### Abstract

A parallel server system with n identical servers is considered. The service time distribution has a finite mean 1/μ, but otherwise is arbitrary. Arriving customers are to be routed to one of the servers immediately upon arrival. Join-Idle-Queue routing algorithm is studied, under which an arriving customer is sent to an idle server, if such is available, and to a randomly uniformly chosen server, otherwise. We consider the asymptotic regime where n → ∞ and the customer input flow rate is λn. Under the condition λ/μ < 1/2, we prove that, as n → ∞, the sequence of (appropriately scaled) stationary distributions concentrates at the natural equilibrium point, with the fraction of occupied servers being constant equal λ/μ. In particular, this implies that the steady-state probability of an arriving customer having to wait for service vanishes.

Original language | English |
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Pages (from-to) | 45-47 |

Number of pages | 3 |

Journal | Performance Evaluation Review |

Volume | 45 |

Issue number | 2 |

DOIs | |

Publication status | Published - 11 Oct 2017 |

### ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications

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## Cite this

*Performance Evaluation Review*,

*45*(2), 45-47. https://doi.org/10.1145/3152042.3152058