On transience of $M/G/\infty$ queues

Serguei Popov

On transience of $M/G/\infty$ queues

Probability 2024-07-12 v2

Authors: Serguei Popov

Abstract

We consider an $M/G/\infty$ 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.

Keywords

M/G/∞ queue transience recurrence infinite service time Markov chain state classification growth speed lower bound

Cite

@article{arxiv.2406.03517,
  title  = {On transience of $M/G/\infty$ queues},
  author = {Serguei Popov},
  journal= {arXiv preprint arXiv:2406.03517},
  year   = {2024}
}

Comments

6 pages, 1 figure; cited a recent paper that provides the recurrence/transience classifiction of the state 0, and also added a bound on the growth speed in the transient case

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