The corridor problem: More comprehensive results on the no-toll equilibrium

The basic corridor problem is significant for the study of traffic congestion and travel behavior, paving way to insights into the spatial dynamics of rush-hour traffic flow pattern. In light of the fact that previous studies have yielded only preliminary results, this paper considers both early and late commuters to provide more comprehensive results. By introducing the continuous schedule preference (CSP), we determine the form and characteristics of the equilibrium solution, deduce the complete governing equations consistent with the departure timing decision, and obtain the explicit expression of the solution through an ingenious numerical analysis technique. We find and confirm that the set of equilibrium departure time-space points (departure set) with early and late commuters is horn-shaped, and the tip of the horn is situated in the central business district (CBD). This is significantly distinct from the departure set when discontinuous schedule preference is assumed. Moreover, the commuting density distribution increases first and then decreases from residential boundary to CBD, which is consistent with the data we have observed in the real world. This study provides avenues for gaining insights into the propagation characteristics of traffic flow, constituting a substantial advance in the corridor problem.