Hierarchical Dynamics, Interarrival Times, and Performance

We report on a model of the distribution of job submission interarrival times in supercomputers. Interarrival times are modeled as a consequence of a complicated set of decisions between users, the queuing algorithm, and other policies. This cascading hierarchy of decision-making processes leads to a particular kind of heavy-tailed distribution. Specifically, hierarchically constrained systems suggest that fatter tails are due to more levels coming into play in the overall decision-making process. The key contribution of this paper is that heavier tials resulting from more complex decision-making processes, that is more hierarchical levels, will lead to overall worse performance, even when the average interarrival time is the same. Finally, we offer some suggestions for how to overcome these issues and the tradeoffs involved.