Macroscopic relations of urban traffic variables: Bifurcations, multivaluedness and instability

Recent experimental work has shown that the average flow and average density within certain urban networks are related by a unique, reproducible curve known as the Macroscopic Fundamental Diagram (MFD). For networks consisting of a single route this MFD can be predicted analytically; but when the networks consist of multiple overlapping routes experience shows that the flows observed in congestion for a given density are less than those one would predict if the routes were homogeneously congested and did not overlap. These types of networks also tend to jam at densities that are only a fraction of their routes’ average jam density.This paper provides an explanation for these phenomena. It shows that, even for perfectly homogeneous networks with spatially uniform travel patterns, symmetric equilibrium patterns with equal flows and densities across all links are unstable if the average network density is sufficiently high. Instead, the stable equilibrium patterns are asymmetric. For this reason the networks jam at lower densities and exhibit lower flows than one would predict if traffic was evenly distributed.Analysis of small idealized networks that can be treated as simple dynamical systems shows that these networks undergo a bifurcation at a network-specific critical density such that for lower densities the MFDs have predictably high flows and are univalued, and for higher densities the order breaks down. Microsimulations show that this bifurcation also manifests itself in large symmetric networks. In this case though, the bifurcation is more pernicious: once the network density exceeds the critical value, the stable state is one of complete gridlock with zero flow. It is therefore important to ensure in real-world applications that a network’s density never be allowed to approach this critical value.Fortunately, analysis shows that the bifurcation’s critical density increases considerably if some of the drivers choose their routes adaptively in response to traffic conditions. So far, for networks with adaptive drivers, bifurcations have only been observed in simulations, but not (yet) in real life. This could be because real drivers are more adaptive than simulated drivers and/or because the observed real networks were not sufficiently congested.     

On the macroscopic stability of freeway traffic

A simple model of traffic flow is used to analyze the spatio-temporal distribution of flow and density on closed-loop homogeneous freeways with many ramps, which produce inflows and allow outflows. As we would expect, if the on-ramp demand is space-independent then this distribution tends toward uniformity in space if the freeway is either: (i) uncongested; or (ii) congested with queues on its on-ramps and enough inflow to cause the average freeway density to increase with time. In all other cases, however, including any recovery phase of a rush hour where the freeway’s average density declines, the distribution of flow and density quickly becomes uneven. This happens even under conditions of perfect symmetry, where the percentage of vehicles exiting at every off ramp is the same. The flow-density deviations from the average are shown to grow exponentially in time and propagate backwards in space with a fixed wave speed. A consequence of this type of instability is that, during recovery, gaps of uncongested traffic will quickly appear in the unevenly congested stream, reducing average flow. This extends the duration of recovery and invariably creates clockwise hysteresis loops on scatter-plots of average system flow vs. density during any rush hour that oversaturates the freeway. All these effects are quantified with formulas and verified with simulations. Some have been observed in real networks. In a more practical vein, it is also shown that the negative effects of instability diminish (i.e., freeway flows increase) if (a) some drivers choose to exit the freeway prematurely when it is too congested and/or (b) freeway access is regulated in a certain traffic-responsive way. These two findings could be used to improve the algorithms behind VMS displays for driver guidance (finding a), and on-ramp metering rates (finding b).     

Drivers’ willingness-to-pay to reduce travel time: evidence from the San Diego I-15 congestion pricing project

The adoption of congestion pricing depends fundamentally upon drivers’ willingness to pay to reduce travel time during the congested morning peak period. Using revealed preference data from a congestion pricing demonstration project in San Diego, we estimate that willingness to pay to reduce congested travel time is higher than previous stated preference results. Our estimate of median willingness to pay to reduce commute time is roughly $30 per hour, although this may be biased upward by drivers’ perception that the toll facility provides safer driving conditions. Drivers also use the posted toll as an indicator of abnormal congestion and increase their usage of the toll facility when tolls are higher than normal.     

A model for assessing the effects of dynamic travel time information via variable message signs

In view of the serious traffic congestion during peak hours in most metropolitan areas around the world and recent improvement of information technology, there is a growing aspiration to alleviate road congestion by applications of electronic information and communication technology. Providing drivers with dynamic travel time information such as estimated journey times on major routes should help drivers to select better routes and guide them to utilise existing expressway network. This can be regarded as one possible strategy for effective traffic management. This paper aims to investigate the effects and benefits of providing dynamic travel time information to drivers via variable message signs at the expressway network. In order to assess the effects of the dynamic driver information system with making use of the variable message signs, a time-dependent traffic assignment model is proposed. A numerical example is used to illustrate the effects of the dynamic travel time information via variable message signs. This revised version was published online in June 2006 with corrections to the Cover Date.     

A comparison of stochastic and deterministic traffic assignment over congested networks

The similarity between link flows obtained from deterministic and stochastic equilibrium traffic assignment models is investigated at different levels of congestion. A probit-based stochastic assignment is used (over a congested network) where the conditions for equilibrium are those given by Daganzo and Sheffi (1977). Stochastic equilibrium flows are generated using an iterative procedure with predetermined step sizes, and the resulting assignment is validated on the basis of the equilibrium criteria. The procedure is intended to assist in the choice of the most appropriate assignment algorithm for a given level of congestion.     

Optimum routing of battery electric vehicles: Insights using empirical data and microsimulation

This study investigates the energy consumption impact of route selection on battery electric vehicles (BEVs) using empirical second-by-second Global Positioning System (GPS) commute data and traffic micro-simulation data. Drivers typically choose routes that reduce travel time and therefore travel cost. However, BEVs’ limited driving range makes energy efficient route selection of particular concern to BEV drivers. In addition, BEVs’ regenerative braking systems allow for the recovery of energy while braking, which is affected by route choices. State-of-the-art BEV energy consumption models consider a simplified constant regenerative braking energy efficiency or average speed dependent regenerative braking factors. To overcome these limitations, this study adopted a microscopic BEV energy consumption model, which captures the effect of transient behavior on BEV energy consumption and recovery while braking in a congested network. The study found that BEVs and conventional internal combustion engine vehicles (ICEVs) had different fuel/energy-optimized traffic assignments, suggesting that different routings be recommended for electric vehicles. For the specific case study, simulation results indicate that a faster route could actually increase BEV energy consumption, and that significant energy savings were observed when BEVs utilized a longer travel time route because energy is regenerated. Finally, the study found that regenerated energy was greatly affected by facility types and congestion levels and also BEVs’ energy efficiency could be significantly influenced by regenerated energy.     

Congestion and safety: A spatial analysis of London

A disaggregate spatial analysis, using enumeration district data for London was conducted with the aim of examining how congestion may affect traffic safety. It has been hypothesized that while congested traffic conditions may increase the number of vehicle crashes and interactions, their severity is normally lower than crashes under uncongested free flowing conditions. This is primarily due to the slower speeds of vehicles when congestion is present. Our analysis uses negative binomial count models to examine whether factors affecting casualties (fatalities, serious injuries and slight injuries) differed during congested time periods as opposed to uncongested time periods. We also controlled for congestion spatially using a number of proxy variables and estimated pedestrian casualty models since a large proportion of London casualties are pedestrians. Results are not conclusive. Our results suggest that road infrastructure effects may interact with congestion levels such that in London any spatial differences are largely mitigated. Some small differences are seen between the models for congested versus uncongested time periods, but no conclusive trends can be found. Our results lead us to suspect that congestion as a mitigator of crash severity is less likely to occur in urban conditions, but may still be a factor on higher speed roads and motorways.     

Ant Colony Routing algorithm for freeway networks

Dynamic traffic routing refers to the process of (re)directing vehicles at junctions in a traffic network according to the evolving traffic conditions. The traffic management center can determine desired routes for drivers in order to optimize the performance of the traffic network by dynamic traffic routing. However, a traffic network may have thousands of links and nodes, resulting in a large-scale and computationally complex non-linear, non-convex optimization problem. To solve this problem, Ant Colony Optimization (ACO) is chosen as the optimization method in this paper because of its powerful optimization heuristic for combinatorial optimization problems. ACO is implemented online to determine the control signal – i.e., the splitting rates at each node. However, using standard ACO for traffic routing is characterized by four main disadvantages: 1. traffic flows for different origins and destinations cannot be distinguished; 2. all ants may converge to one route, causing congestion; 3. constraints cannot be taken into account; and 4. neither can dynamic link costs. These problems are addressed by adopting a novel ACO algorithm with stench pheromone and with colored ants, called Ant Colony Routing (ACR). Using the stench pheromone, the ACR algorithm can distribute the vehicles over the traffic network with less or no traffic congestion, as well as reduce the number of vehicles near some sensitive zones, such as hospitals and schools. With colored ants, the traffic flows for multiple origins and destinations can be represented. The proposed approach is also implemented in a simulation-based case study in the Walcheren area, the Netherlands, illustrating the effectiveness of the approach.     

Modeling drivers' diversion from normal routes under ATIS using generalized estimating equations and binomial probit link function

Advanced Traveler Information Systems (ATIS) provide travelers with real time traffic information to optimize their travel choices. The objective of this paper is to model drivers' diversion from their normal routes in the provision of ATIS. Five different scenarios of traffic information are used. Generalized Estimating Equations (GEE) framework with repeated observations and binomial probit link function is introduced and implemented. GEE with four different correlation structures including the independent case are developed and compared with each other and with regular Maximum Likelihood Estimation (MLE). A travel simulator was used. Sixty-five subjects have traveled 10 simulated trial days each on a 40-link realistic network with real historical congestion levels. The results showed that providing traffic information increases the probability of drivers' diversion from their normal routes. Adding advice to the pre-trip and/or en-route information encourages drivers to divert. Providing en-route in addition to the pre-trip information with or without advice increases the diversion probability. High travel time on the normal route and less travel time on the diverted route increase the probability of diversion. High-educated drivers are less likely to divert. Expressway users are more likely to divert from their normal routes under ATIS. Drivers' familiarity with the device that provides the information and high number of traffic signals on the normal route increase the diversion probability.     

On the fundamental diagram and supply curves for congested urban networks

Macroscopic fundamental diagrams (MFD) of traffic for some networks have been shown to have similar shape to those for single links. They have erroneously been used to help estimate the level of travel in congested networks. We argue that supply curves, which track vehicles in their passage through congested networks, are needed for this purpose, and that they differ from the performance curves generated from MFD. We use a microsimulation model, DRACULA and two networks, one synthesizing the network for Cambridge, England, and one of the city of York, England, to explore the nature of performance curves and supply curves under differing patterns of demand.We show that supply curves differ from performance curves once the onset of congestion is reached, and that the incorrect use of performance curves to estimate demand can thus seriously underestimate traffic levels, the costs of congestion, and the value of congestion relief measures. We also show that network aggregated supply curves are sensitive to the temporal distribution of demand and, potentially, to the spatial distribution of demand. The shape of the supply curve also differs between origin–destination movements within a given network.We argue that supply curves for higher levels of demand cannot be observed in normal traffic conditions, and specify ways in which they can be determined from microsimulation and, potentially, by extrapolating observed data. We discuss the implications of these findings for conventional modelling of network management policies, and for these policies themselves.     

Effect of parking information on travelers' knowledge and behavior

In many urban centers the demand for parking increases sharply before Christmas mainly due to shopping activity — causing parking congestion. One way to ameliorate such congestion is by disseminating parking information. Informed drivers may divert to relatively under-utilized parking facilities relieving the pressure on congested facilities. The City of Nottingham in England tested a real-time parking information system designed to alleviate congestion in the City Center parking facilities. Real-time information was disseminated through the radio, while historical information regarding parking locations was disseminated through newspaper advertisements and leaflets. The objective of this study is to assess impacts of the parking information system on travelers' knowledge and decisions.Survey research was used to understand traveler response. Respondents' levels of knowledge regarding car parks were analyzed by developing Poisson regression models. Drivers were more likely to have greater knowledge of city center car parks if they used several information sources (radio broadcasts, newspaper advertisements or leaflets and word-of-mouth), were active seekers of parking information, and searched for parking rather than going directly to a parking facility. In addition, the study of behavior showed that drivers were more inclined to use the relatively under-utilized Park-and-Ride facilities instead of the city center car parks if they received parking information from Newspaper advertisements/leaflets. Overall, the parking information service in Nottingham was effective; it seems reasonable to establish such information dissemination and monitoring systems at parking facilities in other urban areas. Furthermore, to support informed travel and activity participation decisions, parking information should be integrated with traffic and transit information.     

Routing aspects of electric vehicle drivers and their effects on network performance

This study investigates the routing aspects of battery electric vehicle (BEV) drivers and their effects on the overall traffic network performance. BEVs have unique characteristics such as range limitation, long battery recharging time, and recuperation of energy lost during the deceleration phase if equipped with regenerative braking system (RBS). In addition, the energy consumption rate per unit distance traveled is lower at moderate speed than at higher speed. This raises two interesting questions: (i) whether these characteristics of BEVs will lead to different route selection compared to conventional internal combustion engine vehicles (ICEVs), and (ii) whether such route selection implications of BEVs will affect the network performance. With the increasing market penetration of BEVs, these questions are becoming more important. This study formulates a multi-class dynamic user equilibrium (MCDUE) model to determine the equilibrium flows for mixed traffic consisting of BEVs and ICEVs. A simulation-based solution procedure is proposed for the MCDUE model. In the MCDUE model, BEVs select routes to minimize the generalized cost which includes route travel time, energy related costs and range anxiety cost, and ICEVs to minimize route travel time. Results from numerical experiments illustrate that BEV drivers select routes with lower speed to conserve and recuperate battery energy while ICEV drivers select shortest travel time routes. They also illustrate that the differences in route choice behavior of BEV and ICEV drivers can synergistically lead to reduction in total travel time and the network performance towards system optimum under certain conditions.     

Node modeling for congested urban road networks

First-order network flow models are coupled systems of differential equations which describe the build-up and dissipation of congestion along network road segments, known as link models. Models describing flows across network junctions, referred to as node models, play the role of the coupling between the link models and are responsible for capturing the propagation of traffic dynamics through the network. Node models are typically stated as optimization problems, so that the coupling between the link dynamics is not known explicitly. This renders network flow models analytically intractable. This paper examines the properties of node models for urban networks. Solutions to node models that are free of traffic holding, referred to as holding-free solutions, are formally defined and it is shown that flow maximization is only a sufficient condition for holding-free solutions. A simple greedy algorithm is shown to produce holding-free solutions while also respecting the invariance principle. Staging movements through nodes in a manner that prevents conflicting flows from proceeding through the nodes simultaneously is shown to simplify the node models considerably and promote unique solutions. The staging also models intersection capacities in a more realistic way by preventing unrealistically large flows when there is ample supply in the downstream and preventing artificial blocking when some of the downstream supplies are restricted.     

Do microscopic merging models reproduce the observed priority sharing ratio in congestion?

A classical way to represent vehicle interactions at merges at the microscopic scale is to combine a gap-acceptance model with a car-following algorithm. However, in congested conditions (when a queue spills back on the major road), outputs of such a combination may be irrelevant if anticipatory aspects of vehicle behaviours are disregarded (like in single-level gap-acceptance models). Indeed, the insertion decision outcomes are so closely bound to the car-following algorithm that irrelevant results are produced. On the one hand, the insertion decision choice is sensitive to numerical errors due to the car-following algorithm. On the other hand, the priority sharing process observed in congestion cannot be correctly reproduced because of the constraints imposed by the car-following on the gap-acceptance model. To get over these issues, more sophisticated gap-acceptance algorithms accounting for cooperation and aggressiveness amongst drivers have been recently developed (multi-level gap-acceptance models). Another simpler solution, with fewer parameters, is investigated in this paper. It consists in introducing a relaxation procedure within the car-following rules and proposing a new insertion decision algorithm in order to loosen the links between both model components. This approach will be shown to accurately model the observed flow allocation pattern in congested conditions at an aggregate scale.     

Parking space management via dynamic performance-based pricing

In congested urban areas, it remains a pressing challenge to reduce unnecessary vehicle circling for parking while at the same time maximize parking space utilization. In observance of new information technologies that have become readily accessible to drivers and parking agencies, we develop a dynamic non-cooperative bi-level model (i.e. Stackelberg leader–follower game) to set parking prices in real-time for effective parking access and space utilization. The model is expected to fit into an integrated parking pricing and management system, where parking reservations and transactions are facilitated by sensing and informatics infrastructures, that ensures the availability of convenient spaces at equilibrium market prices. It is shown with numerical examples that the proposed dynamic parking pricing model has the potential to virtually eliminate vehicle circling for parking, which results in significant reduction in adverse socioeconomic externalities such as traffic congestion and emissions.     

Auction-Based Congestion Pricing

Abstract

Planners, engineers and economists have introduced various demand management methods in an attempt to reduce the fast growing traffic congestion. The basic idea behind various demand management strategies is to force drivers to travel and use transportation facilities more during off-peak hours and less during peak hours, as well as to increase the usage of underutilized routes. In this paper, a new demand management concept – Auction-based Congestion Pricing – is proposed and modeled.     

Simplified transport models based on traffic counts

Having accepted the need for the development of simpler and less cumbersome transport demand models, the paper concentrates on one possible line for simplification: estimation of trip matrices from link volume counts. Traffic counts are particularly attractive as a data basis for modelling because of their availability, low cost and nondisruptive character. It is first established that in normal conditions it may be possible to find more than one trip matrix which, when loaded onto a network, reproduces the observed link volumes. The paper then identifies three approaches to reduce this underspecification problem and produce a unique trip matrix consistent with the counts. The first approach consists of assuming that trip-making behaviour can be explained by a gravity model whose parameters can be calibrated from the traffic counts. Several forms of this gravity model have been put forward and they are discussed in Section 3. The second approach uses mathematical programming techniques associated to equilibrium assignment problems to estimate a trip matrix in congested areas. This method can also be supplemented by a special distribution model developed for small areas. The third approach relies on entropy and information theory considerations to estimate the most likely trip matrix consistent with the observed flows. A particular feature of this group is that they can include prior, perhaps outdated, information about the matrix.These three approaches are then compared and their likely areas for application identified. Problems for further research are discussed and finally an assessment is made of the possible role of these models vis-a-vis recent developments in transport planning.     

Dynamic traffic assignment of cooperative adaptive cruise control

Advances in connected and automated vehicle technologies have resulted in new vehicle applications, such as cooperative adaptive cruise control (CACC). Microsimulation models have shown significant increases in capacity and stability due to CACC, but most previous work has relied on microsimulation. To study the effects of CACC on larger networks and with user equilibrium route choice, we incorporate CACC into the link transmission model (LTM) for dynamic network loading. First, we derive the flow-density relationship from the MIXIC car-following model of CACC (at 100% CACC market penetration). The flow-density relationship has an unusual shape; part of the congested regime has an infinite congested wave speed. However, we verify that the flow predictions match observations from MIXIC modeled in VISSIM. Then, we use the flow-density relationship from MIXIC in LTM. Although the independence of separate links restricts the maximum congested wave speed, for common freeway link lengths the congested wave speed is sufficiently high to fit the observed flows from MIXIC. Results on a freeway and regional networks (with CACC-exclusive lanes) indicate that CACC could reduce freeway congestion, but naïve deployment of CACC-exclusive lanes could cause an increase in total system travel time.     

Mitigation of disruptions in public transit by Bee Colony Optimization

Dispatchers in many public transit companies face the daily problem of assigning available buses to bus routes under conditions of bus shortages. In addition to this, weather conditions, crew absenteeism, traffic accidents, traffic congestion and other factors lead to disturbances of the planned schedule. We propose the Bee Colony Optimization (BCO) algorithm for mitigation of bus schedule disturbances. The developed model takes care of interests of the transit operator and passengers. The model reassigns available buses to bus routes and, if it is allowed, the model simultaneously changes the transportation network topology (it shortens some of the planned bus routes) and reassigns available buses to a new set of bus routes. The model is tested on the network of Rivera (Uruguay). Results obtained show that the proposed algorithm can significantly mitigate disruptions.     

Users’ perceptions and willingness to pay in interurban toll roads: identifying differences across regions from a nationwide survey in Spain

Users’ acceptability is considered one of the key drivers for the successful implementation of transport policy measures. This is especially crucial in the case of toll roads since they are financed through drivers’ contributions. Previous literature in this field has mainly focused on measuring users’ attitudes towards urban congestion pricing strategies. However limited research has been developed concerning interurban toll roads. Previous research shows that socioeconomic variables are not conclusive to explain users’ perceptions towards tolls. By contrast, other drivers such as regional differences seem to play a more important role, especially when charging conditions within the same nation greatly vary across regions. This paper analyzes regional differences in users’ attitudes within an asymmetrical distribution of the toll road network across regions. Based on a nationwide survey conducted to road users in interurban toll roads in Spain, we develop both a binomial logit and a censored regression (tobit) model to explore drivers’ perceptions and willingness to pay. The research concludes that users from regions with a more extensive tolled network generally show a more negative attitude towards charges, but not necessarily a lower willingness to pay. The paper also points out that an asymmetrical distribution of toll roads across regions may result in negative perceptions among those users perceiving to be unfairly treated when compared to citizens in other regions.