Optimal capacity sizing of park-and-ride lots with information-aware commuters

We study capacity sizing of park-and-ride lots that offer services to commuters sensitive to congestion and parking availability information. The goal is to determine parking lot capacities that maximize the total social welfare for commuters whose parking lot choices are predicted using the multinomial logit model. We formulate the problem as a nonconvex nonlinear program that involves a lower and an upper bound on each lot's capacity, and a fixed-point constraint reflecting the effects of parking information and congestion on commuters' lot choices. We show that except for at most one lot, the optimal capacity of each lot takes one of three possible values. Based on analytical results, we develop a one-variable search algorithm to solve the model. We learn from numerical results that the optimal capacity of a lot with a high intrinsic utility tends to be equal to the upper bound. By contrast, a lot with a low or moderate-sized intrinsic utility tends to attain an optimal capacity on its effective lower bound. We evaluate the performance of the optimal solution under different choice scenarios of commuters who are shared with real-time parking information. We learn that commuters are better off in an average choice scenario when both the effects of parking information and congestion are considered in the model than when either effect is ignored from the model.