Doubly Dynamic Traffic Assignment

Abstract

This paper presents, and investigates properties of, a doubly dynamic simulation assignment model which involves specifying a day-to-day route choice model as a discrete time stochastic process, combining a between-day driver learning and adjusting model with a continuous time, within-day dynamic network loading. Such a simulation model may be regarded as the realisation of a stochastic process, which under certain mild conditions, admits a unique stationary probability distribution (i.e. an invariant probability distribution over time of network flows and travel times). Such a stationary state of the stochastic process is of interest to transport modellers, as one can then describe the stochastic process by its moments such as the means, variances and covariances of the flow and travel time profiles. The results of a simulation experiment are reported in which the process of individual drivers' day-to-day route choices are based on the aggregate learning of the experienced within-day route costs by all drivers departing in the same period. Experimental results of the stationarity of the stochastic process are discussed, along with an analysis of the sensitivity of autocorrelations of the route flows to the route choice model parameters. The results also illustrate the consistency of the link flow model with properties such as First-In, First-Out (FIFO), and a simple network is used to illustrate the properties.

Preface

“…Evolution in these systems is modelled as a Markov Chain process, defining a unique probability distribution on the link traffic volumes as time-dependent processes from a known initial state. The properties and practical application of DD-DT A models have been shown in various studies, e.g., Casce~ta (1989), Cascetta and Cantarella (1989), Watling (1999), Cascetta et al (1991) and Cantarella and Cascetta (1995), Hazelton and Polak (1997), Hazelton (2002), Watling and Hazelton (2003), Cantarella and Velona (2003), Hazelton and Watling (2004), Lo and Bie (2006), Nakayama (2006), Balijepalli et al (2006) and Bie and Lo (2008). DD-DT A allows one to model convergence to attractors and to analyse equilibrium stability around these attractors.…”