Campbell’s formula and applications to queueing

Campbell’s formula for Palm probabilities is a basic tool for deriving properties of stationary queueing systems and stationary processes in general. This study reviews Campbell’s formula and gives new insights into its versatility by establishing several equivalent versions of it. A few of these are known (e.g., the exchange formula and H=λG). Also included are applications involving integrals with respect to random product-measures, waiting times in systems, rate conservation laws, sojourn times of processes, travel times in networks, ladder heights in risk processes and virtual delays in queueing systems.