Perception is crucial to the operation of autonomous driving systems (ADSs), which rely on multiple sensors, such as cameras and LiDARs, combined with code logic and deep learning models to detect obstacles for time-sensitive decisions. Consequently, the latency of the perception module is critical to the safety and effectiveness of ADSs. However, the latency of the perception module and its resilience to various changes in the LiDAR point cloud are not yet fully understood. In this work, we present the first comprehensive investigation measuring and modeling the availability of an industry-grade ADS multi-sensor fusion (MSF) perception module i.e., Apollo. Learning from this investigation, we introduce ADPerf, a tool modifying the point cloud data (PCD) to generate simple and realistic testing scenarios for LiDAR detection which can increase the detection latency. Increasing latency decreases the availability of the detected obstacles, decreasing the accuracy of the obstacle-dependent decisions in ADSs. We conduct a study to assess the effects of ADPerf-generated PCD on the availability of widely-used LiDAR-based 3D obstacle detections, and in turn, trajectory predictors. Our evaluation highlights the need to assess the availability of perception components, especially LiDAR-based detectors, and their robustness to various noises and modifications as they can be a major bottleneck to the performance of the ADS system. Such an adverse outcome will also further propagate to other modules, reducing the overall reliability of ADSs.