Autonomous electric mobility on demand (AEMoD) has recently emerged as a cyber-physical system aiming to bring automation, electrification, and on-demand services for the future private transportation market. The expected massive demand for such services and its resulting insufficient charging time/resources prohibit the use of centralized management and full vehicle charging. A fog-based multi-class solution for these challenges was recently suggested, by enabling per-zone management and partial charging for different classes of AEMoD vehicles. This paper focuses on finding the optimal vehicle dimensioning for each zone of these systems in order to guarantee a bounded response time of its vehicles. Using a queuing model representing the multi-class charging and dispatching processes, we first derive the stability conditions and the number of system classes to guarantee the response time bound. Decisions on the proportions of each class vehicles to partially/fully charge, or directly serve customers are then optimized so as to minimize the vehicles in-flow to any given zone. Excess waiting times of customers in rare critical events, such as limited charging resources and/or limited vehicles availabilities, are also investigated. Results show the merits of our proposed model compared to other schemes and in usual and critical scenarios.