Quantitative performance analysis plays a pivotal role in theoretically investigating the performance of Vehicular Edge Computing (VEC) systems. Although considerable research efforts have been devoted to VEC performance analysis, all of the existing analytical models were designed to derive the average system performance, paying insufficient attention to the worst-case performance analysis, which hinders the practical deployment of VEC systems to support mission-critical vehicular applications, such as collision avoidance. To bridge this gap, we develop an original performance analytical model by virtue of Stochastic Network Calculus (SNC) to investigate the worst-case end-to-end performance of VEC systems. Specifically, to capture the bursty feature of task generation, an innovative bivariate Markov Chain is first established and rigorously analysed to derive the stochastic task envelope. Then, an effective service curve is created to investigate the severe resource competition among vehicular applications. Driven by the stochastic task envelope and effective service curve, a closed-form end-to-end analytical model is derived to obtain the latency bound for VEC systems. Extensive simulation experiments are conducted to validate the accuracy of the proposed analytical model under different system configurations. Furthermore, we exploit the proposed analytical model as a cost-effective tool to investigate the resource allocation strategies in VEC systems.