Success Probability Analysis of C-V2X Communications on Irregular Manhattan Grids

To overcome the shortcomings of Dedicated Short Range Communications (DSRC), cellular vehicle-to-everything (C-V2X) communications have been proposed recently, which has a variety of advantages over traditional DSRC, including longer communication range, broader coverage, greater reliability, and smooth evolution path towards 5G. In this paper, we consider an LTE-based C-V2X communications network in irregular Manhattan grids. We model the macrobase stations (MBSs) as a 2D Poisson point process (PPP) and model the roads as a Manhattan Poisson line process (MPLP), with the roadside units (RSUs) modeled as a 1D PPP on each road. As an enhancement architecture to DSRC, C-V2X communications include vehicle-to-vehicle (V2V) communication, vehicle-to-infrastructure (V2I) communication, vehicle-to-pedestrian (V2P) communication, and vehicle-to-network (V2N) communication. Since the spectrum for PC5 interface in 5.9 GHz is quite limited, cellular networks could share some channels to V2I links to improve spectral efficiency. Thus, according to Maximum Power-based Scheme, we adopt the stochastic geometry approach to compute the signal-to-interference ratio- (SIR-) based success probability of a typical vehicle that connects to an RSU or an MBS and the area spectral efficiency of the whole network over shared V2I and V2N downlink channels. In addition, we study the asymptotic characteristics of success probability and provide some design insights according to the impact of several key parameters on success probability.

Return to the Poissonian city

Consider the following random spatial network: in a large disk, construct a network using a stationary and isotropic Poisson line process of unit intensity. Connect pairs of points using the network, with initial/final segments of the connecting path formed by travelling off the network in the opposite direction to that of the destination/source. Suppose further that connections are established using ‘near geodesics’, constructed between pairs of points using the perimeter of the cell containing these two points and formed using only the Poisson lines not separating them. If each pair of points generates an infinitesimal amount of traffic divided equally between the two connecting near geodesics, and if the Poisson line pattern is conditioned to contain a line through the centre, then what can be said about the total flow through the centre? In Kendall (2011) it was shown that a scaled version of this flow has asymptotic distribution given by the 4-volume of a region in 4-space, constructed using an improper anisotropic Poisson line process in an infinite planar strip. Here we construct a more amenable representation in terms of two ‘seminal curves’ defined by the improper Poisson line process, and establish results which produce a framework for effective simulation from this distribution up to anL1error which tends to 0 with increasing computational effort.

Return to the Poissonian city

Consider the following random spatial network: in a large disk, construct a network using a stationary and isotropic Poisson line process of unit intensity. Connect pairs of points using the network, with initial/final segments of the connecting path formed by travelling off the network in the opposite direction to that of the destination/source. Suppose further that connections are established using ‘near geodesics’, constructed between pairs of points using the perimeter of the cell containing these two points and formed using only the Poisson lines not separating them. If each pair of points generates an infinitesimal amount of traffic divided equally between the two connecting near geodesics, and if the Poisson line pattern is conditioned to contain a line through the centre, then what can be said about the total flow through the centre? In Kendall (2011) it was shown that a scaled version of this flow has asymptotic distribution given by the 4-volume of a region in 4-space, constructed using an improper anisotropic Poisson line process in an infinite planar strip. Here we construct a more amenable representation in terms of two ‘seminal curves’ defined by the improper Poisson line process, and establish results which produce a framework for effective simulation from this distribution up to an L1 error which tends to 0 with increasing computational effort.