Joint design of parking capacities and fleet size for one-way station-based carsharing systems with road congestion constraints

This paper formulates one-way station-based carsharing systems as a mixed queuing network model and proposes a profit-maximization model for the joint design of fleet size and station capacities. We explicitly model the road congestion by formulating each route as a queue where the travel time is an increasing function of the state. The booking process is also modeled in the rental station queue so that the efficiency loss caused by the reservation policy can be captured. The mixed queuing network falls into Baskett, Chandy, Muntz and Palacios (BCMP) networks with unique product-form equilibrium distribution. We derive the asymptotic behavior as the parking capacities and fleet size grows, and show that the performance of carsharing systems will be proportionally bounded by that of the bottleneck route. The exact mean value analysis (MVA) algorithm and the approximate Schweitzer-Bard mean value analysis (SB-MVA) algorithm are extended here to solve networks with different sizes. The numerical experiments reveal some interesting findings: (1) The higher customer service rate (the smaller pick-up time window) will generate the optimal design with lower parking capacities and lower fleet size; (2) Neglecting the efficiency loss due to reservation will lead to an overestimate of the profit and other system performances as well; and (3) Given different levels of congestion on the existing road network (the non-shared car traffic), the net revenue is maximized when the existing traffic congestion is moderate.