User equilibrium traffic network assignment with stochastic travel times and late arrival penalty

Watling, David

doi:10.1016/j.ejor.2005.02.039

Cited by 189 publications

(115 citation statements)

References 25 publications

Supporting

Mentioning

115

Contrasting

Order By: Relevance

“…The path-based proofs of existence and uniqueness follow those of Watling (2006), originating from Smith (1979) and are only briefly described here.…”

Section: Network Equilibrium Based On Perceived Valuementioning

confidence: 99%

“…A central component of these researches concerns the way travellers decide between routes having different travel time distributions; in particular an unreliable route with low mean travel time and a reliable route that on average takes longer. Typically an additional element of route cost is associated with unreliability, relating directly to the variance of travel times (Noland and Small 1995), to the probability of being late (Watling 2006), or to the safety margin required to arrive on time (Lam et al 2008;Lo et al 2006). Other works concerning risk averse behaviour (Bell and Cassir 2002;Szeto et al 2006) have ascribed a cost to the travel time uncertainty according to travellers' risk attitudes, yet still assuming that travellers accurately perceive the travel time probability distribution.…”

Section: Introductionmentioning

confidence: 99%

“…Such models assume demand and/or supply uncertainty and result in a continuous travel time distribution for each route. Including this travel time uncertainty into transport network modelling has received considerable attention in the literature; Noland and Small (1995), Bates et al (2001), Noland and Polak (2002), de Jong et al (2004), and Watling (2006) provide summaries of contributions to date. A central component of these researches concerns the way travellers decide between routes having different travel time distributions; in particular an unreliable route with low mean travel time and a reliable route that on average takes longer.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A network equilibrium model with travellers’ perception of stochastic travel times

Connors

Sumalee

2009

Transportation Research Part B: Methodological

132

View full text Add to dashboard Cite

In this paper we consider a network whose route travel times are considered to be random variables. In this scenario travellers choose their route, uncertain of the travel time they will experience on any of the available alternative routes. The attractiveness of a given route involves evaluation of both the possible travel time outcomes, and their perceived probability of occurring. We consider a modelling framework where the perceived value and perceived probabilities of travel time outcomes are obtained via nonlinear transformations of the actual travel times and their probabilities. In this context, we present the analysis required to formulate an equilibrium condition analogous to that of User Equilibrium, wherein travellers choose the routes that maximises their perceived value in the face of uncertain travel times. Existence and uniqueness conditions for this equilibrium are established.Cumulative prospect theory (CPT) provides a well supported paradigm for choices made under uncertainty, where each choice alternative presents a discrete probability distribution of a finite number of possible outcomes. Our analysis admits the particular transformations associated with CPT as a special case, and holds for a more general class of transformations and for the case of a continuous distribution of outcomes.

show abstract

“…The path-based proofs of existence and uniqueness follow those of Watling (2006), originating from Smith (1979) and are only briefly described here.…”

Section: Network Equilibrium Based On Perceived Valuementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A network equilibrium model with travellers’ perception of stochastic travel times

Connors

Sumalee

2009

Transportation Research Part B: Methodological

132

View full text Add to dashboard Cite

show abstract

“…The above problem can be solved by minimizing the following gap function (Lo and Chen, 2000;Watling, 2006):…”

Section: Route Choice Problemmentioning

confidence: 99%

“…extended the same model to a model under a multi-modal network. Watling (2006) proposed an equilibrium model under stochastic travel time that followed a normal distribution. The driver's route choice behaviour was expressed by using a probit-based SUE that also considered arrival penalty.…”

Section: Introductionmentioning

confidence: 99%

Estimating the value of travel time and of travel time reliability in road networks

Uchida

2014

Transportation Research Part B: Methodological

View full text Add to dashboard Cite

This study proposes two network models which simultaneously estimate the value of travel time and of travel time reliability based on the risk-averse driver's route choice behaviour. The first model is formulated as a utility maximization problem under monotonic and separable link travel times, whereas the second model is formulated as a utility maximization problem under non-monotonic and non-separable link travel times. The proposed models have the same structure as a user equilibrium (UE) traffic assignment problem with elastic demand. It is shown that the first model, which addresses independent stochastic capacity, is formulated as an optimization problem with a unique solution and is solved by using an algorithm for a UE traffic assignment problem with fixed demand. The second model, which addresses both stochastic Origin-Destination (O-D) flow and stochastic link capacity, is formulated as a nonlinear complementary problem. O-D demand functions formulated in the proposed models are derived from the utility maximization behaviour of the driver in the network. Therefore, the network models proposed in this study are consistent with those of studies that address the value of travel time and of travel time reliability based on utility maximization behaviour without considering the driver's route choice. Numerical experiments are carried out to demonstrate the models presented in this study.Keywords: value of travel time, value of travel time reliability, road network INTRODUCTIONIn light of the need to evaluate travel time reliability in terms of its effect on mobility in transport networks, many studies have developed models that address uncertainties in the network. Uncertainties in the network can be categorized into the three main factors of supply, demand and travel behaviour. Studies on travel time reliability in the network began with those that address stochastic OriginDestination (O-D) demand flow. By assuming O-D demand flow that follows normal distributions, Asakura and Kashiwadani (1991) solved User Equilibrium (UE) traffic assignment problems several times by using a set of O-D demand flows that were sampled from normal distributions for the purpose of estimating travel time reliability. Clark and Watling (2005) proposed an equilibrium model that calculates travel time reliability under stochastic O-D demand flow when that flow follows a Poisson distribution. They employed probit-based Stochastic User Equilibrium (SUE) for the driver's route choice behaviour. They applied a method proposed by Isserlis (1918) for the purpose of calculating travel time reliability, i.e., variance of stochastic travel time. Nakayama and Takayama (2003) proposed an equilibrium model which assumes that O-D demand flow follows a binomial distribution. UE traffic assignment was employed for expressing the driver's route choice behaviour. They calculated travel time reliability by applying a moment-generating function. Zhou and Chen (2008) proposed an equilibrium model which assumes that O-D demand flow follows a...

show abstract

Multiclass fuzzy user equilibrium with endogenous membership functions and risk‐taking behaviors

Miralinaghi

Lou

Hsu

et al. 2016

J of Advced Transportation

View full text Add to dashboard Cite

Over the last decades, several approaches have been proposed in the literature to incorporate users' perceptions of travel costs, their bounded rationality, and risk-taking behaviors into network equilibrium modeling for traffic assignment problem. While theoretically advanced, these models often suffer from high complexity and computational cost and often involve parameters that are difficult to estimate. This study proposes an alternative approach where users' imprecise perceptions of travel times are endogenously constructed as fuzzy sets based on the probability distributions of random link travel times. Two decision rules are proposed accordingly to account for users' heterogeneous risk-taking behaviors, that is, optimistic and pessimistic rules. The proposed approach, namely, the multiclass fuzzy user equilibrium, can be formulated as a link-based variational inequality model. The model can be solved efficiently, and parameters involved can be either easily estimated or treated as factors for calibration against observed traffic flow data. Numerical examples show that the proposed model can be solved efficiently even for a large-scale network of Mashhad, Iran, with 2538 links and 7157 origin-destination pairs. The example also illustrates the calibration capability of the proposed model, highlighting that the model is able to produce much more accurate flow estimates compared with the Wardropian user equilibrium model.

show abstract

User equilibrium traffic network assignment with stochastic travel times and late arrival penalty

Abstract: Article

Cited by 189 publications

References 25 publications

A network equilibrium model with travellers’ perception of stochastic travel times

A network equilibrium model with travellers’ perception of stochastic travel times

Estimating the value of travel time and of travel time reliability in road networks

Multiclass fuzzy user equilibrium with endogenous membership functions and risk‐taking behaviors

Contact Info

Product

Resources

About