Travel Distance Through Transportation Terminals on a Rectangular Grid

Abstract

The number of terminals used in a transportation network affects inventory, transportation and overhead costs. With few terminals, overhead and inventory costs tend to be small, but average travel distance through terminals is large. With many terminals, overhead and inventory costs are large, but average travel distance is small. As a first step toward analyzing this trade-off, this paper develops equations that quantify the relation between number of terminals and average travel distance. These equations are verified by applying them to an example involving the 37 largest cities in the United States. Average travel distance is shown to decrease slowly as the number of terminals increases, declining by no more than one third. Although adding terminals decreases travel distance somewhat, the marginal travel distance reduction quickly becomes quite small.