Parallel server systems with cancel-on-completion redundancy
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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 complete their service, at which point the service of all remaining d_j-k_j components is canceled. The system is in general non-work-conserving – the average amount of new workload added to the system by an arriving class j job depends on the system state. This poses the main challenge for the system analysis. The results of this paper concern both the system with fixed number of servers n and the mean-field asymptotic regime when n→∞ while each job class arrival rate per server remains constant. The main question we address for the asymptotic regime is whether the steady-state asymptotic independence of server workloads holds. We prove that this property does hold under certain conditions, including the important special case when job components of each class j are i.i.d. with an increasing-hazard-rate distribution.
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