This paper formulates a discrete-time dynamic traffic assignment model and, under certain conditions, shows the existence and uniqueness of network equilibrium. Several theoretical issues need to be tackled. In discrete time traffic flow, the inflow to a link (or cell) in a particular discrete time period does not all necessarily exit within the same time period. We consider how flow is passed from one link and time period to the next, and the corresponding costs. Under the proposed model, flow

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... departing within a discrete time period may experience different link travel times in different discrete time 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 dynamic traffic assignment is proposed; a semi-dynamic analogue of user equilibrium. The existence and uniqueness of this equilibrium solution are proven.