On a Shared Scooter Service with Opportunistic Riding under Ring Shape: the S3 Traffic Model and its Equilibrium

Résumé 0

Shared Scooter Services (S3) have been deployed in many cities to provide public transport to individual users on a free-floating basis. The article brings about an analytical traffic model for such service under ring shape, i.e. postulating there is a ring road along which the scooters are required to park and expected to be driven, in order to avoid detours and increase vehicle productivity as well as local availability to potential users. Opportunistic Riding is also postulated: on their way, every user takes the first available vehicle which they encounter. Also postulated are the homogeneity in both space and time. With respect to the ring circumference, the daily volume of potential trips, the statistical distributions of trip lengths, walk speeds an ride speeds, as well as the fleet size, operation period and transaction times, analytical formulas are provided for (i) access lengths and times, together with usage probability, (ii) ride lengths and times, (iii) vehicle occupation at the fleet level, (iv) the average number of available vehicles. Traffic equilibrium is shown to exist and to be unique. Its characteristic equation is recast as a fleet sizing rule according to demand volume and target access length, which stand respectively as the quantitative and qualitative service objectives.