Moments of first passage times in general birth–death processes

Oualid Jouini (1) , Yves Dallery (1)

1 LGI - Laboratoire Génie Industriel - EA 2606

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. Mathematics Subject Classification (2000) 68M20 · 60J80 Keywords Birth–death processes · First passage times · Conditional first passage times · Busy period · Transient analysis

Domaines: Autre

Oualid Jouini, Yves Dallery. Moments of first passage times in general birth–death processes. Mathematical Methods of Operations Research, 2008, 68, pp.49-76. ⟨10.1007/s00186-007-0174-9⟩. ⟨hal-01264961⟩