A model of parking supply and demand is presented, in which the supply is made up of capacitated lots situated along a spatial axis, while the demand is disaggregated continuously in both destination place and preferred time of arrival. Each user selects a parking lot and time from among options on the basis of his own trade-off between walking, driving, parking price and schedule delay. The lot saturation times are the basic state variables for this parking system, since they induce the respective efficiency regions of the lots in the plane of destination places and preferred arrival times. These efficiency regions are dynamic market areas with strong yet simple structural characteristics. They make it easy to assign each parking user to his preferred option and to derive the saturation times. It is shown that the deterministic dynamic user equilibrium of parking traffic amounts to a fixed point problem with respect to the saturation times. If parking capacity exceeds demand volume then an equilibrium must exist. Aside from the model presentation, the paper also provides an application instance and a number of directions for further research.