  Modern multiprocessor system-on-chips (SoCs) integrate multiple heterogeneous
cores to achieve high energy efficiency. The power consumption of each core
contributes to an increase in the temperature across the chip floorplan. In
turn, higher temperature increases the leakage power exponentially, and leads
to a positive feedback with nonlinear dynamics. This paper presents a
power-temperature stability and safety analysis technique for multiprocessor
systems. This analysis reveals the conditions under which the power-temperature
trajectory converges to a stable fixed point. We also present a simple formula
to compute the stable fixed point and maximum thermally-safe power consumption
at runtime. Hardware measurements on a state-of-the-art mobile processor show
that our analytical formulation can predict the stable fixed point with an
average error of 2.6%. Hence, our approach can be used at runtime to ensure
thermally safe operation and guard against thermal threats.
