Parallel Server Systems with Cancel-on-Completion Redundancy

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.