Abstract
In this paper, we study the point process of state transitions in a regular Markov chain. Under a weaker condition, we prove that the point process is a 1-memory self-exciting point process and again obtain four useful formulas of the transition frequency, the absorbing distribution, the renewal distribution and the entering probability. As an application, using these formulas we derive the LS transform of the busy period for theM/M/∞ queue.
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