Applications of sensitivity analysis for probit stochastic network equilibrium

Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is, however, made of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, ‘critical’ parameters; computation of approximate, re-equilibrated solutions following a change (post-optimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported

The flexible coefficient multinomial logit (FC-MNL) model of demand for differentiated products

We show FC-MNL is flexible in the sense of Diewert (1974), thus its parameters can be chosen to match a well-defined class of possible own- and cross-price elasticities of demand. In contrast to models such as Probit and Random Coefficient-MNL models, FC-MNL does not require estimation via simulation; it is fully analytic. Under well-defined and testable parameter restrictions, FC-MNL is shown to be an unexplored member of McFadden’s class of Multivariate Extreme Value discrete-choice models. Therefore, FC-MNL is fully consistent with an underlying structural model of heterogeneous, utility-maximizing consumers. We provide a Monte-Carlo study to establish its properties and we illustrate the use by estimating the demand for new automobiles in Italy

Two Variables Algorithms for Solving the Stochastic Equilibrium Assignment with Variable Demand: Performance Analysis and Effects of Path Choice Models

In this paper a general fixed-point approach dealing with multi-user (stochastic) equilibrium assignment with variable demand is proposed. The main focus is on (i) the implementation and comparison of different algorithm solutions based on successive averages methods calculated on one (arc flows, arc costs) and on two variables (arc flows and path satisfaction; arc costs and demand flows); (ii) the effects of algorithm efficiency on different path choice models and/or travel demand choice models. In terms of the best performing algorithmic solution, the effects of different path choice models, such as Multinomial Logit model, C-Logit model and Multinomial Probit model were implemented, and algorithmic efficiency was investigated w.r.t. a real network