Recently, some studies examined how downtown parking space limitation re-shapes the morning commute in the case of a single origin-destination network. This paper further formulates and analyses the commuting equilibrium problem of both mode and departure time choices in a bi-modal (auto and public transit) many-to-one network. Several properties of the equilibrium under parking space constraints and the proposed parking reservation system are discussed. Procedures for computing the dynamic user equilibrium with a parking space constraint (either trading of reservations is allowed or not) have been developed. We show that parking reservation can help reduce deadweight loss due to parking competition and roadway congestion. We also found that assigning more reservations to travellers from a specific origin does not necessarily reduce total travel cost of them, while doing so might raise the total travel cost of travellers from other origins. When parking supply is less than the potential demand but is relatively large, it is socially preferred to retain some parking spaces open for competition. However, when the total parking supply is relatively small, all parking spaces should be reserved to travellers. Besides, we show that trading of reservations among travellers would yield an efficiency loss. This loss can be fairly large thus trading should be prohibited.