The allocation of buses in heavily utilized networks with overlapping routes

Many transit systems outside North America are characterized by networks with extensively overlapping routes and buses frequently operating at, or close to, capacity. This paper addresses the problem of allocating a fleet of buses between routes in this type of system; a problem that must be solved recurrently by transit planners. A formulation of the problem is developed which recognizes passenger route choice behavior, and seeks to minimize a function of passenger wait time and bus crowding subject to constraints on the number of buses available and the provision of enough capacity on each route to carry all passengers who would select it. An algorithm is developed based on the decomposition of the problem into base allocation and surplus allocation components. The base allocation identifies a feasible solution using an (approx.) minimum number of buses. The surplus allocation is illustrated for the simple objective of minimizing the maximum crowding level on any route. The bus allocation procedure developed in this paper has been applied to part of the Cairo bus system in a completely manual procedure, and is proposed to be the central element of a short-range bus service planning process for that city.