Static network equilibrium continues to be the favoured paradigm used in network modelling and policy appraisal. Underlying much of this work, in particular for network optimisation problems, is the technique of sensitivity analysis, with the inherent assumption that the equilibrium flows are differentiable. Recent research has called into question the validity of conducting such analysis of the user equilibrium (UE) flows, for which the total derivatives do not always exist. For the case of stochastic user equilibrium (SUE) it is clear that the analytical obstacles faced in the case of UE do not arise; differentiability of both logit and probit SUE model has been established. Difficulties arise in calculating derivatives of the link-based probit model whenever rank deficiencies occur in the path covariance matrix, due to the network topology. The nature of this problem is investigated for some simple examples, showing that problems can sometimes be resolved. (A) Reprinted with permission from Elsevier. For the covering abstract see ITRD E134766.
Samenvatting