Optimal parking supply in bi-modal transportation network considering transit scale economies

In this paper, we investigate the optimal parking supply when considering the transit scale economies in a bi-modal network. Firstly, we formulate auto travel cost and transit travel cost and discuss the scale economies of transit service. Considering passenger's waiting time, travel time and in-vehicle crowding cost, the function of transit travel cost is no longer monotone, but a "U" shape. Secondly, we derive the bi-modal equilibrium without parking restraint and analyze the uniqueness of the equilibrium. Then, we investigate the bi-modal equilibrium with parking restraint. When parking spots are inadequate, drivers would depart earlier to obtain parking spots and deadweight loss arises from competition for parking spots. It was found that parking permits distribution is very efficient in reducing the deadweight loss in Zhang et al. (2011). Thirdly, we study optimal parking supply with the schemes of no management and parking permits managements and analytically discuss the implication of restricting parking supply and parking permits distribution in a single OD pair. It is revealed that total travel costs do not always decrease as the provision of parking spots increases and there is an optimal provision of parking spots at the destination. Meanwhile, the optimal parking provision is discussed in the various schemes of parking permit distribution and trading with consideration of scale economy of transit in a many-to-one network. Finally, numerical examples show that restricting parking supply is an effective measure to reduce system cost.