Output process from a continuous token ring local area network

A token-ring local area network (LAN) with an infinite number of nodes uniformly distributed around the ring is considered. A token that circulates around the ring at a constant speed stops to serve fixed length packets that are generated by the nodes. It is assumed that the cumulative arrival process of packets constitutes a two-dimensional Poisson process. Given a fixed point on the ring, called the origin, the first-order statistics of the interarrival times of packets at the origin are obtained in the form of their Laplace-Stieltjes transform