Rail line length in a crosstown corridor with many-to-many demand

An analytical model that determines the optimal location and length of rail line along a crosstown transportation corridor with the objective of minimizing the total transportation cost is presented. A general, many-to-many passenger demand pattern is considered. The objective function, which includes the rail and bus riding costs, rail and bus operating costs, rail fleet costs and rail line costs, is minimized by using the classical optimization method with the aid of a computer program developed for the model. The model is applied to the Northwest-South transportation corridor in Calgary, Alberta, and the sensitivity of the optimal rail line location and length to the unit cost and demand parameters at their reasonable ranges is tested. It is found that although the total passenger demand, unit rail line cost, and unit bus operating cost have greater influence than the unit bus and rail riding costs, and unit rail fleet and operating costs, the optimal line length is generally insensitive to all these parameters. It is also found that the length of the existing LRT line in the corridor is comparable to the optimal line length obtained from the model, but the existing fine should be extended further south in order to meet the heavier demand in that direction optimally.