## Sizing vehicle and bikeshare pools

**Sizing Finite-Population Vehicle Pools
**Range anxiety, or the fear that a battery will run out before reaching a destination, is a factor that prevents customers from buying electric cars. Solutions like battery switching, adding more charging outlets, and larger batteries have been proposed, but in 2014 BMW offered a simpler solution: what if when a dealership sells an electric car, they automatically “subscribe” the buyer to a program that allows them to borrow gasoline cars for longer trips? That is, whenever an EV car owner needs to make a longer trip that will outlast the car’s battery range, they can come to the dealership, trade in a subscription coupon for a gasoline car, and rent out that gasoline car free of charge that day.

The question then becomes: how many gasoline cars does a dealership need to reserve for this program? In this study, we analyzed four different methods of sizing this vehicle pool, one of which doesn’t need any prior data or training. The following paper describes these methods in detail.

J16. Tommy Carpenter and Srinivasan Keshav and Johnny Wong. (2014). Sizing Finite-Population Vehicle Pools. IEEE Trans. Intelligent Transportation Systems. PP(99)

**Bikeshare Pool Sizing for Bike-And-Ride Multimodal Transit
**In shared bike-and-ride systems, commuters can ride a shared bicycle from home to a public transportation station, drop the bicycle off in a pool, take public transportation, pick up another bicycle from a pool at their destination stop, then ride to their final destination. So, how many bicycles would be needed at each transportation stop? A naive solution would be to have two bicycles for each commuter, one at the stop they board public transportation, and one at the stop they get off. The caveat is that this would be prohibitively expensive. So, what would be the

*smallest*number of bikes that should be available at each public transportation station for this to work?

It turns out that the mathematical problem for sizing these bikeshares has the same structure as the mathematical problem for sizing vehicle pools, which was described above. By using this method, we were able to reduce the number of bicycles in each pool by between 39% to 75%, compared to having two bikes per commuter.

J6. G. Tang and S. Keshav and L. Golab and K. Wui. (2018). Bikeshare Pool Sizing for Bike-And-Ride Multimodal Transit. IEEE Transactions on Intelligent Transportation Systems.