Consistent formulation of network equilibrium with stochastic flows

Abstract

Traffic flows in real-life transportation systems vary on a daily basis. According to traffic flow theory, such variability should induce a similar variability in travel times, but this "internal consistency" is generally not captured by existing network equilibrium models. We present an internally-consistent network equilibrium approach, which considers two potential sources of flow variability: i) daily variation in route choice and ii) daily variation in origin-destination demand. We particularly aspire to a flexible formulation that permits alternative statistical assumptions, which allows the best fit to be made to observed variability data in particular applications. Joint probability distributions of routeand therefore link flows are derived under several assumptions concerning stochastic driver behavior. A stochastic network equilibrium model with stochastic demands and route choices is formulated as a fixed point problem. We explore limiting cases which allow an equivalent convex optimization problem to be defined, and finally apply this method to a real-life network of Kanazawa City, Japan.

Statistical models for the estimation of the origin-destination matrix from traffic counts

“…In deterministic models this has been done through equilibrium traf ic assignment. Nevertheless, it is known that the classical de inition of stochastic user equilibrium, due to Daganzo and Shef i (1977), does not imply an equilibrium probability distribution on OD lows (Hazelton, 1998;Nakayama and Watling, 2014). Hence, the modelling of OD lows through a fully probabilistic model which does not assume an equilibrium state may provide new insights into the problem.…”

Link-based day-to-day network traffic dynamics and equilibria

“…It would be interesting to investigate day-to-day traffic dynamics in link variables for other user equilibrium concepts, such as stochastic user equilibrium (Cantarella and Cascetta, 1995;Watling, 1999;Hazelton, 2002;Parry and Hazelton, 2013;Nakayama and Watling, 2014) and bounded rational user equilibrium (Guo and Liu, 2011;Guo, 2013). The day-to-day traffic dynamics can be made in traffic networks with multi-class users, either in terms of different classes of vehicles or modes or in terms of different values of time of travelers (Yang and Huang, 2004;Guo and Yang, 2009).…”

Measuring and reducing the disequilibrium levels of dynamic networks with ride-sourcing vehicle data

“…Zhu and Levinson [64], Jan et al [22] conducted empirical studies using GPS data and found that most travelers do not follow shortest paths in the network, and some studies indicate that travelers are likely to follow the shortest distance paths [1,44] or hyperpaths [30]. Studies also explored alternative models with milder assumptions, such as bounded rationality [34,12], statistical traffic equilibrium [38,32], and mean-excess traffic equilibrium [7].…”