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The minimal quasi-stationary distribution of the absorbed M/M/$\infty$ queue
2023-07-18 · via math.PR updates on arXiv.org

We give in this paper two characterizations of the minimal exponential rate of survival $θ$ * of the M/M/$\infty$ 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 Mart{í}nez 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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