The quantitative performance analysis plays a critical role in assessing the capability of Vehicular Edge Computing (VEC) systems to meet the requirements of vehicular applications. However, developing accurate analytical models for VEC systems is extremely challenging due to the unique features of intelligent vehicular applications. Specifically, recent work revealed that the tasks generated by intelligent vehicular applications exhibit a high degree of burstiness, rendering the existing models that were designed based on the assumption of the non-bursty Poisson process unsuitable for VEC systems. To fill this gap, we developed an original analytical model to investigate the performance of VEC systems with bursty task arrivals. To facilitate vehicle cooperation, a new priority-based resource allocation scheme is exploited to schedule the tasks of vehicular applications, which are modelled by a Markov Modulated Poisson Process (MMPP). Next, a multi-state Markov chain is established to investigate the impact of load sharing strategy on the performance of VEC systems. Then, the end-to-end transmission latency is derived based on the proposed model. Comprehensive experiments are conducted to validate the accuracy of this analytical model under various system configurations. Furthermore, the developed model is used as a cost-effective tool to investigate the performance bottleneck of VEC systems.