In this paper we investigate downlink performance in a non-orthogonal multiple access (NOMA) based vehicular communication network. In contrast to the previous works wherein the vehicles are simply assumed to be located anywhere in the coverage area, we consider practical cases where vehicles are located on a system of roads. We then adopt a system model based on Poisson Line Cox Point (PLC) processes, where the road system is represented through a Poisson Line (PL) Process. Vehicles ordered according to their distances to their corresponding roadside units (RSUs) are then served by using power domain NOMA. Adopting analytical tools from the stochastic geometry, we then analyse the outage performance of the system. Numerical results corroborate our analysis and demonstrate how the system settings influence the considered NOMA based V2X network. Index Terms-Poisson line Cox point (PLC) process , vehicular communications, non-orthogonal multiple access (NOMA) I. INTRODUCTION T He proliferation of intelligent transport systems (ITSs) encourages research on design and performance evaluation of vehicle-to-everything (V2X) communications both in academia and industry [1]. According to [2], V2X communications can be implemented either as a sidelink for direct communications over the PC5 interface, such as vehicle-tovehicle (V2V), vehicle-to-pedestrian (V2P) and vehicle-toinfrastructure (V2I), or as a traditional cellular link over the Uu interface, such as vehicle-to-network (V2N). It is worth pointing out that this paper will only focus on a downlink V2N scenario, where each roadside unit (RSU) needs to transmit different messages to different vehicle users. Existing V2X communications are based on orthogonal multiple access (OMA), where one channel resource block can only be occupied by one user. However, due to the ever increasing number of vehicular users and the scarce bandwidth available for vehicular communications, a dilemma may occur when the number of users is much larger than the number of available resource blocks. As a result, some users have to wait for a period of time before getting service. In this case, the