Vehicle routing problem and driver behaviour: a review and framework for analysis

Vehicle routing problems (VRPs) whose typical objective is to minimise total travel costs over a tour have evolved over the years with objectives ranging from minimising travel times and distances to minimising pollution and fuel consumption. However, driver behaviour continues to be neglected while planning for vehicle routes. Factors such as traffic congestion levels, monotonous drives and fatigue have an impact on the behaviour of drivers, which in turn might affect their speed-choice and route-choice behaviours. The behaviour of drivers and their subsequent decision-making owing to these factors impact the revenue of transport companies and could lead to huge losses in extreme cases. There have been studies on the behaviour of drivers in isolation, without inclusion of the objectives and constraints of the traditional routing problem. This paper presents a review of existing models of VRP, planner behaviour models in the VRP context and driver behaviour models and provides a motivation to integrate these models in a stochastic traffic environment to produce practical, economic and driver-friendly logistics solutions. The paper provides valuable insights on the relevance of behavioural issues in logistics and highlights the modelling implications of incorporating planner and driver behaviour in the framework of routing problems.     

Influence of priority taking and abstaining at single-lane roundabouts using cellular automata

Existing roundabout simulation models fail to consider all types of driver behavior which compromises their accuracy and ability to accurately evaluate roundabout performance. Further, these non-compliant driver behaviors, including priority taking and priority abstaining, are inconsistent with existing traffic flow theories. In this paper, a new cellular automata model, C.A.Rsim, is developed and calibrated with field data from five single-lane roundabouts in four northeastern states. Model results indicate that approximately 20% of the individuals in the driver population are inclined to priority taking and approximately 20% are inclined to priority abstaining behavior, though the observed levels of these types of behavior are naturally lower and vary with traffic volume. The model results also corroborate other research indicating that current models can overestimate capacity at higher circulating volumes, possibly a result of the jamming effect produced by priority taking behavior. The reduction in priority abstaining behavior, which is observed at older roundabouts, significantly reduces delay and queue length in certain traffic volumes. C.A.Rsim is also more parsimonious than many existing microsimulation models. These results provide insight on how variations in conflicting flow (i.e., traffic volume and turning movement balance) impact the amount of observed non-compliant behavior.     

Transport demand model estimation from traffic counts

Many problems in transport planning and management tasks require an origindestination (O-D) matrix to represent the travel pattern. However, O-D matrices obtained through a large scale survey such as home or roadside interviews, tend to be costly, labour intensive and time disruptive to trip makers. Therefore, the use of low cost and easily available data is particularly attractive.The need of low-cost methods to estimate current and future O-D matrices is even more valuable in developing countries because of the rapid changes in population, economic activity and land use. Models of transport demand have been used for many years to synthesize O-D matrices in study areas. A typical example of this is the gravity model; its functional form, plus the appropriate values for the parameters involved, is employed to produce acceptable matrices representing trip making behaviour for many trip purposes and time periods.The work reported in this paper has combined the advantages of acceptable travel demand models with the low cost and availability of traffic counts. Three types of demand models have been used: gravity (GR), opportunity (OP) and gravity-opportunity (GO) models. Three estimation methods have been developed to calibrate these models from traffic counts, namely: non-linear-least-squares (NLLS), weighted-non-linear-least-squares (WNLLS) and maximumlikelihood (ML).The 1978 Ripon (urban vehicle movement) survey was used to test these methods. They were found to perform satisfactorily since each calibrated model reproduced the observed O-D matrix fairly closely. The tests were carried out using two assignment techniques, all-or-nothing and the stochastic method due to Burrell, in determining the routes taken through the network.requests for offprints     

Link-based day-to-day network traffic dynamics and equilibria

A general dynamical system model with link-based variables is formulated to characterize the processes of achieving equilibria from a non-equilibrium state in traffic networks. Several desirable properties of the dynamical system model are established, including the equivalence between its stationary state and user equilibrium, the invariance of its evolutionary trajectories, and the uniqueness and stability of its stationary points. Moreover, it is shown that not only a link-based version of two existing day-to-day traffic dynamics models but also two existing link-based dynamical system models of traffic flow are the special cases of the proposed model. The stabilities of stationary states of these special cases are also analyzed and discussed. In addition, an extension is made to the case with elastic demand. The study is helpful for better understanding the day-to-day adjustment mechanism of traffic flows in networks.     

Modelling acceleration decisions in traffic streams with weak lane discipline: A latent leader approach

Acceleration is an important driving manoeuvre that has been modelled for decades as a critical element of the microscopic traffic simulation tools. The state-of-the art acceleration models have however primarily focused on lane based traffic. In lane based traffic, every driver has a single distinct lead vehicle in the front and the acceleration of the driver is typically modelled as a function of the relative speed, position and/or type of the corresponding leader. On the contrary, in a traffic stream with weak lane discipline, the subject driver may have multiple vehicles in the front. The subject driver is therefore subjected to multiple sources of stimulus for acceleration and reacts to the stimulus from the governing leader. However, only the applied accelerations are observed in the trajectory data, and the governing leader is unobserved or latent. The state-of-the-art models therefore cannot be directly applied to traffic streams with weak lane discipline.This prompts the current research where we present a latent leader acceleration model. The model has two components: a random utility based dynamic class membership model (latent leader component) and a class-specific acceleration model (acceleration component). The parameters of the model have been calibrated using detailed trajectory data collected from Dhaka, Bangladesh. Results indicate that the probability of a given front vehicle of being the governing leader can depend on the type of the lead vehicle and the extent of lateral overlap with the subject driver. The estimation results are compared against a simpler acceleration model (where the leader is determined deterministically) and a significant improvement in the goodness-of-fit is observed. The proposed models, when implemented in microscopic traffic simulation tools, are expected to result more realistic representation of traffic streams with weak lane discipline.     

A marginal utility day-to-day traffic evolution model based on one-step strategic thinking

Most deterministic day-to-day traffic evolution models, either in continuous-time or discrete-time space, have been formulated based on a fundamental assumption on driver route choice rationality where a driver seeks to maximize her/his marginal benefit defined as the difference between the perceived route costs. The notion of rationality entails the exploration of the marginal decision rule from economic theory, which states that a rational individual evaluates his/her marginal utility, defined as the difference between the marginal benefit and the marginal cost, of each incremental decision. Seeking to analyze the marginal decision rule in the modeling of deterministic day-to-day traffic evolution, this paper proposes a modeling framework which introduces a term to capture the marginal cost to the driver induced by route switching. The proposed framework enables to capture both benefit and cost associated with route changes. The marginal cost is then formulated upon the assumption that drivers are able to predict other drivers’ responses to the current traffic conditions, which is adopted based on the notion of strategic thinking of rational players developed in behavior game theory. The marginal cost based on 1-step strategic thinking also describes the “shadow price” of shifting routes, which helps to explain the behavioral tendency of the driver perceiving the cost-sensitivity to link/route flows. After developing a formulation of the marginal utility day-to-day model, its theoretical properties are analyzed, including the invariance property, asymptotic stability, and relationship with the rational behavioral adjustment process.     

Modeling car-following behavior on urban expressways in Shanghai: A naturalistic driving study

Although car-following behavior is the core component of microscopic traffic simulation, intelligent transportation systems, and advanced driver assistance systems, the adequacy of the existing car-following models for Chinese drivers has not been investigated with real-world data yet. To address this gap, five representative car-following models were calibrated and evaluated for Shanghai drivers, using 2100 urban-expressway car-following periods extracted from the 161,055 km of driving data collected in the Shanghai Naturalistic Driving Study (SH-NDS). The models were calibrated for each of the 42 subject drivers, and their capabilities of predicting the drivers’ car-following behavior were evaluated.The results show that the intelligent driver model (IDM) has good transferability to model traffic situations not presented in calibration, and it performs best among the evaluated models. Compared to the Wiedemann 99 model used by VISSIM®, the IDM is easier to calibrate and demonstrates a better and more stable performance. These advantages justify its suitability for microscopic traffic simulation tools in Shanghai and likely in other regions of China. Additionally, considerable behavioral differences among different drivers were found, which demonstrates a need for archetypes of a variety of drivers to build a traffic mix in simulation. By comparing calibrated and observed values of the IDM parameters, this study found that (1) interpretable calibrated model parameters are linked with corresponding observable parameters in real world, but they are not necessarily numerically equivalent; and (2) parameters that can be measured in reality also need to be calibrated if better trajectory reproducing capability are to be achieved.     

An investigation of the reliability of real-time information for route choice decisions in a congested traffic system

This paper investigates the reliability of information on prevailing trip times on the links of a network as a basis for route choice decisions by individual drivers. It considers a type of information strategy in which no attempt is made by some central controller or coordinating entity to predict what the travel times on each link would be by the time it is reached by a driver that is presently at a given location. A specially modified model combining traffic simulation and path assignment capabilities is used to analyze the reliability of the real-time information supplied to the drivers. This is accomplished by comparing the supplied travel times (at the link and path levels) to the actual trip times experienced in the network after the information has been given. In addition, the quality of the decisions made by drivers on the basis of this information (under alternative path switching rules) is evaluated ex-post by comparing the actually experienced travel time (given the decision made) to the time that the driver would have experienced without the real-time information. Results of a series of simulation experiments under recurrent congestion conditions are discussed, illustrating the interactions between information reliability and user response.     

Profile of the accident prone older driver

Accident histories and other related records of elderly drivers were used to develop a profile of the accident prone older driver in Michigan. Elderly drivers were defined as drivers with age greater than or equal to 65 years. The variables used in the study were developed by stratifying drivers age, sex, and residency; type of accident and violation; and number of traffic infraction points received. Comparisons were made between these strata, and the statistical significance of observed patterns in cross tabulated data was tested by performing the chi-square test. The results of the study indicate that, by and large, the elderly drivers from urban areas as compared to those from rural areas, and male drivers as compared to females are more likely to be cited for traffic violations. The statistical analysis showed some recognizable traits of the “young” elderly drivers that suggest prioritized safety countermeasures oriented toward them.     

Effectiveness of using variable message signs to disseminate dynamic traffic information: Evidence from field trails in European cities

Variable message signs (VMS) can provide up‐to‐date traffic information and guidance to drivers through electronic signs at the roadside. The paper draws together the results from VMS field trials conducted in nine cities as part of European Union‐sponsored research projects carried out between 1994 and 1999. The projects followed common guidelines in carrying out field trial evaluations, which has enabled generalized findings to be made on the impacts of the different VMS applications. The main emphasis in the paper is on drivers' reactions to VMS and the impacts of VMS on road network efficiency. Results are reported for four different types of traffic information. For incident messages, it is not only the severity of the problem reported that influences the level of diversions, but also other factors such as the specific location mentioned and the availability of viable alternative routes to avoid the problem location. For route guidance information, it is demonstrated that substantial diversions occur when the route advice differs from that given normally. For continuous information describing the traffic state on a major route, information increases the use of the major route and reduces use of alternative routes if there are no traffic problems reported on the major route. Travel time information was well regarded by drivers and found to be effective in inducing route changes. In general, the deployments of VMS to inform drivers of traffic conditions have proved successful in terms of improving network travel times and reducing environmental impacts. Whilst such changes have been relatively small, driver perception of the benefits is much higher. This is potentially very significant in terms of the role that VMS can play in the development of integrated transport strategies, as the provision of information may encourage greater acceptance of a range of demand management measures.     

A review of Australian traffic system design models

The demands for traffic infrastructure are increasing. Yet over the last decade investment in new infrastructure has decreased at all levels. Traffic systems designers are, therefore, being asked to be more accurate in their prediction of the impacts of changes, to analyse ever more complex situations and to extract more from the existing traffic system. This paper reviews developments in techniques for analysing the impacts of changes in the traffic system. It looks at intersection, route, network, parking lot and public transport design models that have been developed in Australia. Particular emphasis is given to the considerable developments in microcomputers and graphics and the impact these are having on the models. Future developments are also discussed.     

Modelling supported driving as an optimal control cycle: Framework and model characteristics

Driver assistance systems support drivers in operating vehicles in a safe, comfortable and efficient way, and thus may induce changes in traffic flow characteristics. This paper puts forward a receding horizon control framework to model driver assistance and cooperative systems. The accelerations of automated vehicles are controlled to optimise a cost function, assuming other vehicles driving at stationary conditions over a prediction horizon. The flexibility of the framework is demonstrated with controller design of Adaptive Cruise Control (ACC) and Cooperative ACC (C-ACC) systems. The proposed ACC and C-ACC model characteristics are investigated analytically, with focus on equilibrium solutions and stability properties. The proposed ACC model produces plausible human car-following behaviour and is unconditionally locally stable. By careful tuning of parameters, the ACC model generates similar stability characteristics as human driver models. The proposed C-ACC model results in convective downstream and absolute string instability, but not convective upstream string instability observed in human-driven traffic and in the ACC model. The control framework and analytical results provide insights into the influences of ACC and C-ACC systems on traffic flow operations.     

Development of simulated driving cycles for light,medium, and heavy duty trucks: Case of the Toronto Waterfront Area

Driving cycles are an important input for state-of-the-art vehicle emission models. Development of a driving cycle requires second-by-second vehicle speed for a representative set of vehicles. Current standard driving cycles cannot reflect or forecast changes in traffic conditions. This paper introduces a method to develop representative driving cycles using simulated data from a calibrated microscopic traffic simulation model of the Toronto Waterfront Area. The simulation model is calibrated to reflect road counts, link speeds, and accelerations using a multi-objective genetic algorithm. The simulation is validated by comparing simulated vs. observed passenger freeway cycles. The simulation method is applied to develop AM peak hour driving cycles for light, medium and heavy duty trucks. The demonstration reveals differences in speed, acceleration, and driver aggressiveness between driving cycles for different vehicle types. These driving cycles are compared against a range of available driving cycles, showing different traffic conditions and driving behaviors, and suggesting a need for city-specific driving cycles. Emissions from the simulated driving cycles are also compared with EPA’s Heavy Duty Urban Dynamometer Driving Schedule showing higher emission factors for the Toronto Waterfront cycles.     

Network models in traffic management and control

Abstract

The context for network modelling in traffic management and control is described in terms of the current area‐wide nature of traffic management and the range of objectives to which it can contribute. Representation of a road system and traffic management measures in terms of nodes and links and parameters associated with them is described. It is shown that the pattern of traffic has to be represented not only in terms of flows on links of the network but also in terms of numbers of movements per unit time between points of entry to and points of exit from the area being modelled. In modelling so far, these numbers of movements are regarded as given, but the routes taken are estimated by traffic assignment. Models can so far be used for comparison of a range of given schemes and for optimization of traffic control within a scheme. Variation over time is a central feature of the modelling, and this requires the use of time‐dependent queueing theory, and the specification of numbers of movements for a succession of periods of between 10 and 30 minutes. Theoretical approaches to the resulting problems of modelling and optimization are discussed, and the ways in which these are supplemented by heuristic methods in currently available models is described. Some requirements‐for further research are outlined.     

SIV-DSS: Smart In-Vehicle Decision Support System for driving at signalized intersections with V2I communication

In this paper, we present a Smart In-Vehicle Decision Support System (SIV-DSS) to help making better stop/go decisions in the indecision zone as a vehicle is approaching a signalized intersection. Supported by the Vehicle-to-Infrastructure (V2I) communications, the system integrates and utilizes the information from both vehicle and intersection. The effective decision support models of SIV-DSS are realized with the probabilistic sequential decision making process with the capability of combining a variety of advantages gained from a set of decision rules, where each decision rule is responsible to specific situations for making right decisions even without complete information. The decision rules are either extracted from the existing parametric models of the indecision zone problem, or designed as novel ones based on physical models utilizing the integrated information containing the key inputs from vehicle motion, vehicle-driver characteristics, intersection geometry and topology, signal phase and timings, and the definitions of red-light running (RLR). In SIV-DSS, the generality is reached through physical models utilizing a large number of accurate physical parameters, and the heterogeneity is treated by including a few behavioral parameters in driver characteristics. The performance of SIV-DSS is evaluated with systematic simulation experiments. The results show that the system can not only ensure traffic safety by greatly reducing the RLR probability, but also improve mobility by significantly reducing unnecessary stops at the intersection. Finally, we briefly discuss some relevant aspects and implications for SIV-DSS in practical implementations.     

A technique for the investigation of scheme benefits in large-scale transport networks

Existing methods of evaluating large-scale transport networks involve the use of mathematical models of traffic flow which are generally both large and complex. However, the time and cost involved in the use of these models normally restricts their use for the detailed forecasting of traffic flows and costs to the assessment of a relatively small number of alternative patterns of overall investment. In order to evaluate the individual projects and groups of projects which go to make up an overall investment plan, it is, therefore, usually necessary to make simplifying assumptions about the influence of any one project on the overall traffic pattern, so as to isolate it from the influence of neighbouring projects. These assumptions generally result in the loss of a certain amount of the detail normally available from a standard model, and the task of assessing the relative value of different projects and the amount of interaction between them is made more difficult.This paper describes a new technique, designed to permit the evaluation of individual projects whilst still retaining the level of detail available from a full-scale mathematical model. The aim has been to produce a cheap and easy-to-use technique, capable of producing substantially the same results as a standard model. The technique uses newly developed computer algorithms which short-cut the full-scale model by forecasting the changes in an existing travel pattern resulting from the influence of a particular project. Initial tests suggest that approaching the problem in this way can save up to 70% of the computing time and costs involved in the use of a standard model for the evaluation of individual projects.The technique as described here is envisaged as a tool for aiding strategic investment decisions. It can, however, provide data for more detailed investigations, and could, with modifications, carry out these investigations on smaller problems than those for which it was originally designed.Crown copyright reserved, 1973     

Efficient intersection control for minimally guided vehicles: A self-organised and decentralised approach

An important question for the practical applicability of the highly efficient traffic intersection control is about the minimal level of intelligence the vehicles need to have so as to move beyond the traffic light control. We propose an efficient intersection traffic control scheme without the traffic lights, that only requires a majority of vehicles on the road to be equipped with a simple driver assistance system. The algorithm of our scheme is completely decentralised, and takes into full account the non-linear interaction between the vehicles at high density. For vehicles approaching the intersection in different directions, our algorithm imposes simple interactions between vehicles around the intersection, by defining specific conditions on the real-time basis, for which the involved vehicles are required to briefly adjust their dynamics. This leads to a self-organised traffic flow that is safe, robust, and efficient. We also take into account of the driver comfort level and study its effect on the control efficiency. The scheme has low technological barrier, minimal impact on the conventional driving behaviour, and can coexist with the traffic light control. It also has the advantages of being easily scalable, and fully compatible with both the conventional road systems as well as the futuristic scenario in which driverless vehicles dominate the road. The mathematical formulation of our scheme permits large scale realistic numerical simulations of busy intersections, allowing a more complete evaluation of the control performance, instead of just the collision avoidance at the intersection.     

An agent-based approach to modelling driver route choice behaviour under the influence of real-time information

This paper presents an agent-based approach to modelling individual driver behaviour under the influence of real-time traffic information. The driver behaviour models developed in this study are based on a behavioural survey of drivers which was conducted on a congested commuting corridor in Brisbane, Australia. Commuters’ responses to travel information were analysed and a number of discrete choice models were developed to determine the factors influencing drivers’ behaviour and their propensity to change route and adjust travel patterns. Based on the results obtained from the behavioural survey, the agent behaviour parameters which define driver characteristics, knowledge and preferences were identified and their values determined. A case study implementing a simple agent-based route choice decision model within a microscopic traffic simulation tool is also presented. Driver-vehicle units (DVUs) were modelled as autonomous software components that can each be assigned a set of goals to achieve and a database of knowledge comprising certain beliefs, intentions and preferences concerning the driving task. Each DVU provided route choice decision-making capabilities, based on perception of its environment, that were similar to the described intentions of the driver it represented. The case study clearly demonstrated the feasibility of the approach and the potential to develop more complex driver behavioural dynamics based on the belief–desire–intention agent architecture.     

Some observed details of freeway traffic evolution

Certain details of traffic evolution were studied along a 2 km, homogenous freeway segment located upstream of a bottleneck. By comparing (transformed) cumulative curves constructed from the vehicle counts measured at neighboring loop detectors, it was found that waves propagated through queued traffic like a random walk with predictable statistical variation. There was no observed dependency of wave speed on flow. As such, these waves neither focused nor fanned outward and shocks arose only at the interfaces between free-flowing traffic and the back of queues. Although these traffic features may have long been suspected, actual observations of this kind have hitherto not been documented. Also of note, the shocks separating queued and unqueued traffic sometimes exhibited unexpectedly long transitions between these two states. Finally, some observations presented here corroborate earlier reports that, in unqueued traffic, vehicle velocity is insensitive to flows and that forward-moving changes in traffic states therefore travel with vehicles. Taken together, these findings suggest that certain rather simple models suffice for describing traffic on homogeneous freeway segments; brief discussion of this is offered in Section 5.     

A stochastic model of traffic flow: Theoretical foundations

In a variety of applications of traffic flow, including traffic simulation, real-time estimation and prediction, one requires a probabilistic model of traffic flow. The usual approach to constructing such models involves the addition of random noise terms to deterministic equations, which could lead to negative traffic densities and mean dynamics that are inconsistent with the original deterministic dynamics. This paper offers a new stochastic model of traffic flow that addresses these issues. The source of randomness in the proposed model is the uncertainty inherent in driver gap choice, which is represented by random state dependent vehicle time headways. A wide range of time headway distributions is allowed. From the random time headways, counting processes are defined, which represent cumulative flows across cell boundaries in a discrete space and continuous time conservation framework. We show that our construction implicitly ensures non-negativity of traffic densities and that the fluid limit of the stochastic model is consistent with cell transmission model (CTM) based deterministic dynamics.