Throughput of multi-core processors under thermal constraints

We analyze the effect of thermal constraints on the performance and power of multi-core processors. We propose system-level power and thermal models, and derive expressions for (a) the maximum number of cores that can be activated, with and without throttling, (b) the speedup (multi-core over single core), and the total power consumption, both as functions of the number of active cores. These expressions involve parameters like power per core, thermal resistance of hottest die block and package, and leakage dependence on temperature. We also computed the above metrics (a) and (b) numerically by solving the detailed Hotspot circuit of an multicore processor driven by a block-level exponential temperature-dependent leakage model. When compared to these numerical results, we found that the above expressions for (a) were at most 8% underpredicted, while those for (b) were accurately predicted. The proposed analytical approach is the first of its kind to relate metrics of interest in multi-core processors to high-level design parameters. Compared to numerical approaches, it provides much faster computation time, and valuable insight for processor designers.