Communication is essential for Cooperative Intelligent Transportation Systems (C-ITS) to achieve better road efficiency, especially for Autonomous Intersection Management (AIM) which coordinates vehicles to pass the intersection safely and efficiently. Communication delays cause severe safety crises (i.e., collisions) and vehicular-performance degradation regarding intersection capacities and vehicular delays. Targeting the delays, network researchers have been working on low-latency communication technologies, and C-ITS researchers have proposed delay-tolerant AIM systems to avoid collisions in intersections. The impacts of communication delays are observed and discussed in the literature; however, models and assessments of the delay requirements for AIM are needed to provide insights for future network and C-ITS research. Here, we model the impact of communication delays on vehicular performance at an autonomous intersection and validate the models with the simulation results from over two million experiments, two types of multi-lane intersections (a typical 4-legged intersection and a roundabout), and four AIM systems. The simulations are conducted with SUMO simulator and AIM systems, where communication delays are inserted into the message exchanges during the simulation. The models are represented in linear, quintic, and cubic polynomials, showing that communication delay between 0 to 100 milliseconds is linearly related to vehicular performance in terms of intersection capacity and vehicular delay. According to the models, we show that by reducing communication delay from 100 to 10 milliseconds, the capacity degradation can be reduced from 7-10% to 0.7-1.0%. Moreover, communication delays must be less than 247 milliseconds to allow AIM systems to outperform traditional traffic lights.
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