On Stochastic-User-Equilibrium-Based Day-to-Day Dynamics

Researchers have proposed many different concepts and models to study day-to-day dynamics. Some explicitly model travelers’ perceiving learning on travel costs, some other do not consider the cost perception but instead formulate dynamics of flows as functions measured costs (which are determined by flows). This paper investigates interconnection between these two types models, in particular, those whose fixed points a stochastic user equilibrium. Specifically, widely used that combines exponential-smoothing logit network loading (called logit-ESL this paper) is proved be equivalent based purely flows, which logit-based extension first-in-first-out dynamic Jin [Jin W (2007) A dynamical system traffic assignment problem. Transportation Res. Part B Methodological 41(1):32–48]. Via form, globally stable under nonseparable monotone functions. Moreover, Cantarella Cascetta shown second-order incorporating separable link [Cantarella GE, E (1995) Dynamic processes equilibrium transportation networks: Towards unifying theory. Sci. 29(4):305–329]. Further, discrete choice such C-logit, path-size logit, weibit, introduced into model, leading several new also conditions.