In the future, vehicle sharing platforms for passenger transport will be unmanned, autonomous, and electric. These platforms must decide which vehicle should pick up which type of customer based on the vehicle’s battery level and customer’s travel distance. We design dynamic vehicle allocation policies for matching appropriate vehicles to customers using a Markov decision process model. To obtain the model parameters, we first model the system as a semi-open queuing network (SOQN) with multiple synchronization stations. At these stations, customers with varied battery demands are matched with semi-shared vehicles that hold sufficient remaining battery levels. If a vehicle’s battery level drops below a threshold, it is routed probabilistically to a nearby charging station for charging. We solve the analytical model of the SOQN and obtain approximate system performance measures, which are validated using simulation. With inputs from the SOQN model, the Markov decision process minimizes both customer waiting cost and lost demand and finds a good heuristic vehicle allocation policy. The experiments show that the heuristic policy is near optimal in small-scale networks and outperforms benchmark policies in large-scale realistic scenarios. An interesting finding is that reserving idle vehicles to wait for future short-distance customer arrivals can be beneficial even when long-distance customers are waiting.