# Stochastic Ridesharing User Equilibrium in Transport Networks

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## Abstract

With the development of the Internet and mobile phone technology, it is much easier to access ridesharing information via mobile applications. In this paper, the relationship between the demand of ridesharing passengers (RPs), ridesharing drivers (RDs) and solo drivers (SDs) in a ridesharing compensation scheme is studied by a stochastic ridesharing user equilibrium (SRUE), which contains a mode choice model and a route choice model. The mode choice model and the route choice model influence each other. The SRUE is first expressed as a fixed-point problem mathematically. Six possible states of OD pairs are discussed. Then the existence of SRUE is proved. The method of successive weighted averages is adopted to solve the problem. It is found that there will be a higher demand of ridesharing passengers for journeys with longer travel time. Moreover, with the increase of the ridesharing compensation, the demand of ridesharing passengers is not always decreasing, and the demand of ridesharing drivers is not always increasing.

## Keywords

Transportation Network equilibrium Ridesharing Demand Expected cost## Notes

### Acknowledgements

This work was supported by the Key Research and Development Program (No. 2016YFC0802508), and the National Natural Science Foundation of China (Nos.11672289, 71621001, 71631002).

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