Moments of first passage times in general birth–death processes

Oualid Jouini () and Yves Dallery ()

Mathematical Methods of Operations Research, 2008, vol. 68, issue 1, 49-76

Abstract: We consider ordinary and conditional first passage times in a general birth–death process. Under existence conditions, we derive closed-form expressions for the kth order moment of the defined random variables, k ≥ 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. Copyright Springer-Verlag 2008

Keywords: 68M20; 60J80; Birth–death processes; First passage times; Conditional first passage times; Busy period; Transient analysis (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s00186-007-0174-9

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