On transience of M/G/∞ queues

2024/06/05 by Popov, Serguei
#60G55 #60K25 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2406.03517

Abstract

We consider an M/G/∞ queue with infinite expected service time. We then provide the transience/recurrence classification of the states (the system is said to be at state n if there are n customers being served), observing also that here (unlike e.g. irreducible Markov chains) it is possible for recurrent and transient states to coexist. We also prove a lower bound on the growth speed in the transient case.

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