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

Abstract

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...

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“…As shown in Clark and Watling [6], (19) and (20) can be calculated by applying a method proposed by Isserlis [35] given the moments of by assuming that the link flow follows normal distribution [17,18,33]. This assumption was supported by Rakha et al [36], which demonstrated that the normality assumption may be sufficient from a practical standpoint given its computational simplicity.…”

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