Improved Convolution-Based Analysis for Worst-Case Probability Response Time of CAN
Haozhe Yi, Junyi Liu, Maolin Yang, Zewei Chen, Xu Jiang
TL;DR
The paper tackles probabilistic worst-case response time (pWCRT) analysis for CAN under error retransmission, addressing the inadequacy of simulation-based predictions for rare events. It introduces an improved convolution-based algorithm that uses busy-window and backlog techniques to compute the pWCRT distribution, incorporating an error model with retransmissions capped by a maximum retry count $k$ and error overhead $E$, under a Poisson error rate $\lambda$. Empirical evaluation on the SAE CAN benchmark and random message sets shows substantially reduced pessimism and closer alignment with Monte Carlo results (very small MSE, on the order of $10^{-12}$) as well as lower computational overhead compared to prior methods. The approach offers more accurate, efficient probabilistic guarantees for safety-critical CAN-based real-time systems, enabling tighter deadline assurance in practical automotive and factory automation contexts.
Abstract
Controller Area Networks (CANs) are widely adopted in real-time automotive control and are increasingly standard in factory automation. Considering their critical application in safety-critical systems, The error rate of the system must be accurately predicted and guaranteed. Through simulation, it is possible to obtain a low-precision overview of the system's behavior. However, for low-probability events, the required number of samples in simulation increases rapidly, making it difficult to conduct a sufficient number of simulations in practical applications, and the statistical results may deviate from the actual outcomes. Therefore, a formal analysis is needed to evaluate the error rate of the system. This paper improves the worst-case probability response time analysis by using convolution-based busy-window and backlog techniques under the error retransmission protocol of CANs. Empirical analysis shows that the proposed method improves upon existing methods in terms of accuracy and efficiency.