### Abstract

Power-of-d-choices is a popular load balancing algorithm for many-server systems such as large-scale data centers. For each incoming job, the algorithm probes d servers, chosen uniformly at random from a total of N servers, and routes the job to the least loaded one. It is well known that power-of-d-choices reduces queueing delays by orders of magnitude compared to the policy that routes each incoming job to a randomly selected server. The question to be addressed in this paper is how large d needs to be so that power-of-d-choices achieves asymptotic zero delay like the join-the-shortest-queue (JSQ) algorithm, which is a special case of power-of-d-choices with d=N. We are interested in the heavy-traffic regime where the load of the system, denoted by lambda, approaches to one as N increases, and assume lambda=1-gamma N-{-alpha} for 0 < gamma < 1 and 0leqalpha < 1/6. This paper establishes that when d=omega-left(frac{1}{1-lambda}right), the probability that an incoming job is routed to a busy server is asymptotically zero, i.e. a job experiences zero queueing delay with probability one asymptotically; and when d=Oleft(frac{1}{1-lambda}right)' the probability that a job is routed to a busy server is lower bounded by a positive constant independent of N. Therefore, our results show that d=omega(frac{1}{1-lambda}) is sufficient and almost necessary for achieving zero delay with the power-of-d-choices load balancing policy.

Original language | English (US) |
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Title of host publication | INFOCOM 2018 - IEEE Conference on Computer Communications |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 297-305 |

Number of pages | 9 |

Volume | 2018-April |

ISBN (Electronic) | 9781538641286 |

DOIs | |

State | Published - Oct 8 2018 |

Event | 2018 IEEE Conference on Computer Communications, INFOCOM 2018 - Honolulu, United States Duration: Apr 15 2018 → Apr 19 2018 |

### Other

Other | 2018 IEEE Conference on Computer Communications, INFOCOM 2018 |
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Country | United States |

City | Honolulu |

Period | 4/15/18 → 4/19/18 |

### ASJC Scopus subject areas

- Computer Science(all)
- Electrical and Electronic Engineering

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## Cite this

*INFOCOM 2018 - IEEE Conference on Computer Communications*(Vol. 2018-April, pp. 297-305). [8485827] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/INFOCOM.2018.8485827