In the rapidly evolving urban advanced mobility (UAM) sphere, Vehicular Ad Hoc Networks (VANETs) are crucial for robust communication and operational efficiency in future urban environments. This paper quantifies VANETs to improve their reliability and availability, essential for integrating UAM into urban infrastructures. It proposes a novel Stochastic Petri Nets (SPN) method for evaluating VANET-based Vehicle Communication and Control (VCC) architectures, crucial given the dynamic demands of UAM. The SPN model, incorporating virtual machine (VM) migration and Edge Computing, addresses VANET integration challenges with Edge Computing. It uses stochastic elements to mirror VANET scenarios, enhancing network robustness and dependability, vital for the operational integrity of UAM. Case studies using this model offer insights into system availability and reliability, guiding VANET optimizations for UAM. The paper also applies a Design of Experiments (DoE) approach for a sensitivity analysis of SPN components, identifying key parameters affecting system availability. This is critical for refining the model for UAM efficiency. This research is significant for monitoring UAM systems in future cities, presenting a cost-effective framework over traditional methods and advancing VANET reliability and availability in urban mobility contexts.