  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.
