also vary both together. The results show that coordinated discretisation is usually the most efficient in approximating the limit solution (continuous time, continuous space) and, even when it is not the most efficient, it has other advantages. The results have implications for algorithms for DTA and for the choice of discrete versus continuous time models. For example, refining the discretisation of time (without refining it for space) can make the solution less accurate, so that in the widely used whole-link models (i.e. without spatial discretisation) it is more efficient to use the largest feasible time steps, close to the link travel time.     

车路协同环境下基于动态车速的相位差优化模型

针对基于固定路段行驶车速的相位差优化模型在优化双向滤波时存在的不足,本文基于车路协同环境下车辆–信号控制系统双向、实时通信的运行环境,研究并建立了车辆动态速度与交叉口相位差的整合优化模型.首先,基于对上游交叉口流出的两类交通流,即饱和交通流和非饱和交通流运行特征分析,建立了速度与相位差相互影响关系模型,在此基础上,分别针对两种不同的交通流,以干道实时流量与速度乘积最大为目标,考虑初始排队清空时间,可变速度范围,和相位差取值空间等约束条件,建立了车辆速度与相位差的动态优化模型,从而实现干道交通流不停车通过量最大且延误最小的目的.最后,对比分析了本文模型与经典Maxband绿波优化模型及Synchro软件的信号协调控制优化方案,结果表明,相比其他两种典型优化方法,本文模型能显著提高双向绿波带宽并大幅减少停车次数,提高协调控制的效益.