A quasi-dynamic assignment model that guarantees unique network equilibrium

Abstract

This article formulates a discrete-time dynamic traffic assignment (DTA) model and, under certain conditions, shows the existence and uniqueness of network equilibrium. Several theoretical issues need to be tackled. The inflow to a link in a particular discrete (time) period does not necessarily exit within the same period. We consider how flow is passed from one link and period to the next, and the corresponding costs. Under the proposed model, flow departing within a discrete period may experience different link travel times in different discrete periods, even if the flow chooses a single route. Route travel time must then be defined so that route and OD costs are meaningful. To this end, quasi-real route travel time is defined. Based on this definition, a quasi-equilibrium condition for DTA is proposed; a semi-dynamic analogue of user equilibrium. The existence and uniqueness of this equilibrium solution are proven.

Keywords:

• dynamic user equilibrium
• quasi-real travel time
• unique network flow
• link-based formulation
• discrete time

Notes

1. A more obvious term may be mean real travel time, however, the model in this study is deterministic, rather than stochastic. To avoid confusion, quasi-real travel time is adopted.