Sensitivity analysis of the variable demand probit stochastic user equilibrium with multiple user classes

This paper presents a formulation of the multiple user class, variable demand, probit stochastic user equilibrium model. Sufficient conditions are stated for differentiability of the equilibrium flows of this model. This justifies the derivation of sensitivity expressions for the equilibrium flows, which are presented in a format that can be implemented in commercially available software. A numerical example verifies the sensitivity expressions, and that this formulation is applicable to large networks

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 influence of intra-daily activities and settings upon weekday violent crime in public space in Manchester, UK

People ebb and flow across the city. The spatial and temporal patterning of crime is, in part, reflective of this mobility, of the scale of the population present in any given setting at a particular time. It is also a function of capacity of this population to perform an active role as an offender, victim or guardian in any specific crime type, itself shaped by the time-variant activities undertaken in, and the qualities of, particular settings. To this end, this paper explores the intra-daily influence of activities and settings upon the weekday spatial and temporal patterning of violent crime in public spaces. This task is achieved through integrating a transient population dataset with travel survey, point-of-interest and recorded crime data in a study of Great Manchester (UK). The research deploys a negative binomial regression model controlling for spatial lag effects. It finds strong and independent, but time-variant, associations between leisure activities, leisure settings and the spatial and temporal patterning of violent crime in public space. The paper concludes by discussing the theoretical and empirical implications of these findings

Modeling children’s school travel mode and parental escort decisions

Children’s school travel, Mode choice, Parental escort, Household interactions,