Dynamic ridesharing with variable-ratio charging-compensation scheme for morning commute

•Variable-ratio charging-compensation scheme (VCS) can help achieve desirable objectives of ridesharing.•User equilibrium coincides with system optimum when the platform minimizes system disutility with VCS.•Ridesharing participants depart at the two tails of the peak hour to commute with no queue.•Fuel cost and inconvenience costs of ridesharing drivers and passengers play a vital role. This paper investigates the dynamic ridesharing with the variable-ratio charging-compensation scheme (VCS) in morning commute, with the continuous-time point-queue model applied to a single bottleneck. The optimal VCS without imposing road pricing when the ridesharing platform minimizes the disutility or maximizes its profit is analyzed. It is found that the user equilibrium coincides with the system optimum when the platform minimizes the system disutility with VCS, and the corresponding platform's profit is negative with high travel demand. Considering this, the optimal VCS when the platform minimizes the system disutility with zero profit is examined. Moreover, to ensure ridesharing participants commute with no queue, they need to depart at the two tails of the departure time window. Under that case, the optimal VCS are investigated with desirable objectives of the ridesharing platform. The analytical results indicate there should be fewer commuters involved in ridesharing when the platform maximizes its profit compared to that when the platform minimizes the system disutility with zero profit.