In this paper, we develop an urban space model that describes travel demand as well as distributions of residential area and transportation area. The area considered is a square consisting of square zones laid on a grid pattern. In each zone i, land is allocated to residential area and transportation area, and only one building is built on the residential area. The population density is assumed to be consistent so that the size of the building is proportional to the number of residents xi in zone i. The principle that plays an important role in this model is that the transportation area must have sufficient capacity to manage the traffic passing there. Therefore, if the traffic volume in a zone is large, the area available for the site of a building becomes small. In this case, the population in that zone should be small, or the building should be high to accommodate large population and this leads to increase the travel time in the building. Trip generation and trip distribution in our model are performed very simply in the sense that for each pair of residents, one trip is made in unit time with constant probability b. The residents in each zone are aggregated so that the number of trips that originate in zone i and terminate in zone j is bxixj. A route followed by a trip consists of three parts. One starts a trip at his or her location and goes down to the ground, then follows one of the alternative routes on land and finally goes up to the location of the other. We consider two alternative routes on land, both are the shortest distance routes with respect to L1 metric, one route contains only one left-turn, and the other contains only one right-turn. In order to determine the necessary transportation area in each zone in terms of the traffic volume passing through it, we introduce the transportation capacity of unit area of road and define it as a function of vehicle speed. We also introduce the congestion phenomena in such a way that capacity increases linearly from in light traffic condition to heavy traffic condition as vehicle speed decreases. The system principle of our model is to minimize the total travel time of trips between the residents' locations. We define the minimization problem whose variables are the population xi in each zone i and the route choice probability between each pair of zones. We solve some numerical examples using three slightly different models. The first one is the least flexible one, the capacity and the speed are fixed and the route between origin and destination is specified to one left-turn only. In this case, as the population of the whole area becomes large, the traffic volume passing through the central district increases so that the height of the buildings as well as the travel time consumed there grows rapidly. The second one adopts the functional relation such that the capacity of unit transportation area can be increased at the cost of decrease in vehicle speed. This moderates the rapid increase in the proportion of transportation area especially in the central district. In the last one, trips between each origin–destination zone can be assigned to each one of the alternative routes. This brings to the solution the remarkable feature that the proportion of transportation area in the central district is lower than that in surrounding area.
