Transferability of M/M/k asymptotic results to parallelizable-job scheduling

Determine which asymptotic properties and performance results established for the M/M/k queue (e.g., queueing probabilities and delays across scaling regimes) continue to hold when scheduling multiple classes of malleable parallelizable jobs across k identical servers.

Background

The paper reviews well-known asymptotic behaviors for M/M/k systems across scaling regimes (mean-field, Halfin-Whitt, NDS, Super-NDS) and uses them as reference points.

The authors explicitly state uncertainty about the extent to which these results carry over to systems with parallelizable (malleable) jobs, motivating their subsequent analysis and results in distinct scaling regimes.