Day-To-Day Dynamic Network Disequilibria and Idealized Traveler Information Systems

Abstract

In this paper we present tatonnement models for calculating static Wardropian user equilibria on congested networks with fully general demand and cost structures. We present both a qualitative analysis of stability and numerical studies which show that such an approach provides a reliable means for determining static user equilibria. We also describe circumstances for which these models depict day-to-day adjustments from one realizable disequilibrium state to another and how these adjustment processes differ depending on the “quality” of the information being provided by (abstract) traveler information systems. Specifically, we demonstrate that such dynamic adjustment processes settle down to equilibria both when information is complete and when it is incomplete.

Exploration of day-to-day route choice models by a virtual experiment

“…The network tatonnement process (NTP) (Friesz et al, 1994) and the projected dynamic system (PDS) (Zhang and Nagurney, 1996;Nagurney and Zhang, 1997) are not investigated here for two reasons: first, they will degenerate to XYY dynamics under mild conditions ; second, their parameters cannot be estimated by the regression method used in this paper. The parameter  in Eq.…”

“…The interaction between day-to-day dynamic route flows and other components of the transportation system is widely studied in the analytical way, which includes the traffic information system (Bifulco et al, 2016;Cantarella, 2013;Cho and Hwang, 2005;Friesz et al, 1994), fixed or responsive signal control strategies (Cantarella et al, 2012;Huang et al, 2016;Liu and Smith, 2015;Smith et al, 2015;Smith and Mounce, 2011;Xiao and Lo, 2015), congestion pricing (Friesz et al, 2004;Farokhi and Johansson, 2015;Guo, 2013;Guo et al, 2016;Tan et al, 2015;Wang et al, 2015;Xu et al, 2016;Yang, 2007;Yang and Szeto, 2006;Yang et al, 2007;Ye et al, 2015), and tradable credit scheme (Ye and Yang, 2013). Day-to-day dynamics in other travel modes are also studied, such as in railway (Wu et al, 2013) and transit (Bar-Yosef et al, 2013;Cantarella et al, 2015;Li and Yang, 2016).…”

The projection dynamic and the geometry of population games

“…first appears in the transportation literature in the work of Friesz et al (1994), and is dubbed the target projection dynamic in Sandholm (2005), where a common mathematical ancestry is provided for this dynamic and the projection dynamic (P). Tsakas and Voorneveld (2007) show that the dynamic (TP) can be derived from a revision protocol based on best responses, if payoffs to mixed strategies are subjected to state-dependent perturbations:…”

Resolvent dynamical systems and mixed variational inequalities

“…The fixed point formulation of the variational inequalities has been used to suggest two type of dynamical systems. The first one, is due to Friesz et al [9] is designated as global projected dynamical systems, whereas the second which is mainly due to Dupuis and Nagurney [8] is called the local dynamical system. We would like to mention that novel and innovative features of these projected dynamical systems is that the set of the stationary points of the dynamical systems correspond to the set of the solutions of the variational inequalities.…”