Line Ride-Sharing as a bi-sided mobility service with price schedule, transactional protocol and waiting policy: a Time&Money traffic assignment model and its equilibrium

A line ride-sharing service is supplied along a given roadway path by an operator that matches Users (riders) and Agents (drivers), under specific protocol that involves price schedule on both the U and A sides, waiting policy on either side and transaction times. The resulting time and money items add up over trip legs, yielding trip time and money cost depending on the service role, A or U, compared to Non-commitment, called role N for Neutral. The article brings about a traffic model of people involvement in the service. Service conditions of frequency φ and average number of users per car run ω are key factors of the time and money features of the alternative roles A, U and N. Individual choice of role is modeled as a rational behavior of minimizing the generalized cost depending on the individual Value-of-Time (VoT). Aggregation over trip-makers according to the statistical distribution of VoT yields the respective role flows (y_A,y_U,y_N), which in turn determine the macroscopic factors (φ,ω). Traffic equilibrium is defined as a balance condition between the "supplied flows" and the "demanded flows" of the three roles. A computational scheme is provided, with graphical interpretation in the (y_A,y_U) plane as well as in the (φ,ω) plane. A numerical experiment is conducted, showing that two alternative configurations can arise at equilibrium: either {A,U,N} with less wealthy Agents driving wealthier Users, or {U,A,N} where less wealthy Users are driven by wealthier Agents: in both cases the Neutral role attracts the upper range of the VoT distribution.