Density of alternative fuel stations and refueling availability

•Develops an analytical model for sufficient density of alternative fuel stations.•Focuses on whether the vehicle can make the repeated round trip.•Examines the effects of the vehicle range and the trip length.•Considers three cases for the refueling availability at origin and destination.

This paper develops an analytical model for determining sufficient density of alternative fuel stations required to achieve a certain level of service. The service level is represented as the probability that the vehicle can make the repeated round trip between randomly selected origin and destination. Distance is measured as the Euclidean distance on a continuous plane. The probability is obtained for regular and random patterns of stations for three cases: fuel is available at both origin and destination, fuel is available at either origin or destination, and fuel is available at neither origin nor destination. The analytical expressions for the probability demonstrate how the density of stations, the vehicle range, and the trip length, as well as the refueling availability at origin and destination affect the service level. The result shows that the effect of the refueling availability at origin and destination is significant.