Modeling User Responses to Pricing: Simultaneous Route and Departure Time Network Equilibrium with Heterogeneous Users

An important dimension in users’ responses to dynamic pricing schemes is the possible shift in the timing of trips, in addition to changing travel routes. User responses to pricing are governed by individual tripmakers’ preferences, such as their value of time, and the cost they attach to late vs. early arrival relative to the destination. These behavioral characteristics vary across users. Capturing the heterogeneity of users in this regard is important in predicting the impact of dynamic pricing schemes. While previous models have been proposed to find simultaneous route and departure time user equilibrium (SRDUE) in a network, these have not considered the heterogeneity of users in the underlying departure time and path choice decision framework. In a previous contribution, the authors have shown how to incorporate user heterogeneity in determining equilibrium route choices in a network in response to pricing. This paper presents a generalization of that framework to incorporate joint consideration of route and departure time, as well as heterogeneity in a wider range of behavioral characteristics. A model for a multi-criterion SRDUE (or MSRDUE) is presented, along with a simulation-based solution algorithm intended for practical network application. The model explicitly considers heterogeneous users with different values of time (VOT) and values of (early or late) schedule delay (VOESD or VOLSD), in their joint choice of departure times and paths characterized by a set of trip attributes that include travel time, out-of-pocket cost, and schedule delay cost. The MSRDUE problem is formulated as an infinite dimensional variational inequality (VI) problem and solved by a column generation-based algorithmic framework that embeds (i) an extreme non-dominated alternative-finding algorithm to obtain the VOT, VOESD, and VOLSD breakpoints that define multiple user classes, and the associated least trip cost (joint departure time and path) alternative for each user class, (ii) a traffic simulator to capture traffic flow dynamics and determine experienced travel costs; and (iii) a path swapping multi-class alternative flow updating scheme to solve the restricted multi-class SRDUE problem defined by a subset of feasible alternatives. Application to an actual network illustrates the properties of the algorithm, and underscores the importance of capturing user heterogeneity and temporal shifts in the appraisal of dynamic pricing schemes.