Day-to-day needs-based activity-travel dynamics and equilibria in multi-state supernetworks

This study proposes a new framework for studying activity-travel dynamics in multi-state supernetworks based on a needs-based theory. The framework postulates that temporal fluctuations in human needs are the source of dynamically generated activities, which in turn are manifested in the choice of day-to-day activity-travel patterns (ATPs) and dynamics in day-to-day traffic. Specifically, the net utility of a daily ATP is determined jointly by the degree of satisfying particular needs and the traffic conditions when conducting the ATP. Needs are updated after completing the activities and so is the net utility of the ATP, which means that the net utility that is derived from conducting a particular ATP varies across time. Thus, the choice of a daily ATP is determined not only by the needs reflected in past ATP choices but also on current traffic conditions and usage of facilities. We formulate these dynamics in terms of an activity-travel adjustment process, through which the proposed needs-based activity-travel dynamic system converges to a steady state, coinciding with the Wardropian user equilibrium and the equivalent mixed-strategy Nash equilibrium. This formalism integrates activity generation, activity-travel scheduling, and traffic flow evolution, and offers appealing explanations for day-to-day traffic dynamics and equilibria.