Random Travel Times Research Articles

Proactive route choice with real-time information: Learning and effects of network complexity and cognitive load

Proactive route choice refers to a driver’s taking into account future diversion possibilities enabled by real-time information in a network with random travel times. Route choice experiments were conducted in three types of networks with increasing complexity, where the simplest one has no diversion possibilities and is used to gauge risk attitude. Two apparatuses with different cognitive load, a driving simulator and PC were used. Aggregate analyses show that network complexity negatively affects subjects’ ratio of choosing the risky option on a driving simulator; cognitive load negatively affects subject’s ratio of choosing the risky option in the simplest network, but not in more complex networks. A mixed Logit model with two latent classes, proactive and myopic, is specified and estimated. Results show that subjects learn to be more proactive over time. The impact of network complexity or cognitive load on being proactive is not statistically significant. Cognitive load however increases myopic subjects’ risk aversion.

Stochastic optimization models for a home service routing and appointment scheduling problem with random travel and service times

We address a routing and appointment scheduling problem with uncertain service and travel times arising from home service practice. Specifically, given a set of customers within a service region that an operator needs to serve, we seek to find the operator’s route and time schedule. The quality of routing and scheduling decisions is a function of the total operational cost, consisting of customers’ waiting time, and the operator’s travel time, idle time and overtime. We propose and rigorously analyze a stochastic programming model and two distributionally robust optimization (DRO) models to solve the problem, assuming known and unknown service and travel time distributions, respectively. We consider two popular types of ambiguity sets for the DRO models: mean-support and 1-Wasserstein ambiguity sets. We derive equivalent mixed-integer linear programming (MILP) reformulations of both DRO models that can be implemented and efficiently solved using off-the-shelf optimization software, thereby enabling practitioners to use these models. In an extensive numerical experiment, we investigate the proposed models’ computational and operational performance and derive insights into the problem.

High-Resolution, Quantitative Signal Subspace Imaging for Synthetic Aperture Radar

We consider synthetic aperture radar imaging of a region containing point-like targets. Measurements are the set of frequency responses to scattering by the targets taken over a collection of individual spatial locations along the flight path making up the synthetic aperture. Because signal subspace imaging methods do not work on these measurements directly, we rearrange the frequency response at each spatial location using the Prony method and obtain a matrix that is suitable for these methods. We arrange the set of these Prony matrices as one block-diagonal matrix and introduce a signal subspace imaging method for it. We show that this signal subspace method yields high-resolution and quantitative images provided that the signal-to-noise ratio is sufficiently high. We give a resolution analysis for this imaging method and validate this theory using numerical simulations. Additionally, we show that this imaging method is stable to random perturbations to the travel times and validate this theory with numerical simulations using the random travel time model for random media.

A Multi-Objective Mathematical Model for the Population-Based Transportation Network Planning

The current article introduces a three-objective model for the problem of location, allocation, and routing, taking into account the travel times depending on the population on the route. Objective functions include minimizing the total network transit time, maximizing travel attractiveness for travel applicants, and balanced allocation of travel applicants to each service area. In this research, a general form of the proposed three-objective mathematical planning model is formulated. The proposed model seeks to select a suitable place or places as places of service, allocate people or vehicles in each area to these places and determine the transportation route of each person or vehicle in each area to reach the service provider in question. Getting a direct impact of random factors and population flow on the random travel times of each bow so that all three goals are met simultaneously. The cuckoo optimization algorithm is developed to solve this model. A sample problem is also examined to show the validity and behavior of the proposed model. The numerical results indicate the high performance of the cuckoo optimization algorithm.

Modeling and Solution of Vehicle Routing Problem with Grey Time Windows and Multiobjective Constraints

Purpose. In order to study the impact of grey delivery time uncertainty on customer satisfaction and delivery costs, a vehicle routing problem with grey delivery time windows and multiobjective constraints is defined. Method. The paper first defines the uncertainty of the delivery vehicle’s arrival time to the customer as grey uncertainty and then whitens the grey time windows; at the same time, the customer’s hard time windows is expanded into a soft time windows to measure customer satisfaction when the vehicle arrives. Experiment. In order to verify the validity of the established model, numerical experiments are carried out in two groups based on the Solomon example, and the solution is solved based on the improved quantum evolution algorithm. Analysis. Distribution cost fluctuations and customer satisfaction fluctuations with grey time windows are relatively small; under different satisfaction threshold conditions, the distribution cost is increased gently with the satisfaction threshold. Conclusion. The grey delivery time windows have certain advantages in solving the random travel time vehicle routing problem.

Optimization Method of Customized Shuttle Bus Lines under Random Condition

Transit network optimization can effectively improve transit efficiency, improve traffic conditions, and reduce the pollution of the environment. In order to better meet the travel demands of passengers, the factors influencing passengers’ satisfaction with a customized bus are fully analyzed. Taking the minimum operating cost of the enterprise as the objective and considering the random travel time constraints of passengers, the customized bus routes are optimized. The K-means clustering analysis is used to classify the passengers’ needs based on the analysis of the passenger travel demand of the customized shuttle bus, and the time stochastic uncertainty under the operating environment of the customized shuttle bus line is fully considered. On the basis of meeting the passenger travel time requirements and minimizing the cost of service operation, an optimization model that maximizes the overall satisfaction of passengers and public transit enterprises is structured. The smaller the value of the objective function is, the lower the operating cost. When the value is negative, it means there is profit. The model is processed by the deterministic processing method of random constraints, and then the hybrid intelligent algorithm is used to solve the model. A stochastic simulation technique is used to train stochastic constraints to approximate uncertain functions. Then, the improved immune clonal algorithm is used to solve the vehicle routing problem. Finally, it is proved by a case that the method can reasonably and efficiently realize the optimization of the customized shuttle bus lines in the region.

An agent-based model for real-time bus stop-skipping and holding schemes

This paper develops a real-time agent-based simulation model to optimize the dynamic bus stop-skipping and holding schemes. The proposed agent-based simulation model is capable of modeling, scheduling and solving control strategy problems in real-time complex, dynamic and stochastic scenarios of the transport systems. To this end, random bus travel times and passenger arrivals are incorporated in the agent-based model to evaluate the integrated bus operation strategies. Apart from the total costs, the performance of the proposed strategies is evaluated with respect to the buses’ headway deviation and reliability index, the passengers’ travel time and the overall system cost, respectively. The results show the benefits of different strategies under different scenarios. The RTSSH (real-time stop-skipping and holding) strategy performs the best when buses are not reused, whilst RTSS (real-time stop-skipping) outperforms RTSSH strategy when buses are allowed to be reused.

An integrated car-and-ride sharing system for mobilizing heterogeneous travelers with application in underserved communities

The fast-growing carsharing and ride-hailing businesses are generating economic benefits and societal impacts in modern society, while both have limitations to satisfy diverse users, e.g., travelers in low-income, underserved communities. In this article, we consider two types of users: Type 1 drivers who rent shared cars and Type 2 passengers who need shared rides. We propose an integrated car-and-ride sharing (CRS) system to enable community-based shared transportation. To compute solutions, we propose a two-phase approach where in Phase I we determine initial car allocation and Type 1 drivers to accept; in Phase II we solve a stochastic mixed-integer program to match the accepted Type 1 drivers with Type 2 users, and optimize their pick-up routes under a random travel time. The goal is to minimize the total travel cost plus expected penalty cost of users’ waiting and system overtime. We demonstrate the performance of a CRS system in Washtenaw County, Michigan by testing instances generated based on census data and different demand patterns. We also demonstrate the computational efficacy of our decomposition algorithm benchmarked with the traditional Benders decomposition for solving the stochastic model in Phase II. Our results show high demand fulfillment rates and effective matching and scheduling with low risk of waiting and overtime.

Route choice, travel time variability, and rational inattention

This paper sets up a rational inattention model for the route choice problem in a stochastic network where travelers face random travel time. Previous research has assumed that travelers incorporate all provided information without effort. This study assumes that information is costly and that travelers rationally choose how much information to acquire prior to choosing route. We begin with a single traveler and then extend the model to heterogeneous travelers where rationally inattentive user equilibrium (RIUE) is achieved. From the perspective of a single traveler, more information always reduces the impact of travel time variability and increases the probability of choosing a less costly route. However, in RIUE, more information may reduce the social welfare in some scenarios.

Route choice, travel time variability, and rational inattention

Abstract This paper sets up a rational inattention model for the route choice problem in a stochastic network where travelers face random travel time. Previous research has assumed that travelers incorporate all provided information without effort. This study assumes that information is costly and that travelers rationally choose how much information to acquire prior to choosing route. We begin with a single traveler and then extend the model to heterogeneous travelers where rationally inattentive user equilibrium (RIUE) is achieved. From the perspective of a single traveler, more information always reduces the impact of travel time variability and increases the probability of choosing a less costly route. However, in RIUE, more information may reduce the social welfare in some scenarios.

Travel time variability and rational inattention

This paper sets up a rational inattention model for the choice of departure time for a traveler facing random travel time. In this model, the traveler chooses in advance an information strategy for the travel time outcome, and then chooses departure time each day given the information received that day. The model describes how cheaper information allows the traveler to expand his/her consideration set and adapt more flexibly to changing conditions. This increases the traveler's payoff. The marginal cost of travel time variability is always positive. The ability to choose the information strategy reduces the cost of travel time variability compared to neoclassical travelers whose information is exogenously given.

An empirical investigation of values of travel time savings from stated preference data and revealed preference data

ABSTRACTA number of studies have found that the willingness-to-pay (WTP) results estimated from revealed preference (RP) and stated preference (SP) data tend to be different. In this paper, we empirically estimate values of travel time savings from an SP data set and an RP data set and compare the findings within this study and between studies. The evidence shows that the design of a stated choice experiment has a significant impact on the ratio of SP and RP WTP values and reveals that presenting a full distribution of travel time to address random travel time variation in the choice scenarios, along with using a real market reference alternative as a pivot in the SP design, significantly reduces the gap between values of travel time savings estimated from SP data and RP data.

Robust Shortest Path Problem With Distributional Uncertainty

Routing service considering uncertainty is at the core of intelligent transportation systems and has attracted increasing attention. Existing stochastic shortest path models require the exact probability distributions of travel times and usually assume that they are independent. However, the distributions are often unavailable or inaccurate due to insufficient data, and correlation of travel times over different links has been observed. This paper presents a robust shortest path (RSP) model that only requires partial distribution information of travel times, including the support set, mean, variance, and correlation matrix. We introduce a concept of robust mean-excess travel time to hedge against the risk from both the uncertainty of the random travel times and the uncertainty in their distributions. To solve the RSP problem, an equivalent dual formulation is derived and used to design tight lower and upper bound approximation methods, which adopt the scenario approach and semi-definite programming approach, respectively. To solve large problems, we further propose an efficient primal approximation method, which only needs to solve two deterministic shortest path problems and a mean-standard deviation shortest path problem, and analyze its approximation performance. Experiments validate the tightness of the proposed bounds and demonstrate the impact of uncertainty on the relative benefit and cost of robust paths.

Travel Time Variability and Rational Inattention

This paper sets up a rational inattention model for the choice of departure time for a traveler facing random travel time. The traveler chooses how much information to acquire about the travel time out-come before choosing departure time. This reduces the cost of travel time variability compared to models in which the information is exogenously fixed.

An exploratory study of instance-based learning for route choice with random travel times

Availability of individual-level longitudinal data provides the opportunity to better understand travelers' day-to-day learning behavior, enabling more accurate predictions of traffic patterns in a network with random travel times. In this paper, an instance-based learning (IBL) model that can capture the recency, hot stove and payoff variability effects embedded in travelers' day-to-day learning processes is developed for route-choice based on the power law of forgetting and practice. Experiments based on synthetic datasets show that the true parameter values of the IBL model can be consistently retrieved and the model can potentially predict different traffic patterns compared to non-learning models. The IBL model is compared with a baseline learning model using an experimental dataset of repeated route-choice. Estimation results show that the IBL model reveals higher sensitivity to perceived travel time and achieves better model fit. Cross validation experiments suggest that the forecasting ability of the IBL model is consistently better than the baseline learning model. Practical considerations for choice modeling are further discussed.

A two-stage scheduling method for global humanitarian logistics in large-scale disaster response

Large-scale disaster response is a global issue. Planners must make effective logistics plans to deliver vital first-aid resources (e.g., medicine, food, clothing, machinery) to affected areas from all over the world. Furthermore, planners must consider surging demand and uncertain transportation situations. To explain the efficiency of distribution plans, this study addresses the resource allocation effectiveness losses, which are the losses caused by the mismatch between supply and demand in affected areas, and the emergency logistics time losses, which are the time losses caused by logistics processes under emergency conditions. A two-stage scheduling method is then proposed that considers random demand and travel time. In consideration of the incompleteness or lack of information in real situations, the scheduling method with Bayesian information updates is proposed by assuming that demand and transportation uncertainty are represented by population transfer rate (PTR) and road affected level (RAL), respectively. Next, a simulation study on Wenchuan earthquake response is conducted to illustrate the proposed method. Finally, the insights derived from the study are provided in the conclusion.

Risk-averse toll pricing in a stochastic transportation network

We consider the toll pricing problem under uncertain network conditions resulting in stochastic travel times. Using the conditional value-at-risk (CVaR) as a risk measure on the alternate functions of the random travel times we introduce several travel time reliability-related network performance measures. CVaR is used to control the undesired realisations of random outcomes based on travel times, and consequently, improve the reliability of the transportation system. We characterise the random network parameters, which are in general highly correlated, by a set of scenarios and propose alternate risk-averse toll pricing models. These optimisation models involve decisions of transportation managers aiming to improve the system-wide network reliability and decisions of network users who are assumed to choose routes to minimise their expected total travel costs. We describe a solution method integrating mathematical programming approaches with a genetic algorithm. We also conduct a computational study to illustrate the effectiveness of the proposed approaches. [Received 26 December 2014; Revised 26 May 2016; Accepted 24 July 2016]

Additive Consistency of Risk Measures and Its Application to Risk-Averse Routing in Networks

We investigate the use of risk measures and theories of choice to model risk-averse routing and traffic equilibrium on networks with random travel times. We interpret the postulates of these theories in the context of routing, identifying additive consistency as a plausible condition that allows to reduce risk-averse route choice to a standard shortest path problem. Within the classical theories of choice, we show that the only preferences that satisfy this condition are the ones induced by the entropic risk measures.

The impact of travel time variability and travelers’ risk attitudes on the values of time and reliability

In this paper, we derive implementable measures of travelers’ willingness to pay to save travel time (vot) and to improve the reliability ( vor) of a given trip. We set out a simple microeconomic model of transport mode choice in which each trip is fully characterized by its price and the statistical distribution of its random travel time, assuming that travelers have expected utility preferences over the latter. We then explore how the vot and vor are affected by the statistical distribution of travel time and by travelers’ preferences towards travel time variability.

A nonlinear model for a capacitated random transportation network

In this study, we consider a capacitated location–multi-allocation–routing problem with population-dependent random travel times. The objective is to find appropriate locations as server locations among the candidate locations, allocate the existing population in each demand node to server locations, and determine the movement path of each member to reach its corresponding server with respect to the simultaneous change of the random travel times so that the expected total transportation time is minimized. In our study, the concept of population-dependent random travel times incurs two issues: (1) consideration of some random factors in computing the travel times and (2) impact of the traveling population (presence of people or vehicles) on these random factors simultaneously. Here, three random factors of the time spent in traffic, the number of accidents, and the number of road failures are considered. Also, the capacities of server nodes for servicing the people or vehicles and the capacities of arcs to pass the people or vehicles are assumed to be limited. Defining a linear function for population-dependent random travel time, we formulate the problem as a mixed-integer nonlinear programming model. Also, to investigate the validation and behavior of the proposed random model, several network examples are provided and computational results are analyzed.