The utilization of autonomous vehicles (AVs) has emerged as a pivotal factor in addressing the rising costs and safety concerns associated with modern travel. As technology advances and traffic challenges intensify, enhancing accessibility stands out as a critical goal for transportation experts. Accessibility, constrained by factors like travel time, underscores the increasing need for AVs to mitigate these limitations. This study aimed to model the influence of AVs on the accessibility index within transportation networks and discuss system optimization based on user equilibrium (UE) and system optimum (SO) outcomes. The research conducted numerical analysis employing the Hearn network as a fundamental system to validate a mixed assignment model and ascertain baseline accessibility. Additionally, the Sioux Falls network, a medium-sized network, was employed for analysis. A hybrid heuristic assignment algorithm was introduced, concurrently assigning different percentages of AV presence alongside the remaining non-AV percentage in three distinct scenarios. These scenarios ranged from 0 to 100% AV presence: the first scenario maintained constant network capacity, the second scenario adjusted network capacity based on AV presence, and the third scenario incorporated capacity adjustments in the assignment stage. In all three scenarios, network accessibility was evaluated using gravity and accessibility index methods derived from the hybrid assignment model output. The findings demonstrated that as the percentage of AVs increased, accessibility improved in both Hearn and Sioux Falls networks across all scenarios. The second and third scenarios exhibited higher accessibility increases compared to the first, attributable to augmented capacity resulting from increased AV presence. In the Sioux Falls network, the first scenario showed enhanced SO and UE due to increased AV presence and enhanced system operator management. Conversely, the second and third scenarios, with increased AVs and subsequent capacity increments, displayed reduced UE and SO results. Despite the decline in UE and SO, traffic flow assignment and overall network accessibility improved. These findings highlight the positive correlation between AV presence, network capacity, and enhanced accessibility. The study underscores the potential benefits of AV integration in optimizing transportation networks and improving overall accessibility, albeit with nuances in capacity adjustments impacting traffic flow dynamics. Further research avenues could explore complex traffic flow scenarios and delve into more specific optimization strategies.