Path Size Logit route choice models attempt to capture the correlation between routes by including correction terms within the route utility functions. This provides a convenient closed-form solution for implementation in traffic network models. The path size terms measure distinctiveness of routes; a route is penalised based on the number of other routes sharing its links, and the costs of those shared links. Typically, real road networks have many very long routes that should be considered unrealistic. Such unrealistic routes are problematic for the Path Size Logit (PSL) model because they negatively impact the choice probabilities of realistic routes when links are shared. The Generalised Path Size Logit (GPSL) model attempts to address this problem by weighting the contributions of routes to path size terms according to the ratio of route travel costs. However, the GPSL model is not internally consistent in how it defines routes as being unrealistic: the path size terms consider only travel cost, whereas the route choice probability relation considers disutility including the correction term. To solve these challenges, this paper formulates a new internally consistent Adaptive Path Size Logit (APSL) model wherein routes contribute to path size terms according to the ratio of route choice probabilities, ensuring that routes defined as unrealistic by the path size terms, are exactly those with very low choice probabilities. The APSL route choice probability relation is an implicit function, naturally expressed as a fixed-point problem. A proof is provided for the guaranteed existence of solutions, as well as conditions for the uniqueness of solutions. A Maximum Likelihood Estimation procedure is given for estimating the APSL model with tracked route observation data, and this procedure is investigated in a simulation study where it is shown it is generally possible to reproduce assumed true parameters. APSL is then estimated using real tracked route GPS data on a large-scale network, and results are compared with other PSL models.

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The aim of this paper is to remove the known limitations of Deterministic and Stochastic User Equilibrium (DUE and SUE), namely that only routes with the minimum cost are used in DUE, and that all permitted routes are used in SUE regardless of their costs. We achieve this by combining the advantages of the two principles, namely the definition of unused routes in DUE and mis-perception in SUE, such that the resulting choice sets of used routes are equilibrated. Two model families are formulated to address this issue: the first is a generalised version of SUE permitting bounded and discrete error distributions; the second is a Restricted SUE model with an additional constraint that must be satisfied for unused paths.The overall advantage of these model families consists in their ability to combine the unused routes with the use of random utility models for used routes, without the need to pre-specify the choice set. We present model specifications within these families, show illustrative examples, evaluate their relative merits, and identify key directions for further research.

This study emphasizes the need for thinking about traffic calming measures, illumination solutions, road maintenance programs, and speed limit reductions. Moreover, this study emphasizes the role of the built environment, because shopping areas, residential areas, and walking traffic density are positively related to a reduction in pedestrian injury severity. Often, these areas have in common a larger pedestrian mass that is more likely to make other road users more aware and attentive, whereas the same does not seem to apply to areas with lower pedestrian density.

We propose a new class of path-based solution algorithms to solve the Restricted Stochastic User Equilibrium (RSUE), as introduced in Watling et al (2014). The class allows a flexible specification of how the choice sets are 'systematically' grown by considering congestion effects and how the flows are allocated among routes. The specification allows adapting traditional pathbased stochastic user equilibrium flow allocation methods (designed for pre-specified choice sets) to the generic solution algorithm. We also propose a cost transformation function and show that by using this we can, for certain Logit-type choice models, modify existing path-based Deterministic User Equilibrium solution methods to fit the RSUE solution algorithm. The transformation function also leads to a two-part relative gap measure for consistently monitoring convergence to a RSUE solution. Numerical tests are reported on two real-life cases, in which we explore convergence patterns and choice set composition and size, for alternative specifications of the RSUE solution algorithm.