## Abstract

We consider a parallel server system with so-called cancel-on-completion redundancy. There are n servers and multiple job classes j. An arriving class j job consists of d_{j} components placed on a randomly selected subset of servers; the job service is complete as soon as k_{j} components out of d_{j} (with k_{j} ≤ d_{j}) complete their service, at which point the unfinished service of all remaining d_{j} − k_{j} components is canceled. The system is in general non-work-conserving in the sense that the average amount of new workload added to the system by an arriving class j job is not defined a priori—it depends on the system state at the time of arrival. This poses the main challenge for the system analysis. For the system with a fixed number of servers n, our main results include: the stability properties; the property that the stationary distributions of the relative server workloads remain tight uni-formly in the system load. We also consider the mean-field asymptotic regime when n → ∞ while each job class arrival rate per server remains constant. The main question we address here is: under which conditions the steady-state asymptotic independence (SSAI) of server workloads holds and, in particular, when the SSAI for the full range of loads (SSAI-FRL) holds. (Informally, SSAI-FRL means that SSAI holds for any system load less than one.) We obtain sufficient conditions for SSAI and SSAI-FRL. In particular, we prove that SSAI-FRL holds in the important special case when job components of each class j are independent and identically distributed with an increasing-hazard-rate distribution.

Original language | English (US) |
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Pages (from-to) | 340-372 |

Number of pages | 33 |

Journal | Stochastic Systems |

Volume | 12 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2022 |

## Keywords

- asymptotic independence
- cancel-on-completion
- load distribution and balancing
- mean-field limit
- multicomponent jobs
- parallel service systems
- particle systems
- redundancy
- replication
- steady state

## ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Statistics, Probability and Uncertainty
- Management Science and Operations Research