Expected Travel Time Research Articles

Stick to the Plan? A Revealed-Preference Study of Behavioural Impacts of Traffic Information

We estimate a revealed-preference scheduling model of morning peak behaviour that allows us to determine the impact of traffic information on traveller behaviour. Specifically, we distinguish between the marginal impact of expected travel times versus that of deviations from this expectation upon user behaviour. We find that participants that chose to receive a smart-phone with traffic information as a reward in our experiment respond to the deviation of actual travel times from the expectation, which they did not do before. This we interpret as evidence that traffic information indeed affects behaviour. We also find that participants who did not choose the smart-phone, but instead opted for monetary rewards, also respond to the deviation of actual travel times from the expectation. This suggests that these drivers use other sources of information to help their trip planning.

Data fusion for updating information in modelling drivers’ choice behaviour

In this article, a method for fusing fuzzy data relevant both to drivers’ experience and provided information is presented. Expected travel time is then updated according to the results of fusion. The method takes into account the ‘compatibility’ of data originating from different sources, and provides information about acceptability of results. Influence of uncertainty on drivers’ compliance with provided information is examined in detail, according to uncertainty-based information theory.

Modeling of Workflow Congestion and Optimization of Flow Routing in a Manufacturing/Warehouse Facility

This paper discusses the notion of workflow congestion in the context of material handling equipment interruptions in a manufacturing or warehousing facility. Development of a combination of probabilistic and physics-based models for workflow interruptions permits evaluation of the expected link travel time. The problem is then of routing in a way that minimizes total expected travel time. The rerouting problem is modeled as a multicommodity flow problem with link capacity design. A greedy upper bounding and Lagrangean relaxation algorithm are developed to solve this efficiently. To calibrate our modeling process we develop an object-oriented simulation model that explicitly considers various workflow interruptions. Our major finding is that rerouting traffic in a congested facility can significantly alleviate congestion delays and improve the efficiency of material movement. A managerial insight derived from this work is that rerouting is most effective in medium traffic-intensity situations.

Travel Time Reliability for Stockholm Roadways

In recent years, there has been an increasing awareness that travel time reliability, apart from expected travel time, is an important component of cost–benefit analysis, especially during congested traffic conditions. A common measure of travel time reliability is standard deviation, and it has been shown that this is a theoretically sound measure under scheduling constraints, provided that the mean lateness factor is known. Hence, in applied cost–benefit analyses, one will need both the standard deviation and the mean lateness factor. These analyses would be particularly simple if the mean lateness were constant across time of day and for different routes chosen. A study was done to explore how the mean lateness varies and how its variations can be approximated. With the use of travel time measurements on individual links, it is shown how mean lateness varies considerably across time and space. It is shown that mean lateness exhibits a time-varying pattern depending on the characteristics of congestion on the link. It is also shown that the location of the link in the network is a significant determinant. The resulting model for mean lateness represents a considerable improvement over existing practice, where the mean lateness is implicitly assumed constant, yet a large portion of its variation remains unexplained. The model is useful for informing future research but is of less value for predicting the mean lateness in broad applied settings.

Boarding and Alighting in Frequency-Based Transit Assignment

Several models of route choice in frequency-based assignment are compared for underlying assumptions on service regularity, passenger information, and choice set structure. Numerical results for some simple examples show that route splits differ significantly under different assumptions, so for practical applications the selection of the most suitable choice model is important and none of the models can be regarded as a good approximation for all possible assumptions. Sensitivity of route choice against perturbations of running times or service frequencies is another consideration, because a continuous response improves convergence in demand models with feedback. Finally, it is demonstrated that in terms of expected travel time, the decision about when to alight (and where to continue the journey) is just as important as the decision of which line to board.

Travel time prediction under heterogeneous traffic conditions using global positioning system data from buses

Travel time information is a vital component of many intelligent transportation systems (ITS) applications. In recent years, the number of vehicles in India has increased tremendously, leading to severe traffic congestion and pollution in urban areas, particularly during peak periods. A desirable strategy to deal with such issues is to shift more people from personal vehicles to public transport by providing better service (comfort, convenience and so on). In this context, advanced public transportation systems (APTS) are one of the most important ITS applications, which can significantly improve the traffic situation in India. One such application will be to provide accurate information about bus arrivals to passengers, leading to reduced waiting times at bus stops. This needs a real-time data collection technique, a quick and reliable prediction technique to calculate the expected travel time based on real-time data and informing the passengers regarding the same. The scope of this study is to use global positioning system data collected from public transportation buses plying on urban roadways in the city of Chennai, India, to predict travel times under heterogeneous traffic conditions using an algorithm based on the Kalman filtering technique. The performance of the proposed algorithm is found to be promising and expected to be valuable in the development of APTS in India. The work presented here is one of the first attempts at real-time short-term prediction of travel time for ITS applications in Indian traffic conditions.

Prospects for the Detection of the Deep Solar Meridional Circulation

We perform helioseismic holography to assess the noise in p-mode travel-time shifts which would form the basis of inferences of large-scale flows throughout the solar convection zone. We also derive the expected travel times from a parameterized return (equatorward) flow component of the meridional circulation at the base of the convection zone from forward models under the assumptions of the ray and Born approximations. From estimates of the signal-to-noise ratio for measurements focused near the base of the convection zone, we conclude that the helioseismic detection of the deep meridional flow including the return component may not be possible using travel-time measurements spanning an interval less than a solar cycle. We speculate that this conclusion may be generally true for other helioseismic methods under the assumption that the underlying measurements are equivalently limited by solar realization noise.

Dynamic Late Lane Merge System at Freeway Construction Work Zones

In normal work zones with lane closures, drivers do not merge at any one definite point, a situation thus often causing a sudden interruption in traffic flow and sometimes higher delay and longer queue. The Dynamic Late Lane Merge System (DLLMS) is used to specify a definite merge point, improve the flow of congested work zones, and reduce queue lengths in travel lanes. The DLLMS was implemented in Michigan on three freeway segments that were reduced from two lanes to one lane because of highway construction work zones. The DLLMS directed traffic to use both lanes (open and closed lanes) until the designated “merge point” (close to the taper) where traffic from each lane was instructed to take turns merging into the open lane. On the basis of travel time characteristics, merge locations, and throughput, the effectiveness of the DLLMS was evaluated as a part of this study. The before period data were not available; therefore, a conventional work zone merge system, located on eastbound I-94, was used as a control site for the westbound I-94 test site. Comparison of the I-94 control and test sites indicated that the presence of the DLLMS improved the flow of travel and increased the percentage of vehicles that merged at or near the designated taper location. Based on the expected travel time savings, at a $5/h value of time, the benefit-cost ratio will be greater than 1, indicating that the monetary benefits of the DLLMS outweigh the cost of the system.

Adaptive Route Choice Models in Stochastic Time-Dependent Networks

Adaptive route choice models are studied that explicitly capture travelers’ route choice adjustments according to information on realized network conditions in stochastic time-dependent networks. Two types of adaptive route choice models are explored: an adaptive path model in which a sequence of path choice models are applied at intermediate decision nodes and a routing policy choice model in which the alternatives correspond to routing policies rather than paths at the origin. A routing policy in this study is a decision rule that maps from all possible pairs (e.g., node, time) to the next links out of the node. Existing route choice models that can be estimated on disaggregate revealed preferences assume a deterministic network setting from the traveler's perspective and cannot capture the traveler's proactive adaptive behavior under uncertain traffic conditions. The literature includes a number of algorithmic studies of optimal routing policy problems, but the estimation of a routing policy choice model is a new research area. The specifications of estimating the two adaptive route choice models are established and the feasibility of estimation from path observations is demonstrated on an illustrative network. Prediction results from three models–nonadaptive path model, adaptive path model, and routing policy model–are compared. The routing policy model is shown to better capture the option value of diversion than the adaptive path model. The difference between the two adaptive models and the nonadaptive model is larger in terms of expected travel time if the network is more stochastic, indicating that the benefit of adaptivity is more significant in a more unpredictable network.

Helioseismic Holography of Simulated Solar Convection and Prospects for the Detection of Small‐Scale Subsurface Flows

We perform helioseismic holography on realistic solar convection simulations and compare the observed travel-time perturbations with the expected travel times from the horizontal flows in the simulations computed from forward models under the assumption of the Born approximation. We demonstrate reasonable agreement between the observed and model travel times which reinforces the validity of helioseismic holography in the detection of subsurface horizontal flows. From the variation of the signal-to-noise ratio with depth, we conclude that the helioseismic detection of individual flow structures with spatial scales of supergranulation or smaller is not possible for depths below about 5 Mm below the surface over time scales less than a day. Approximately half of the observed signal originates within the first 2 Mm below the surface. A consequence of this is a rapid decrease (and reversal in some cases) of the travel-time perturbations with depth due to the contribution to the measurements of oppositely directed surface flows in neighboring convective cells. This confirms an earlier interpretation of similar effects reported from observations.

Travel time estimation on a freeway using Discrete Time Markov Chains

Travel time is widely recognized as an important performance measure for assessing highway operating conditions. There are two methods for obtaining travel time: direct measurement, or estimation. For the latter, previously developed models tend to underestimate travel times under congested conditions because of the difficulties of calculations of vehicle queue formations and dissipations. The purpose of this study is to develop a model that can estimate travel time on a freeway using Discrete Time Markov Chains (DTMC) where the states correspond to whether or not the link is congested. The expected travel time for a given route can be obtained for time periods during which the demand is relatively constant. Estimates from the model are compared to field-measured travel time. Statistical analyses suggest that the estimated travel times do not differ from the measured travel time at the 99% confidence level.

A Queueing Framework for Routing Problems with Time-dependent Travel Times

Assigning and scheduling vehicle routes in a dynamic environment is a crucial management problem. Despite numerous publications dealing with efficient scheduling methods for vehicle routing, very few addressed the inherent stochastic and dynamic nature of travel times. In this paper, a vehicle routing problem with time-dependent travel times due to potential traffic congestion is considered. The approach developed introduces the traffic congestion component based on queueing theory. This is an innovative modelling scheme to capture the stochastic behavior of travel times as it generates an analytical expression for the expected travel times as well as for the variance of the travel times. Routing solutions that perform well in the face of the extra complications due to congestion are developed. These more realistic solutions have the potential to reduce real operating costs for a broad range of industries which daily face routing problems. A number of datasets are used to illustrate the appropriateness of the novel approach. Moreover it is shown that static (or time-independent) solutions are often infeasible within a congested traffic environment which is generally the case on European road networks. Finally, the effect of travel time variability (obtained via the queueing approach) is quantified for the different datasets.

Equilibria and Information Provision in Risky Networks with Risk-Averse Drivers

We study the impact of information on risk-averse drivers who maximize their expected utility (rather than minimizing expected travel time). For two routes in parallel with risky travel time, we show that equilibrium travel times depend on the distribution of risk aversion as well as on provision of information. Besides the mean variance model used so far in transportation, we consider three other standard utility functions. Interestingly, we find that optimal route choice may depend on global factors such as the length of the journey. Finally, we study the benefit of information according to the level of risk aversion.

Costs of travel time uncertainty and benefits of travel time information: Conceptual model and numerical examples

A negative effect of congestion that tends to be overlooked is travel time uncertainty. Travel time uncertainty causes scheduling costs due to early or late arrival. The negative effects of travel time uncertainty can be reduced by providing travellers with travel time information, which improves their estimate of the expected travel time, thereby reducing scheduling costs. In order to assess the negative effects of uncertainty and the benefits of travel time information, this paper proposes a conceptual model of departure time choice under travel time uncertainty and information. The model is based on expected utility theory, and includes the variation in travel time, the quality of travel time information and travellers’ perception of the travel time. The model is illustrated by an application to the case of the A2 motorway between Beesd and Utrecht in the Netherlands.

The Impact of Travel Time Information on Travelers’ Learning under Uncertainty

In this work, laboratory experiment was conducted in order to evaluate the effect of feedback on decision-making under uncertainty, with and without provided information about travel times. We discuss the prediction of travelers’ response to uncertainty in two route–choice situations. In the first situation travelers are faced with a route–choice problem in which travel times are uncertain but some external information about routes’ travel times is provided. The second situation takes place in a more uncertain environment in which external information about travel times is not provided, and the travelers’ only source of information is their own experience. Experimental results are in conflict with the paradigm about traveler information systems: As a consequence of information, the propensity of travelers to minimize expected travel time is not necessarily increased. Providing travelers with static information about expected travel times reveals an increase in the heterogeneity of travelers’ choices and reduces the maximization rate.

Valuation of Different Types of Travel Time Reliability in Route Choice

Travelers sometimes experience extremely long travel times on a route. The Travel Simulator Laboratory (TSL) of Delft University of Technology is used to study the effect of these extreme experiences on route choice. The TSL allows for a completely controlled experiment and good research methodology. It is hypothesized that together with the average travel time and the variance, the most extreme travel times experienced influence a person's perception of the attractiveness of the route. Travel information is assumed to be able to alter this perception. Data from 2,500 respondents were gathered with the TSL. Route switching behavior after a regular experience and after an extreme experience was analyzed. People switched routes after an extreme experience significantly more often when the information that they received before the route choice was wrong than they did when it was correct. Moreover, travelers clearly preferred a route that is sometimes bad and most of the time good over a route that is symmetrically distributed with a large variance and thus less predictable. Furthermore, mixed multinomial logit models for panel data were estimated. Expected travel time, expected variance, and worst experience were found to be negatively valued. The posed hypothesis seems to be correct on a qualitative level and proves to be a promising field of research. However, much work still has to be done on the mathematical model to draw more specific conclusions on a quantitative level as well.

Doubly Uncertain Transport Network: Degradable Link Capacity and Perception Variations in Traffic Conditions

Minor incidents such as signal failure and vehicle breakdown are common in day-to-day travel. These incidents cause random link capacity degradations, leading to travel time uncertainty. Over time, commuters take account of the routes’ travel time variability and factor it into their route choice decisions. To hedge against this travel time uncertainty, travelers typically add a travel time margin to the expected travel time of a trip to form the travel time budget (i.e., the time set aside for the trip so as to maintain a preferred probability of punctual arrival). Nevertheless, in this learning process, commuters may experience perception variations in the traffic conditions that they actually encounter. To sum up, travelers face two types of uncertainty in their daily commutes: uncertainty in the actual travel time due to random link capacity degradations and perception variations in their travel time budget due to imperfect traffic information. In this study, a stochastic equilibrium was formulated to address both types of uncertainty. With this stochastic formulation as a platform, through a set of numerical studies, the effects of network link strengthening and traffic information provision were studied. The results showed that the provision of quality information was effective only in certain situations, whereas network link strengthening always improved system performance.

Arriving-on-Time Problem: Discrete Algorithm That Ensures Convergence

Finding optimal paths in stochastic networks is an important topic in many scientific and engineering fields. To cope with uncertainty, various performance measures, including expected travel time, reliability, value at risk, and expectation with chance constraint, have been introduced. The literature has shown that adaptive strategies that incorporate both anticipation and real-time information are more efficient than a preplanned strategy in a stochastic environment. Most adaptive optimal-path algorithms focus on least-expected travel time. Recently, an adaptive path-finding strategy, named the stochastic on-time arrival (SOTA) algorithm, was proposed to maximize the travel time reliability for any given time threshold. However, the originally proposed SOTA algorithm is based on the classic successive approximation. Whether this algorithm converges within a finite number of successive approximation steps is an open question. In this study, the proposed discrete SOTA algorithm runs in an optimal polynomial time and thus improves the computational efficiency significantly. Numerical examples are provided, and future extensions are proposed.

Probit-Type Reliability-Based Transit Network Assignment

This paper proposes a new probit-type reliability-based transit assignment model in a congested network with unreliable transit services. A new disutility function is developed to model the passenger route choice behavior under unreliable conditions; passengers will make a trade-off between the transit service reliability and the expected travel time for their route choice. In the proposed model, the total transit passenger demand is fixed, but the in-vehicle travel times by transit routes are formulated stochastically because of unreliable traffic conditions, particularly for buses on the road network. The effects of congestion on transit networks, such as elastic transit line frequencies and passenger overload delays, are also considered in the proposed model. A numerical example is provided to illustrate the applications of the proposed model and solution algorithm. It is shown that the traditional probit-type stochastic user equilibrium transit assignment is a special case of the proposed model. The findings also reveal the distribution of passenger waiting times and their overload delays at congested transit stations.

Arriving-on-Time Problem

Finding optimal paths in stochastic networks is an important topic in many scientific and engineering fields. To cope with uncertainty, various performance measures, including expected travel time, reliability, value at risk, and expectation with chance constraint, have been introduced. The literature has shown that adaptive strategies that incorporate both anticipation and real-time information are more efficient than a preplanned strategy in a stochastic environment. Most adaptive optimal-path algorithms focus on least-expected travel time. Recently, an adaptive path-finding strategy, named the stochastic on-time arrival (SOTA) algorithm, was proposed to maximize the travel time reliability for any given time threshold. However, the originally proposed SOTA algorithm is based on the classic successive approximation. Whether this algorithm converges within a finite number of successive approximation steps is an open question. In this study, the proposed discrete SOTA algorithm runs in an optimal polynomial time and thus improves the computational efficiency significantly. Numerical examples are provided, and future extensions are proposed.