The extended compound renewal process, a generalization of the concept of filtered Poisson process, is introduced. It is shown that its characteristic function is expressible as the solution of a second type Volterua integral equation is solved for some special cases. Moreover, the equation is used to find the first moment and a recursive relationship for the higher order raw moment of the process. Finally, several areas of applications to theGIx/G/∞queue are investigates including the size of the system, the queue output and the total backlog