The minimal quasi-stationary distribution of the absorbed M/M/∞ queue
Résumé
We give in this paper two characterizations of the minimal exponential rate of survival θ * of the M/M/∞ queue. The first one is a derivation of a known result on the duration of excursions of this process. The second one was conjectured by Martínez and Ycart [8] and is proved using complex analysis by establishing a connection with the first characterization in terms of the incomplete gamma function.
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