This paper deals with a wide class of point processes which are subsumed under the name of $z$-processes. These processes are generalizations, in the sense that the initial distribution of the vehicles are not necessarily stationary Poisson, of point processes occurring in a traffic model of Renyi (1964). Using the Laplace functional, we derive the distributions of various $z$-processes when the initial process is stationary Poisson and prove a weak convergence result to the doubly stochastic Poisson process when the initial process is not necessarily Poisson distributed.
"Laplace Functional Approach to Point Processes Occurring in a Traffic Model." Ann. Probab. 9 (6) 1034 - 1040, December, 1981. https://doi.org/10.1214/aop/1176994274