Application of advanced sampling for efficient probabilistic traffic modelling

In probabilistic traffic models, consideration of stochasticity in the dynamics of traffic gives a closer representation of a traffic system in comparison to that of a deterministic approach. Monte Carlo simulation is a broadly accepted method to consider variations in traffic within modelling. In this contribution, the possibility of increasing the efficiency of probabilistic traffic flow models using Monte Carlo simulation is analysed using variance reduction techniques and sequencing, for varied capacity and traffic demand values. The techniques of Importance Sampling, Latin Hypercube Sampling and Quasi-Random Sequencing are compared in a dynamic macroscopic traffic model to demonstrate the effectiveness of these techniques for reduction of the computational load when considering multiple input variations. Demonstration of their efficiency in traffic modelling is expected to lead to a wider application of the methods in practice.     

Specification tests for probabilistic choice models

Probabilistic choice models, such as logit and probit models, are highly sensitive to a variety of specification errors, including the use of incorrect functional forms for the systematic component of the utility function, incorrect specification of the probability distribution of the random component of the utility function, and incorrect specification of the choice set. Specification errors can cause large forecasting errors, so it is of considerable importance to have means of testing for the presence of these errors. A number of tests based on the likelihood ratio statistic have been developed. These tests and available information on their power are summarized in this paper. The likelihood ratio test can entail considerable computational diffuculty, owing to the need to evaluate the likelihood function for both the null and alternative hypotheses. Substantial gains in computational efficiency can be achieved through the use of a test that requires evaluating the likelihood function only for the null hypothesis. A Lagrangian multiplier test that has this property is described, and numerical examples of its computational properties are given.An important disadvantage of conventional specification tests is that they do not permit comparisons of models that belong to different parametric families in order to determine which model best explains the available data. Thus, these tests cannot be used to compare models whose utility functions have substantially different functional forms or models that are based on different behavioral paradigms. Several methods for dealing with this problem, including the construction of hybrid models and the Cox test of separate families of hypotheses, are described.     

A probabilistic model for traffic at actuated control signals

Vehicle actuated controls are designed to adapt green and red times automatically, according to the actual dynamics of the arrival, departure and queuing processes. In turn, drivers experience variable delays and waiting times at these signals. However, in practice, delays and waiting times are computed at these systems with models that assume stationariety in the arrival process, and that are capable of computing simply expectation values, while no information is given on the uncertainty around this expectation. The growing interest on measures like travel time reliability, or network robustness motivates the development of models able to quantify the variability of traffic at these systems.This paper presents a new modeling approach for estimating queues and signal phase times, based on probabilistic theory. This model overcomes the limitations of existing models in that it does not assume stationary arrival rates, but it assumes any temporal distribution as input, and allows one to compute the temporal evolution of queue length and signal sequence probabilities. By doing so, one can also quantify the uncertainty in the estimation of delays and waiting times as time-dependent processes. The results of the probabilistic approach have been compared to the results of repeated microscopic simulations, showing good agreement. The smaller number of parameters and shorter computing times required in the probabilistic approach makes the model suitable for, e.g., planning and design problems, as well as model-based travel time estimation.     

Behavior-consistent information-based network traffic control for evacuation operations

The evacuation operations problem aims to avoid or mitigate the potential loss of life in a region threatened or affected by a disaster. It is shaped to a large extent by the evolution of evacuation traffic resulting from the demand–supply interactions of the associated transportation network. Information-based control is a strategic tool for evacuation traffic operations as it can enable greater access to the affected population and more effective response. However, comparatively few studies have focused on the implementation of information-based control in evacuation operations. This study develops a control module for evacuation operations centered on addressing the demand–supply interactions by using behavior-consistent information strategies. These strategies incorporate the likely responses of evacuees to the information provided in the determination of route guidance information. The control module works as an iterative computational process involving an evacuee route choice model and a control model of information strategies to determine the route guidance information to direct evacuation traffic so as to approach a desired network traffic flow pattern. The problem is formulated as a fuzzy logic based optimization framework to explicitly incorporate practical concerns related to information dissemination characteristics and social equity in evacuation operations. Numerical experiments highlight the importance of accounting for the demand–supply interactions, as the use of behavior-consistent information strategies can lead evacuee route choices to approach the operator-desired proportions corresponding to the desired traffic pattern. The results also indicate that while a behavior-consistent information strategy can be effective, gaps with the desired route proportions can exist due to the discrete nature of the linguistic messages and the real-world difficulty in accurately modeling evacuees’ actual route choice behavior.     

Extending Time to Collision for probabilistic reasoning in general traffic scenarios

Vehicle-to-vehicle communication systems allow vehicles to share state information with one another to improve safety and efficiency of transportation networks. One of the key applications of such a system is in the prediction and avoidance of collisions between vehicles. If a method to do this is to succeed it must be robust to measurement uncertainty and to loss of communication links. The method should also be general enough that it does not rely on constraints on vehicle motion for the accuracy of its predictions. It should work for all interactions between vehicles and not just a select subset. This paper presents a method to calculate Time to Collision for unconstrained vehicle motion. This metric is gated using a novel technique based on relative vehicle motion that we call “looming”. Finally, these ideas are integrated into a probabilistic framework that accounts for uncertainty in vehicle state and loss of vehicle-to-vehicle communication. Together this work represents a new way of considering vehicle collision estimation. These algorithms are validated on data collected from real world vehicle trials.     

Goodness-of-fit measures for probabilistic travel demand models

This paper is concerned with the assessment of the goodness-of-fit of nonlinear models of the type currently being used in the development of the disaggregate, behavioral travel demand approach. These models are emerging as a potential new technique for many transportation planning problems, although much research is yet needed before they are sufficiently developed for operational use. In order to pursue the necessary research, and also for the later assessment of operational models, it is necessary to have adequate measures of the goodness-of-fit.The paper examines the adequacy of standard measures of goodness-of-fit as applied to any nonlinear estimating equation and they are found to be inappropriate and inadequate. A little-known statistic, called the correlation ratio, is then defined and derived, and is explored as a substitute for the standard measures. In both theoretical and empirical tests, the correlation ratio is found to be a significantly more useful and appropriate measure of goodness-of-fit.Some further properties of the correlation ratio are examined, and the ratio is found to possess some degree of arbitrariness when applied to typical travel demand models. This arbitrariness, however, only impairs the usefulness of the correlation ratio in the absolute assessment of a model, but not for the comparative assessment of two or more models. Finally, a number of research tasks, relating to the correlation ratio, are identified.     

A probabilistic model for the behaviour of traffic at a roundabout

A discrete-time, Markov chain model is proposed to describe the behaviour of traffic travelling on a single-lane roundabout and queueing on approach roads to enter the roundabout. A general origin-destination matrix is allowed for trip ends, there is an arbitrary number of approach roads and there is room for a general number of vehicles on each weaving section. Attention is given to the equilibrium régime at an approach subject to heavy traffic conditions. It is shown that for such an approach the moments of the distribution of the length of the queue of waiting vehicles may be found by a heavy traffic approximation.     

Heteroscedastic Gaussian processes for uncertainty modeling in large-scale crowdsourced traffic data

Accurately modeling traffic speeds is a fundamental part of efficient intelligent transportation systems. Nowadays, with the widespread deployment of GPS-enabled devices, it has become possible to crowdsource the collection of speed information to road users (e.g. through mobile applications or dedicated in-vehicle devices). Despite its rather wide spatial coverage, crowdsourced speed data also brings very important challenges, such as the highly variable measurement noise in the data due to a variety of driving behaviors and sample sizes. When not properly accounted for, this noise can severely compromise any application that relies on accurate traffic data. In this article, we propose the use of heteroscedastic Gaussian processes (HGP) to model the time-varying uncertainty in large-scale crowdsourced traffic data. Furthermore, we develop a HGP conditioned on sample size and traffic regime (SSRC-HGP), which makes use of sample size information (probe vehicles per minute) as well as previous observed speeds, in order to more accurately model the uncertainty in observed speeds. Using 6 months of crowdsourced traffic data from Copenhagen, we empirically show that the proposed heteroscedastic models produce significantly better predictive distributions when compared to current state-of-the-art methods for both speed imputation and short-term forecasting tasks.     

An integrated multi‐objective model to determine the optimal rescue path and traffic controlled arcs for disaster relief operations under uncertainty environments

This study proposes an integrated multi‐objective model to determine the optimal rescue path and traffic controlled arcs for disaster relief operations under uncertainty environments. The model consists of three sub‐models: rescue shortest path model, post‐disaster traffic assignment model, and traffic controlled arcs selection model to minimize four objectives: travel time of rescue path, total detour travel time, number of unconnected trips of non‐victims, and number of police officers required. Since these sub‐models are inter‐related with each other, they are solved simultaneously. This study employs genetic algorithms incorporated with traffic assignment and K‐shortest path methods to determine optimal rescue path and controlled arcs. To cope with uncertain information associated with the damaged network, fuzzy system reliability theory (weakest t‐norm method) is used to measure the access reliability of rescue path. To investigate the validity and applicability of the proposed model, studies on an exemplified case and a field case of Chi‐Chi earthquake in Taiwan are conducted. The performances of three rescue strategies: without traffic control, selective traffic control (i.e. the proposed model) and absolute traffic control are compared. The results show that the proposed model can maintain the efficiency of rescue activity with minimal impact to ordinary trips and number of police officers required.     

Bayesian inference for day-to-day dynamic traffic models

There is significant current interest in the development of models to describe the day-to-day evolution of traffic flows over a network. We consider the problem of statistical inference for such models based on daily observations of traffic counts on a subset of network links. Like other inference problems for network-based models, the critical difficulty lies in the underdetermined nature of the linear system of equations that relates link flows to the latent path flows. In particular, Bayesian inference implemented using Markov chain Monte Carlo methods requires that we sample from the set of route flows consistent with the observed link flows, but enumeration of this set is usually computationally infeasible.We show how two existing conditional route flow samplers can be adapted and extended for use with day-to-day dynamic traffic. The first sampler employs an iterative route-by-route acceptance–rejection algorithm for path flows, while the second employs a simple Markov model for traveller behaviour to generate candidate entire route flow patterns when the network has a tree structure. We illustrate the application of these methods for estimation of parameters that describe traveller behaviour based on daily link count data alone.     

Autonomous and conventional bus fleet optimization for fixed-route operations considering demand uncertainty

Transportation - The emerging technology of autonomous vehicles has been widely recognized as a promising urban mobility solution in the future. This paper considers the integration of autonomous...     

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.     

Comparison of parametric and nonparametric models for traffic flow forecasting

Single point short-term traffic flow forecasting will play a key role in supporting demand forecasts needed by operational network models. Seasonal autoregressive integrated moving average (ARIMA), a classic parametric modeling approach to time series, and nonparametric regression models have been proposed as well suited for application to single point short-term traffic flow forecasting. Past research has shown seasonal ARIMA models to deliver results that are statistically superior to basic implementations of nonparametric regression. However, the advantages associated with a data-driven nonparametric forecasting approach motivate further investigation of refined nonparametric forecasting methods. Following this motivation, this research effort seeks to examine the theoretical foundation of nonparametric regression and to answer the question of whether nonparametric regression based on heuristically improved forecast generation methods approach the single interval traffic flow prediction performance of seasonal ARIMA models.     

Approximate queueing models for analyzing harbor terminal operations

The purpose of this paper is to present approximate queueing models to help assess the impacts of tug services on congested harbor terminals. The models are intended for harbors in which tug shortages are rare. A congested harbor terminal is modelled as a queueing system with m identical tugs (servers) and n identical berths (customers), and with general probability distributions of tug service time and berth cargo-handling time. The distribution of the number of berths in the system, a basic element to analyze the system performance, was established for two cases. For large m, the distribution was approximated by a binomial model and the respective accuracy tested. For small m, an approximate model for this distribution was developed. Particular emphasis was given to developing explicitly the probability of having one berth in queue and establishing the remaining probabilities of the distribution approximately. The model for small m was validated by means of simulation for various cases of harbor terminal operations exhibiting different ranges of the coefficient of variation of tug service time. The models were found to be reasonably accurate within a certain range covering situations in which tug shortages are in the order of 10% of the time or less.     

Optimal tolls for multi-class traffic: Analytical formulations and policy implications

This paper puts together an analytical formulation to compute optimal tolls for multi-class traffic. The formulation is comprised of two major modules. The first one is an optimization component aimed at computing optimal tolls assuming a Stackelberg game in which the toll agency sets the tolls, and the equilibrating traffic plays the role of the followers. The optimization component is supported by a set of cost models that estimate the externalities as a function of a multivariate vector of traffic flows. These models were estimated using Taylor series expansions of the output obtained from traffic simulations of a hypothetical test case. Of importance to the paper is the total travel time function estimated using this approach that expresses total travel time as a multivariate function of the traffic volumes. The formulation presented in the paper is then applied to a variety of scenarios to gain insight into the optimality of current toll policies. The optimal tolls are computed for two different cases: independent tolls, and tolls proportional to passenger car equivalencies (PCE).The numerical results clearly show that setting tolls proportional to PCEs leads to lower values of welfare that are on average 15% lower than when using independent tolls, though, in some cases the total welfare could be up to 33% lower. This is a consequence of two factors. First, the case of independent tolls has more degrees of freedom than the case of tolls proportional to PCEs. Second, tolls proportional to PCEs do not account for externalities other than congestion, which is likely to lead to lower welfare values.The analytical formulations and numerical results indicate that, because the total travel time is a non-linear function of the traffic volumes, the marginal social costs and thus the optimal congestion tolls also depend on the traffic volumes for each vehicle class. As a result of this, for the relatively low volumes of truck traffic observed in real life, the optimal congestion tolls for trucks could indeed be either lower or about the same as for passenger cars. This stand in sharp contrast with what is implied in the use of PCEs, i.e., that the contribution to congestion are constant. This latter assumption leads to optimal truck congestion tolls that are always proportional to the PCE values.The comparison of the toll ratios (truck tolls divided by passenger car tolls) for both observed and optimal conditions suggests that the tolls for small trucks are about the right level, maybe a slightly lower than optimal. However, the analysis of the toll ratio for large trucks seems to indicate a significant overcharge. The estimates show that the average observed toll ratio for large trucks is even higher than the maximum optimal toll ratio found in the numerical experiments. This suggests that the tolls for large trucks are set on the basis of revenue generation principles while the passenger car tolls are being set based on a mild form of welfare maximization. This leads to a suboptimal cross-subsidization of passenger car traffic in detriment of an important sector of the economy.     

On the probabilistic origin of dial's multipath traffic assignment model

Dial's multipath traffic assignment model is interpreted as a probabilistic choice model. Anomalies in path assignments generated by Dial's algorithm are related to the independence-of-irrelevant alternatives axiom.     

Macroscopic traffic models for vehicle-follower automated transportation systems

The problem of distributing and routing vehicles in a large automated transportation network may be approached through the design of on-line control algorithms, particularly when the network contains many origin-destination pairs and alternate routes. To develop such algorithms, it is necessary to obtain models that accurately represent the dynamic behavior of vehicles on the guideway network. In this paper, models based on density, flow and average velocity variables are derived for the vehicle-follower longitudinal control scheme. Models suitable for use in analysis and simulation work are developed for links, merges, diverges, and stations. The proposed models are shown to compare favorably with simulation results that use explicit modeling of vehicle dynamic modeling of vehicle dynamic interaction.     

Properties of a traffic control policy which ensure the existence of a traffic equilibrium consistent with the policy

We consider a network with interactions and capacity constraints at each junction. We give conditions on the interactions and constraints which, if satisfied at each separate junction, ensure that any feasible assignment problem has an equilibrium solution. Two illustrative examples are provided; the first arises naturally and does not satisfy our conditions, while the second does satisfy our conditions but is somewhat unnatural.     

Genetics of traffic assignment models for strategic transport planning

This paper presents a review and classification of traffic assignment models for strategic transport planning purposes by using concepts analogous to genetics in biology. Traffic assignment models share the same theoretical framework (DNA), but differ in capability (genes). We argue that all traffic assignment models can be described by three genes. The first gene determines the spatial capability (unrestricted, capacity restrained, capacity constrained, and capacity and storage constrained) described by four spatial assumptions (shape of the fundamental diagram, capacity constraints, storage constraints, and turn flow restrictions). The second gene determines the temporal capability (static, semi-dynamic, and dynamic) described by three temporal assumptions (wave speeds, vehicle propagation speeds, and residual traffic transfer). The third gene determines the behavioural capability (all-or-nothing, one shot, and equilibrium) described by two behavioural assumptions (decision-making and travel time consideration). This classification provides a deeper understanding of the often implicit assumptions made in traffic assignment models described in the literature. It further allows for comparing different models in terms of functionality, and paves the way for developing novel traffic assignment models.