In vehicular ad hoc networks (VANETs), one of the important challenges is the lack of precise mathematical modeling taking into account the passive vacation triggered by the zero-arrival state of nodes. Therefore, a polling-based access control is proposed in this paper using a sleeping schema to meet the challenge of quality of service (QoS) and energy-efficient transport in VANET environments for smart cities. Based on IEEE 802.11p, it was developed in an attempt to improve the energy efficiency of the hybrid coordination function of controlled channel access (HCCA) through a self-managing sleeping mechanism for both the roadside unit (RSU) and on-board units (OBUs) or sensor nodes according to the traffic load in vehicle -to-infrastructure (V2I) scenarios. Additionally, a Markov chain was developed for analyzing the proposed mechanism, and the exact mathematical model is provided with regard to the passive vacation. Then, the performance characteristics—including the mean cyclic period, delay, and queue length—were accurately obtained. In addition, the closed-form expression of the quantitative relationship among sleeping time, performance characteristics, and service parameters was obtained, which can easily evaluate the energy efficiency. It was proven that theoretical calculations were completely consistent with simulation results. The simulation results demonstrate that the suggested method had much lower energy consumption than the standard strategy at the expense of rarely access delay.