Morning commuters often choose their departure times not only to trade off bottleneck congestion and schedule delays, but also in order to secure a parking spot due to limited parking spaces. It is the combination of these two forces that governs the commuters' departure time choices. This paper investigates the morning commute problem in a two-to-one network with both bottleneck congestion and parking space constraints; particularly when some commuters have reserved parking spots or parking permits and other commuters have to compete for public parking spots on a first-come first-served basis. Distinguished from the traditional pure bottleneck model, the rush-hour dynamic traffic pattern with binding parking capacity constraints varies with the relative portions of the two classes of commuters: those with and those without a reserved parking spot. It has been found that when the parking capacity is greater than half of the potential parking demand, it is socially preferred to retain some parking spots unreserved in a two-to-one network.