Quantifying uncertainties in a national forecasting model

Uncertainties related to demand model system outputs is an important issue in travel demand models. This paper focuses on uncertainties arisen from the fact that models are estimated on a sample of the population (and not the whole population). Forecasting systems can be quite complex, and may contain procedures that not easily permit analytically derived statistical measures of uncertainty. In this paper, the possibilities to use computer-intensive numerical methods to compute statistical measures for very complex systems, without being bound to an analytical approach, are explored. Here, the bootstrap method is used to obtain statistical measures of outputs produced by the forecasting system SAMPERS. The SAMPERS system is used by Swedish transport authorities. The bootstrap method is briefly described as well as the procedure of applying bootstrap on the SAMPERS system. Numerical results are presented for selected forecast results at different levels such as total traffic demand, origin–destination demand, train line demand and the demand on specific links. Also, the uncertainty related to the value of time estimate is analysed.     

The treatment of uncertainty in the dynamic origin–destination estimation problem using a fuzzy approach

Regardless of existing types of transportation and traffic model and their applications, the essential input to these models is travel demand, which is usually described using origin–destination (OD) matrices. Due to the high cost and time required for the direct development of such matrices, they are sometimes estimated indirectly from traffic measurements recorded from the transportation network. Based on an assumed demand profile, OD estimation problems can be categorized into static or dynamic groups. Dynamic OD demand provides valuable information on the within-day fluctuation of traffic, which can be employed to analyse congestion dissipation. In addition, OD estimates are essential inputs to dynamic traffic assignment (DTA) models. This study presents a fuzzy approach to dynamic OD estimation problems. The problems are approached using a two-level model in which demand is estimated in the upper level and the lower level performs DTA via traffic simulation. Using fuzzy rules and the fuzzy C-Mean clustering approach, the proposed method treats uncertainty in historical OD demand and observed link counts. The approach employs expert knowledge to model fitted link counts and to set boundaries for the optimization problem by defining functions in the fuzzification process. The same operation is performed on the simulation outputs, and the entire process enables different types of optimization algorithm to be employed. The Box-complex method is utilized as an optimization algorithm in the implementation of the approach. Empirical case studies are performed on two networks to evaluate the validity and accuracy of the approach. The study results for a synthetic network and a real network demonstrate the robust performance of the proposed method even when using low-quality historical demand data.     

Robust network pricing and system optimization under combined long-term stochasticity and elasticity of travel demand

Network pricing serves as an instrument for congestion management, however, agencies and planners often encounter problems of estimating appropriate toll prices. Tolls are commonly estimated for a single-point deterministic travel demand, which may lead to imperfect policy decisions due to inherent uncertainties in future travel demand. Previous research has addressed the issue of demand uncertainty in the pricing context, but the elastic nature of demand along with its uncertainty has not been explicitly considered. Similarly, interactions between elasticity and uncertainty of demand have not been characterized. This study addresses these gaps and proposes a framework to estimate nearest optimal first-best tolls under long-term stochasticity in elastic demand. We show first that the optimal tolls under the deterministic-elastic and stochastic-elastic demand cases coincide when cost and demand functions are linear, and the set of equilibrium paths is constant. These assumptions are restrictive, so three larger networks are considered numerically, and the subsequent pricing decisions are assessed. The results of the numerical experiments suggest that in many cases, optimal pricing decisions under the combined stochastic-elastic demand scenario resemble those when demand is known exactly. The applications in this study thus suggest that inclusion of demand elasticity offsets the need of considering future demand uncertainties for first-best congestion pricing frameworks.     

Designing heterogeneous sensor networks for estimating and predicting path travel time dynamics: An information-theoretic modeling approach

With a particular emphasis on the end-to-end travel time prediction problem, this paper proposes an information-theoretic sensor location model that aims to minimize total travel time uncertainties from a set of point, point-to-point and probe sensors in a traffic network. Based on a Kalman filtering structure, the proposed measurement and uncertainty quantification models explicitly take into account several important sources of errors in the travel time estimation/prediction process, such as the uncertainty associated with prior travel time estimates, measurement errors and sampling errors. By considering only critical paths and limited time intervals, this paper selects a path travel time uncertainty criterion to construct a joint sensor location and travel time estimation/prediction framework with a unified modeling of both recurring and non-recurring traffic conditions. An analytical determinant maximization model and heuristic beam-search algorithm are used to find an effective lower bound and solve the combinatorial sensor selection problem. A number of illustrative examples and one case study are used to demonstrate the effectiveness of the proposed methodology.     

Does uncertainty make cost-benefit analyses pointless?

Cost-benefit analysis (CBA) is widely used in public decision making on infrastructure investments. However, the demand forecasts, cost estimates, benefit valuations and effect assessments that are conducted as part of CBAs are all subject to various degrees of uncertainty. The question is to what extent CBAs, given such uncertainties, are still useful as a way to prioritize between infrastructure investments, or put differently, how robust the policy conclusions of CBA are with respect to uncertainties. Using simulations based on real data on national infrastructure plans in Sweden and Norway, we study how investment selection and total realized benefits change when decisions are based on CBA assessments subject to several different types of uncertainty. Our results indicate that realized benefits and investment selection are surprisingly insensitive to all studied types of uncertainty, even for high levels of uncertainty. The two types of uncertainty that affect results the most are uncertainties about investment cost and transport demand. Provided that decisions are based on CBA outcomes, reducing uncertainty is still worthwhile, however, because of the huge sums at stake. Even moderate reductions of uncertainties about unit values, investment costs, future demand and project effects may increase the realized benefits infrastructure investment plans by tens or hundreds of million euros. We conclude that, despite the many types of uncertainties, CBA is able to fairly consistently separate the wheat from the chaff and hence contribute to substantially improved infrastructure decisions.     

Rationing and pricing strategies for congestion mitigation: Behavioral theory,econometric model,and application in Beijing

Some travel demand management policies such as road pricing have been widely studied in literature. Rationing policies, including vehicle ownership quota and vehicle usage restrictions, have been implemented in several megaregions to address congestion and other negative transportation externalities, but not well explored in literature. Other strategies such as Vehicle Mileage Fee have not been well accepted by policy makers, but attract growing research interest. As policy makers face an increasing number of policy tools, a theoretical framework is needed to analyze these policies and provide a direct comparison of their welfare implications such as efficiency and equity. However, such a comprehensive framework does not exist in literature. To bridge this gap, this study develops an analytical framework for analyzing and comparing travel demand management policies, which consists of a mathematical model of joint household vehicle ownership and usage decisions and welfare analysis methods based on compensating variation and consumer surplus. Under the assumptions of homogenous users and single time period, this study finds that vehicle usage rationing performs better when relatively small percentages of users (i.e. low rationing ratio) are rationed off the roads and when induced demand elasticity resulting from congestion mitigation is low. When the amount of induced demand exceeds a certain level, it is shown analytically that vehicle usage restrictions will always cause welfare losses. When the policy goal is to reduce vehicle travel by a fixed portion, road pricing provides a larger welfare gain. The performance of different policies is influenced by network congestion and congestibility. This paper further generalizes the model to consider heterogenous users and demonstrates how it can be applied for policy analysis on a real network after careful calibration.     

Long-term trends in domestic US passenger travel: the past 110 years and the next 90

Based upon a long-term historical data set of US passenger travel, a model is estimated to project aggregate transportation trends through 2100. One of the two model components projects total mobility (passenger-km traveled) per capita based on per person GDP and the expected utility of travel mode choices (logsum). The second model component has the functional form of a logit model, which assigns the projected travel demand to competing transportation modes. An iterative procedure ensures the average amount of travel time per person to remain at a pre-specified level through modifying the estimated value of time. The outputs from this model can be used as a first-order estimate of a future benchmark against which the effectiveness of various transportation policy measures or the impact of autonomous behavioral change can be assessed.     

Capturing the conditions that introduce systematic variation in bike-sharing travel behavior using data mining techniques

The potential of smart-card transactions within bike-sharing systems (BSS) is still to be explored. This research proposes an original offline data mining procedure that takes advantage of the quality of these data to analyze the bike usage casuistry within a sharing scheme. A difference is made between usage and travel behavior: the usage is described by the actual trip-chaining gathered with every smart-card transaction and is directly influenced by the limitations of the BSS as a public renting service, while the travel behavior relates to the spatio-temporal distribution, the travel time and trip purpose. The proposed approach is based on the hypothesis that there are systematic usage types which can be described through a set of conditions that permit to classify the rentals and reduce the heterogeneity in travel patterns. Hence, the proposed algorithm is a powerful tool to characterize the actual demand for bike-sharing systems. Furthermore, the results show that its potential goes well beyond that since service deficiencies rapidly arise and their impacts can be measured in terms of demand. Consequently, this research contributes to the state of knowledge on cycling behavior within public systems and it is also a key instrument beneficial to both decision makers and operators assisting the demand analysis, the service redesign and its optimization.     

A new schedule-based transit assignment model with travel strategies and supply uncertainties

This paper proposes a new scheduled-based transit assignment model. Unlike other schedule-based models in the literature, we consider supply uncertainties and assume that users adopt strategies to travel from their origins to their destinations. We present an analytical formulation to ensure that on-board passengers continuing to the next stop have priority and waiting passengers are loaded on a first-come-first-serve basis. We propose an analytical model that captures the stochastic nature of the transit schedules and in-vehicle travel times due to road conditions, incidents, or adverse weather. We adopt a mean variance approach that can consider the covariance of travel time between links in a space–time graph but still lead to a robust transit network loading procedure when optimal strategies are adopted. The proposed model is formulated as a user equilibrium problem and solved by an MSA-type algorithm. Numerical results are reported to show the effects of supply uncertainties on the travel strategies and departure times of passengers.     

Spatiotemporal influence of land use and household properties on automobile travel demand

Understanding the patterns of automobile travel demand can help formulate policies to alleviate congestion and pollution. This study focuses on the influence of land use and household properties on automobile travel demand. Car license plate recognition (CLPR) data, point-of-interest (POI) data, and housing information data were utilized to obtain automobile travel demand along with the land use and household properties. A geographically and temporally weighted regression (GTWR) model was adopted to deal with both the spatial and temporal heterogeneity of travel demand. The spatial-temporal patterns of GTWR coefficients were analyzed. Also, comparative analyses were carried out between automobile and total person travel demand, and among travel demand of taxis, heavily-used private cars, and total automobiles. The results show that: (I) The GTWR model has significantly higher accuracy compared with the Ordinary Least Square (OLS) model and the Geographically Weighted Regression (GWR) model, which means the GTWR model can measure both the spatial and temporal heterogeneity with high precision; (II) The influence of built environment and household properties on automobile travel demand varies with space and time. In particular, the temporal distribution of regression coefficients shows significant peak phenomenon; and (III) Comparative analyses indicate that residents’ preference for automobiles over other travel modes varies with their travel purpose and destination. The above findings indicate that the proposed method can not only model spatial-temporal heterogeneous travel demand, but also provide a way to analyze the patterns of automobile travel demand.     

Optimal transit fare in a bimodal network under demand uncertainty and bounded rationality

This paper investigates the optimal transit fare in a simple bimodal transportation system that comprises public transport and private car. We consider two new factors: demand uncertainty and bounded rationality. With demand uncertainty, travelers are assumed to consider both the mean travel cost and travel cost variability in their mode choice decision. Under bounded rationality, travelers do not necessarily choose the travel mode of which perceived travel cost is absolutely lower than the one of the other mode. To determine the optimal transit fare, a bi‐level programming is proposed. The upper‐level objective function is to minimize the mean of total travel cost, whereas the lower‐level programming adopts the logit‐based model to describe users' mode choice behaviors. Then a heuristic algorithm based on a sensitivity analysis approach is designed to solve the bi‐level programming. Numerical examples are presented to illustrate the effect of demand uncertainty and bounded rationality on the modal share, optimal transit fare and system performance. Copyright © 2013 John Wiley & Sons, Ltd.     

Using survival models to estimate bus travel times and associated uncertainties

Transit agencies often provide travelers with point estimates of bus travel times to downstream stops to improve the perceived reliability of bus transit systems. Prediction models that can estimate both point estimates and the level of uncertainty associated with these estimates (e.g., travel time variance) might help to further improve reliability by tempering user expectations. In this paper, accelerated failure time survival models are proposed to provide such simultaneous predictions. Data from a headway-based bus route serving the Pennsylvania State University-University Park campus were used to estimate bus travel times using the proposed survival model and traditional linear regression frameworks for comparison. Overall, the accuracy of point estimates from the two approaches, measured using the root-mean-squared errors (RMSEs) and mean absolute errors (MAEs), was similar. This suggests that both methods predict travel times equally well. However, the survival models were found to more accurately describe the uncertainty associated with the predictions. Furthermore, survival model estimates were found to have smaller uncertainties on average, especially when predicted travel times were small. Tests for transferability over time suggested that the models did not over-fit the dataset and validated the predictive ability of models established with historical data. Overall, the survival model approach appears to be a promising method to predict both expected bus travel times and the uncertainty associated with these travel times.     

Adaptive traffic signal control with equilibrium constraints under stochastic demand

This study develops a methodology to model transportation network design with signal settings in the presence of demand uncertainty. It is assumed that the total travel demand consists of commuters and infrequent travellers. The commuter travel demand is deterministic, whereas the demand of infrequent travellers is stochastic. Variations in demand contribute to travel time uncertainty and affect commuters’ route choice behaviour. In this paper, we first introduce an equilibrium flow model that takes account of uncertain demand. A two-stage stochastic program is then proposed to formulate the network signal design under demand uncertainty. The optimal control policy derived under the two-stage stochastic program is able to (1) optimize the steady-state network performance in the long run, and (2) respond to short-term demand variations. In the first stage, a base signal control plan with a buffer against variability is introduced to control the equilibrium flow pattern and the resulting steady-state performance. In the second stage, after realizations of the random demand, recourse decisions of adaptive signal settings are determined to address the occasional demand overflows, so as to avoid transient congestion. The overall objective is to minimize the expected total travel time. To solve the two-stage stochastic program, a concept of service reliability associated with the control buffer is introduced. A reliability-based gradient projection algorithm is then developed. Numerical examples are performed to illustrate the properties of the proposed control method as well as its capability of optimizing steady-state performance while adaptively responding to changing traffic flows. Comparison results show that the proposed method exhibits advantages over the traditional mean-value approach in improving network expected total travel times.     

Modelling rain effects on risk‐taking behaviours of multi‐user classes in road networks with uncertainty

This paper proposes a new travel time reliability‐based traffic assignment model to investigate the rain effects on risk‐taking behaviours of different road users in networks with day‐to‐day demand fluctuations and variations in travel time. A generalized link travel time function is used to capture the rain effects on vehicle travel times and road conditions. This function is further incorporated into daily demand variations to investigate those travel time variations arising from demand uncertainty and rain condition. In view of these rain effects, road users' perception errors on travel times and risk‐taking behaviours on path choices are incorporated in the proposed model with the use of a logit‐based stochastic user equilibrium framework. This new model is formulated as a variational inequality problem in terms of path flows. A numerical example is used to illustrate the application of the proposed model for assessment of the rain effects on road networks with uncertainty.     

A hyperpath-based network generalized extreme-value model for route choice under uncertainties

Previous route choice studies treated uncertainties as randomness; however, it is argued that other uncertainties exist beyond random effects. As a general modeling framework for route choice under uncertainties, this paper presents a model of route choice that incorporates hyperpath and network generalized extreme-value-based link choice models. Accounting for the travel time uncertainty, numerical studies of specified models within the proposed framework are conducted. The modeling framework may be helpful in various research contexts dealing with both randomness and other non-probabilistic uncertainties that cannot be exactly perceived.     

A bayesian dynamic linear model approach for real-time short-term freeway travel time prediction

This paper presents a Bayesian inference-based dynamic linear model (DLM) to predict online short-term travel time on a freeway stretch. The proposed method considers the predicted freeway travel time as the sum of the median of historical travel times, time-varying random variations in travel time, and a model evolution error, where the median is employed to recognize the primary travel time pattern while the variation captures unexpected supply (i.e. capacity) reduction and demand fluctuations. Bayesian forecasting is a learning process that revises sequentially the state of a priori knowledge of travel time based on newly available information. The prediction result is a posterior travel time distribution that can be employed to generate a single-value (typically but not necessarily the mean) travel time as well as a confidence interval representing the uncertainty of travel time prediction. To better track travel time fluctuations during non-recurrent congestion due to unforeseen events (e.g., incidents, accidents, or bad weather), the DLM is integrated into an adaptive control framework that can automatically learn and adjust the system evolution noise level. The experiment results based on the real loop detector data of an I-66 segment in Northern Virginia suggest that the proposed method is able to provide accurate and reliable travel time prediction under both recurrent and non-recurrent traffic conditions.     

Sensitivity analysis for energy demand estimation of electric vehicles

We present a sensitivity analysis for a mechanical model, which is used to estimate the energy demand of battery electric vehicles. This model is frequently used in literature, but its parameters are often chosen incautiously, which can lead to inaccurate energy demand estimates. We provide a novel prioritization of parameters and quantify their impact on the accuracy of the energy demand estimation, to enable better decision making during the model parameter selection phase. We furthermore determine a subset of parameters, which has to be defined, in order to achieve a desired estimation accuracy. The analysis is based on recorded GPS tracks of a battery electric vehicle under various driving conditions, but results are equally applicable for other BEVs. Results show that the uncertainty of vehicle efficiency and rolling friction coefficient have the highest impact on accuracy. The uncertainty of power demand for heating and cooling the vehicle also strongly affects the estimation accuracy, but only at low speeds. We also analyze the energy shares related to each model component including acceleration, air drag, rolling and grade resistance and auxiliary energy demand. Our work shows that, while some components make up a large share of the overall energy demand, the uncertainty of parameters related to these components does not affect the accuracy of energy demand estimation significantly. This work thus provides guidance for implementing and calibrating an energy demand estimation based on a longitudinal dynamics model.     

A multi‐class mean‐excess traffic equilibrium model with elastic demand

Recent empirical studies have revealed that travel time variability plays an important role in travelers' route choice decisions. To simultaneously account for both reliability and unreliability aspects of travel time variability, the concept of mean‐excess travel time (METT) was recently proposed as a new risk‐averse route choice criterion. In this paper, we extend the mean‐excess traffic equilibrium model to include heterogeneous risk‐aversion attitudes and elastic demand. Specifically, this model explicitly considers (1) multiple user classes with different risk‐aversions toward travel time variability when making route choice decisions under uncertainty and (2) the elasticity of travel demand as a function of METT when making travel choice decisions under uncertainty. This model is thus capable of modeling travelers' heterogeneous risk‐averse behaviors with both travel choice and route choice considerations. The proposed model is formulated as a variational inequality problem and solved via a route‐based algorithm using the modified alternating direction method. Numerical analyses are also provided to illustrate the features of the proposed model and the applicability of the solution algorithm. Copyright © 2012 John Wiley & Sons, Ltd.     

First-best marginal cost toll for a traffic network with stochastic demand

First-best marginal cost pricing (MCP) in traffic networks has been extensively studied with the assumption of deterministic travel demand. However, this assumption may not be realistic as a transportation network is exposed to various uncertainties. This paper investigates MCP in a traffic network under stochastic travel demand. Cases of both fixed and elastic demand are considered. In the fixed demand case, travel demand is represented as a random variable, whereas in the elastic demand case, a pre-specified random variable is introduced into the demand function. The paper also considers a set of assumptions of traveler behavior. In the first case, it is assumed that the traveler considers only the mean travel time in the route choice decision (risk-neutral behavior), and in the second, both the mean and the variance of travel time are introduced into the route choice model (risk-averse behavior). A closed-form formulation of the true marginal cost toll for the stochastic network (SN-MCP) is derived from the variational inequality conditions of the system optimum and user equilibrium assignments. The key finding is that the calculation of the SN-MCP model cannot be made by simply substituting related terms in the original MCP model by their expected values. The paper provides a general function of SN-MCP and derives the closed-form SN-MCP formulation for specific cases with lognormal and normal stochastic travel demand. Four numerical examples are explored to compare network performance under the SN-MCP and other toll regimes.