In this research, the problems of finding the optimum positions of bus routes and the optimum frequency of buses on each route in an urban area are considered, the criterion of optimality being that the sum of the time-costs of the journeys and the cost of providing the bus service should be a minimum. The problem is studied theoretically by examining a model of a bus system operating in a large uniform area, with the routes forming a square grid, buses running right across the area, and the same frequency of buses on each route. Formulae are derived giving the average times on a journey spent walking, waiting for buses, and riding on buses, in terms of the parameters of the model. The cost of providing the bus service is also found in terms of these parameters. By adding the time-costs of the journeys, the total cost of travel is obtained. The values of the route-spacing and the service-interval which minimize this total cost are found in terms of the other parameters. An alternative method of selecting routes is indicated, which leads to similar formula by a simpler argument. Some suggestions are made for further research.
Abstract