A New Model for Disaggregate Traffic Assignment Making Explicit the Spatial Distribution of Trip Extremities
V Benezech LVMT, Universite Paris-Est, Ecole des Ponts ParisTech, IFSTTAR, FR
The spatial distribution of trip extremities influences greatly traffic assignment and taking account of the distribution of network access times is necessary. Two new stochastic models tackling this problem are introduced and compared.
Traffic demand modelling relies on the partitioning of the region studied into smaller Transport Analysis Zones (TAZ) inside which data are aggregated. Each zone is represented by a point, the centroid: all trips starting and ending in a zone are supposed to do so at its centroid. Data aggregation and the use of centroids affect models twice, through access link and egress link modelling. In the paper, we investigate the effects of data aggregation on traffic assignment, limiting the study to access links. The paper is divided into three parts.
The first part consists of a brief literature review on zone design, replacing all results within the framework of traffic assignment. There has been work on the effects of zone size, zone delineation or centroid positioning on traffic demand models, and many rules of thumb have been enunciated. More recently, at a talk at the ETC last year, Florian introduced a new model by Constantin and himself which used logit discrete choice models at each link considered during the traffic assignment phase to account for people's variety of choice patterns. According to the author, this can be applied to access links, yielding good results for big zones with uneven population density. However, there seems to be no paper investigating specifically the spatial distribution of trip extremities within TAZs and its implications for travel time and traffic assignment.
In the second part, we consider a simple situation with trips originating in one square zone, all trips having the same destination. The zone is connected to the network through a certain number of access links, from which the time to destination is known and deterministic. Using this simple model, we compare three assignment methods. For the first one, the journey times associated to access links are deterministic, i.e. the spatial distribution of trip extremities is completely ignored. In the second one, we use a logit discrete choice model: the network access time is assumed to follow a generalised extreme-value (GEV) distribution. In the third one, a new probit model is used, corresponding access times are normally distributed. The comparison between the deterministic model and the two stochastic ones show the importance of accounting for the diversity of network access times. The probit model yields better results when the covariance among the various connector times is not negligible or when the variances of the access times differ greatly.
In the third part, we discuss the pros and cons of the two stochastic models. With the probit model, a wide range of covariance structure can be used for the access times, which is useful for instance in public transit assignment to model zones where one station is clearly walked to and another one driven to. Variants of the logit model, such as the cross-nested logit model, allow for varied (but not all) covariance structure. Unfortunately, most times, the nesting structure does not clearly appear. Moreover, the observed distributions of access times are often symmetric, which is in favor of the normal distribution; this is not extremely convincing, though, due to the proximity of GEV and normal distributions. Finally, orders of magnitude of the error stemming from the centroid approximation are derived; in many cases, we show that it cannot be neglected a priori even though, in traffic assignment softwares, the problem is made less acute by the use of various submodes or mode combinations. As well, when studying a whole territory, all the zones interact with each other and the error from one zone can be compensated by the error from another zone.
Altogether, the probit version seems the most promising. Current work focuses on two points concerning this model: the development of a practice-ready version and the study of the possible interactions between access links and egress links.
Association for European Transport