Whether the current IEEE 802.11p communication system meets the stringent quality of service (QoS) requirements for safety applications or not is still not very clear. Signal-to-interference-plus-noise ratio (SINR) distribution plays a primary role in quantifying the QoS as well as link capacity of IEEE 802.11p in one-dimensional (1-D) highway and two-dimensional (2-D) intersection road. Most of the analytical models based on stochastic geometry assumed ALOHA access to analyze the SINR distribution, while few of the works developed the stochastic geometry based model considering CSMA access but derived the SINR distribution utilizing statistical estimator. On the other hand, the current interference based probability analytic model for the SINR distribution limit the 1-D extension to 2-D, due to the very high numerical computational complexity at 2-D. In this paper, we propose an analytic model under more general non-homogeneous Poisson process (NHPP) node distribution, more general channel fading model (Nakagami) with path loss, and noise, for the study of QoS and capacity of VANET for BSM based safety applications in both 1-D highway and 2-D intersection road. The proposed model derives QoS and capacity of VANET BSM broadcast through evaluation of SINR distribution using probability theory and ordered statistics, which has much lower computational complexity compared with the unordered statistic model. The proposed model is validated by NS2 simulation and extended to the derivation of other QoS metrics such as packet reception probability, packet reception ratio, and broadcast link capacity, etc. The performance comparisons between 1-D and 2-D are implemented, and the QoS sensitivity analyses regarding the extension to multi-intersection as well as enlarging interference range are discussed.