**6. Conclusions**

In this study, a route guidance problem was formulated by combining the time-varying road network and stochastic charging demands. To address the problem, we proposed two heuristic-based route guidance strategies from two different perspectives, namely, the SDD and CSB strategies. The SDD strategy uses the driving distance as the optimization criterion based on the travel cost of individual drivers. By contrast, the CSB strategy selects the charging stations with the minimum EV number based on the vehicle balance in charging stations. Despite their differences, both strategies can guarantee the reachability of selected charging stations in a time-varying road network. Simulation experiments were implemented to explore the performances of the SDD and CSB strategies. The results indicate that the CSB strategy has an advantage over the SDD strategy in avoiding the negative influence of mass EV charging on the charging station operation, especially in the situation with a relatively long time horizon.

Furthermore, the parameter analysis was carried out through changing the scenario parameters in the simulation experiments. The results present the different performances of SDD and CSB strategies as parameter scenarios vary. For the SDD strategy, the maximum EV number at different charging stations had a significant gap and ranged from approximately 30 to 100. By contrast, for the CSB strategy, the maximum EV number at different charging station exhibited a moderate degree of change and mainly ranged from 25 to 30. Moreover, the SDD strategy may be unable to stabilize the charging service system in some heavily loaded scenarios (i.e., low μ and high λ), but the CSB strategy can stabilize the charging service system for all parameter scenarios. However, if the charging service is in lightly loaded scenarios (i.e., high μ and low λ), the SDD strategy could be employed due to its similar effects on charging stations with the CSB strategy and consideration of the travel cost of individual drivers.

Each normal node is assumed to generate at most one charging demand in every time slot to simplify the problem formulation. Such an assumption is reasonable if each time slot has a relatively short duration. However, as the scale of EVs increases in the urban transportation system, multiple charging demands may occur simultaneously in the same location on road networks, thereby significantly complicating the solving processes for the stochastic charging demands. On the basis of the proposed strategies, a distribution rule regarding the number of charging demand occurrence will be further explored in future work and considered to improve the route guidance strategies. Furthermore, other evaluation metrics, such as waiting time, trip length extension, and energy efficiency, will be introduced in a future study.

**Author Contributions:** Conceptualization, Y.W. and J.B.; methodology, Y.W.; validation, Y.W. and C.L.; writing, Y.W.; visualization, Y.W., C.L., and C.D.; supervision, J.B., C.L., and C.D.; funding acquisition, J.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the National Natural Science Foundation of China (Nos. 71961137008 and 71621001).

**Acknowledgments:** The authors gratefully acknowledge fruitful discussions with Prof. Bin Li in the University of Rhode Island, as well as financial support from the China Scholarship Council.

**Conflicts of Interest:** The authors declare no conflict of interest.
