The characterization of the stationary distribution of the supplemented Self-Clocking Jump Process

The paper introduces a Self-Clocking Jump Process (SCJP), which is a natural generalization of a generalized semi-Markov process and applies to a large class of queueing models. As a stochastic process, a SCJP is a special case of a process with an embedded marked point process. The paper characterizes the stationary distribution of the supplemented SCJP and discusses some properties of it. It also gives a mathematical base to the usual approach of Kolmogorov differential equations. An operator theoretic argument is used, but most of the proofs are elementary.