Time Value Distribution and Multi-modal Intercity Travel Network Shape: Theoretical Analysis for the Typical Setting

In a period of declining demand, should we sustain some intercity transport even if it is unprofitable? And in which situations should we sustain the plurality of modes of transport? In this paper, we analyze the relationship between time-value distribution and multi-modal network shapes. The network shapes considered are dual-mode or single-mode, and a random parameter model is used to describe the route choice of travelers, which takes the time-value distribution into account. First, the relationship between parameters of time-value distribution (i.e., average and dispersion) and the optimal network shape is analyzed; we find that a dual-mode network is optimal when the time-value dispersion is large. Second, as demand declines, the optimal network may change from a dual-mode network to a single-mode network. Third, the conditions in which an equilibrium dual-mode network can be established in a given transport market are described. From a comparison between the equilibrium and optimal conditions for a dual-mode network, we find that dual-mode networks may be in equilibrium even though they are not optimal. It follows that we need not sustain unprofitable mode service in order to realize the optimal network shape. Moreover, in a period of declining demand, it may be beneficial to move from a dual-mode network to a single-mode network from a market driven dual-mode network.