Generalization to non-exponential job size distributions

Ascertain how the asymptotic optimality results for scheduling multiple classes of parallelizable jobs extend when job sizes follow general (non-exponential) distributions, beyond the exponential case analyzed in the paper.

Background

Throughout most analyses, job sizes are assumed exponential by class. The authors discuss challenges and partial extensions when job sizes are generally distributed, noting that analysis techniques become more complex.

They subsequently show that Gittins-index-based prioritization remains optimal in conventional heavy traffic for parallelizable jobs, but broader generalization across other regimes remains uncertain.