Mathematical Modeling and Control of Multifractal Workloads for Data-Center-on-a-Chip Optimization

Building autonomous data-centers-on-chip (DCoC) for exascale computing requires mathematical frameworks that account and exploit the non-stationary and multi-fractal characteristics of computation and communication workloads. Towards this end, relying on DCoC (Intel's SCC) measurements, we propose a complex dynamical modeling approach that captures the observed multi-fractal characteristics of inter-event times between successive workload changes and the magnitude of the increments in DCoC workloads. Our novel mathematical framework allows for the analysis of higher order moments and enables the formulation of more accurate model predictive control strategies for multi-fractal dynamics. We investigate the impact of the multi-fractal spectrum richness on the performance of the control algorithm. Our mathematical formalism can further be used to model, analyze and solve DCoC design problems (e.g., topology reconfiguration, buffer sizing, mapping, scheduling, resource management, congestion control).