Moments of first passage times in general birth-death processes. (English) Zbl 1158.60372
Summary: We consider ordinary and conditional first passage times in a general birth-death process. Under existence conditions, we derive closed-form expressions for the \(k\)th order moment of the defined random variables, \(k \geq 1\). We also give an explicit condition for a birth-death process to be ergodic degree 3. Based on the obtained results, we analyze some applications for Markovian queueing systems. In particular, we compute for some non-standard Markovian queues, the moments of the busy period duration, the busy cycle duration, and the state-dependent waiting time in queue.
MSC:
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
Keywords:
birth-death processes; first passage times; conditional first passage times; busy period; transient analysisReferences:
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