Charging station planning based on the accumulation prospect theory and dynamic user equilibrium

This study investigates the electric vehicle (EV) traffic equilibrium and optimal deployment of charging locations subject to range limitation. The problem is similar to a network design problem with traffic equilibrium, which is characterized by a bilevel model structure. The upper level objective is to optimally locate charging stations such that the total generalized cost of all users is minimized, where the user’s generalized cost includes two parts, travel time and energy consumption. The total generalized cost is a measure of the total societal cost. The lower level model seeks traffic equilibrium, in which travelers minimize their individual generalized cost. All the utilized paths have identical generalized cost while satisfying the range limitation constraint. In particular, we use origin-based flows to maintain the range limitation constraint at the path level without path enumeration. To obtain the global solution, the optimality condition of the lower level model is added to the upper level problem resulting in a single level model. The nonlinear travel time function is approximated by piecewise linear functions, enabling the problem to be formulated as a mixed integer linear program. We use a modest-sized network to analyze the model and illustrate that it can determine the optimal charging station locations in a planning context while factoring the EV users’ individual path choice behaviours.

A Strategic Markovian Traffic Equilibrium Model for Capacitated Networks

In the realm of traffic assignment over a network involving rigid arc capacities, the aim of the present work is to generalize the model of Marcotte, Nguyen, and Schoeb [Marcotte P, Nguyen S, Schoeb A (2004) A strategic flow model of traffic assignment in static capacitated networks. Oper. Res. 52(2):191–212.] by casting it within a stochastic user equilibrium framework. The strength of the proposed model is to incorporate two sources of stochasticity stemming, respectively, from the users’ imperfect knowledge regarding arc costs (represented by a discrete choice model) and the probability of not accessing saturated arcs. Moreover, the arc-based formulation extends the Markovian traffic equilibrium model of Baillon and Cominetti [Baillon JB, Cominetti R ( 2008 ) Markovian traffic equilibrium. Math. Programming 111(1-2):33–56.] through the explicit consideration of capacities. This paper is restricted to the case of acyclic networks, for which we present solution algorithms and numerical experiments.

The Effect of Regret-Based Risky Route Choice on the Traffic Equilibrium for Emergency Evacuation

Following the research on human decision-making under risk and uncertainty, the purpose of this paper is to analyze evacuees’ risky route decision behavior and its effect on traffic equilibrium. It examines the possibility of applying regret theory to model travellers’ regret-taking behavior and network equilibrium in emergency context. By means of modifying the utility function in expected utility theory, a regret-based evacuation traffic equilibrium model is established, accounting for the evacuee’s psychological behavior of regret aversion and risk aversion. Facing two parallel evacuation routes choice situation, the effect of evacuees’ risk aversion and regret aversion on traffic equilibrium is numerically investigated as well as the road capacity reduction from natural disaster. The findings reveal that evacuees prefer the riskless route with the lower travel time as the increase of the regret aversion degree. The equilibrium tends to be achieved when more evacuees choose the safer route jointly affected by risk aversion and regret aversion. Moreover, an optimization model for disaster occurring possibility is formulated to assess the traffic system performance for evacuation management. These findings are helpful for understanding how the regret aversion and risk aversion influence traffic equilibrium.

A Hybrid Newton Method for Stochastic Variational Inequality Problems and Application to Traffic Equilibrium

In this paper, we consider a class of stochastic variational inequality problems (SVIPs). Different from the classical variational inequality problems, the SVIP contains a mathematical expectation, which may not be evaluated in an explicit form in general. We combine a hybrid Newton method for deterministic cases with an unconstrained optimization reformulation based on the well-known D-gap function and sample average approximation (SAA) techniques to present an SAA-based hybrid Newton method for solving the SVIP. We show that the level sets of the approximation D-gap function are bounded. Furthermore, we prove that the sequence generated by the hybrid Newton method converges to a solution of the SVIP under appropriate conditions, and some numerical experiments are presented to prove the effectiveness and competitiveness of the hybrid Newton method. Finally, we apply this method to solve two specific traffic equilibrium problems.