Trips between a metropolitan region and its CBD during peak periods are served by a coordinated rail and bus transit system. Each locality is served only by a direct bus to the CBD or by a feeder bus to a railway station from which train service to the CBD is provided. Optimal transit service characteristics that minimize the sum of the transit operating costs and passenger time costs are determined.

To formulate a mathematical model of the system it is assumed that a radiocentric regional highway network centered at the CBD exists. Rail-way lines are assumed to be radial. The demand for, public transit is known, deterministic and varies slowly with location. The optimization is accomplished mainly by the use of basic calculus in conjunction with continuum approximations of certain discrete parameters.

An optimal feeder-bus-service zone is shown to exist and its con- figuration is analyzed. Approximate but simple and explicit formulations for the optimal railway interstation spacings, bus-service shed areas, and transit vehicle headways are determined. The relationship of the interstation spacing at a given location to two local demand parameters and to a cumulative demand parameter is shown clearly. The sensitivity of the above transit service characteristics to various travel-time and cost parameters is discussed.

Several numerical examples are presented. A one dimensional version of the model is applied to the San Francisco Peninsula Commuter Railway service.