Linear location-dependent parking fees and integrated daily commuting patterns with late arrival and early departure in a linear city

This paper extends the work of Zhang et al. (2008) to investigate the daily commuting patterns allowing both late arrival in the morning and early departure in the evening in a linear city. Given the fixed parking locations of morning commuters, the Nash equilibrium principle is employed to formulate commuters’ departure time choice in the evening and the user equilibrium principle in terms of daily travel cost is adopted to formulate the departure time choice of morning commuters. A combined regime of linear location-dependent parking fee and time-varying road toll is then proposed to reduce the total social cost (TSC) for the linear city. All the possible equilibrium traffic flows are analytically derived. The analytical results show that (1) commuters, who arrive at work early in the morning, may not depart early in the evening, but their evening trip costs must be lower; (2) when the parking spaces become denser, the evening commute starts earlier and the morning commute starts later; (3) a linear location-dependent parking fee could either advance or postpone the earliest departure time in the morning; (4) three parking modes, distinguished by the order in which commuters park, occur successively as the parking fee rate increases; and (5) an appropriate parking fee can always improve the system efficiency, but no matter how the parking fee is changed, it is impossible to completely eliminate the efficiency loss in the morning. Furthermore, a parking reservation regime joint with time-varying road toll is designed to minimize the TSC for the linear city. Finally, a set of numerical examples are presented to demonstrate the model's properties and these proposed regimes’ performance.