Large-scale parallel server system with multi-component jobs

Seva Shneer () and Alexander L. Stolyar ()
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Seva Shneer: Heriot-Watt University
Alexander L. Stolyar: University of Illinois at Urbana-Champaign

Queueing Systems: Theory and Applications, 2021, vol. 98, issue 1, No 3, 48 pages

Abstract: Abstract A broad class of parallel server systems is considered, for which we prove the steady-state asymptotic independence of server workloads, as the number of servers goes to infinity, while the system load remains sub-critical. Arriving jobs consist of multiple components. There are multiple job classes, and each class may be of one of two types, which determines the rule according to which the job components add workloads to the servers. The model is broad enough to include as special cases some popular queueing models with redundancy, such as cancel-on-start and cancel-on-completion redundancy. Our analysis uses mean-field process representation and the corresponding mean-field limits. In essence, our approach relies almost exclusively on three fundamental properties of the model: (a) monotonicity, (b) work conservation and (c) the property that, on average, “new arriving workload prefers to go to servers with lower workloads.”

Keywords: Large-scale service systems; Steady-state; Asymptotic independence; Multi-component jobs; Redundancy; Replication; Cancel on start; Cancel on completion; Load distribution and balancing; 90B15; 60K25 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11134-021-09686-y

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