Theoretical Foundations of Multicore Systems Design: A Dynamical Systems Perspective

The proliferation of complex phenomena and the tightening competition for limited resources are two fundamental challenges for the modeling, analysis, and optimization of dynamical processes taking place in networked environments/architectures. Modes of collective and competitive behavior can be noticed across a wide array of social, biological, and technological contexts. From urban crowds to bacterial colonies, from brain neurons to human cells and even electron-hole interactions in semiconductors, dynamical phase transitions influence the macroscopic behavior of complex networks. To address these challenges, we focus on understanding, modeling, analyzing, and optimizing large-scale interconnected systems, such as future thousand-core Networks-on-Chip (NoC), biologically propelled Cyber-Physical Systems (CPS) consisting of micro-robotic swarms, or biological networks of stem cells, for performance, power, or fault-tolerance.

Enabled by recent advances in CMOS technology, the integration of tens and soon thousands of heterogeneous processing cores communicating via the NoC paradigm brings into the discussion the traffic modeling problem. Traffic modeling is of crucial importance for both static and dynamic NoC design and optimization problems such as topology selection and resource allocation, mapping, scheduling, routing or power management. The approaches proposed so far exhibit major limitations. For example, many of the queuing theory based modeling and optimization approaches proposed for NoC architectures ignore the traffic characteristics (e.g., non-stationarity, fractality). In many situations, these models lead to buffer overflow or deadline missing situations and so poor (non-optimal) performance levels.

In this thesis, we show how this state of affairs can be changed by embracing a statistical physics inspired approach in order to insure accurate network traffc characterization. By using an analogy between a thermodynamic gas and a networked multicore architecture, our model captures the relevant traffc characteristics (e.g., fractality, non-stationarity) via a dynamical master equation. Our approach not only leads to a more accurate estimation of performance metrics over Markovian models, but also helps at defining new state space model for dynamical systems that can be used for online optimization. Besides being an important contribution by itself, this radically new approach enhances the efficiency of resource allocation in nanoscale networks and overcomes the prior limitations of performance analysis approaches based on queuing models.

Building on statistical physics grounds, we model and analyze a biologically inspired communication protocol, namely the stochastic communication protocol. Under the stochastic communication protocol aiming at mitigating the nanoscale challenges (e.g., particle hits, cross-talk) in multi-core platforms, each node in the network disseminates packets multiple times via multiple paths. Hence, fault-tolerance is enforced at system-level by exploiting path diversity. To characterize such a dynamic behavior, we concentrate on estimating various performance metrics via a master equation approach capturing communication events such as packet duplication, packet transmission, and packet corruption. The proposed statistical physics model allows us to identify the benefits of this protocol for future communication fabrics.

To address the power consumption issues in large scale on-chip networks, we formulate the power and peak temperature management of heterogeneous NoC platforms as constrained finite horizon fractal optimal control problem. We show not only that fractal characteristics can be accounted for via fractional calculus state space models, but also that the online controller can be reduced to a linear program and efficiently computed via parallel algorithms. Our approach not only leads to significant power savings, but it also opens new avenues for dynamic optimization of large-scale systems exhibiting fractal dynamics.

Based on the proposed framework for modeling, analysis, and optimization of dynamical processes taking place on networked architectures, we formulate general guidelines for CPS design. As a concrete CPS example, we consider the design problem of the control algorithm of a pacemaker, which takes into account at run-time the fractal characteristics exhibited by heart rate variability.

In summary, this thesis offers a statistical physics view on using the network-paradigm in multicore and cyber-physical system design. The results and discussion presented herein can be further extended to other classes of systems and applications. One research direction is represented by modeling and optimization of bacteria propelled micro-robotic swarms. Another research direction concerns the modeling of human dynamic processes such as car traffic, which can enable road structure optimization. Moreover, by relying on this statistical physics inspired framework, we can define models for biological communication and heterogeneous population growth with applications in regenerative medicine.