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A probabilistic method is presented to analyze the temperature and the maximum frequency for multicore processors based on consideration of workload variation, in this paper. Firstly, at the microarchitecture level, dynamic powers are modeled as the linear function of IPCs (instructions per cycle), and leakage powers are approximated as the linear function of temperature. Secondly, the microarchitecture-level hotspot temperatures of both active cores and inactive cores are derived as the linear functions of IPCs. The normal probabilistic distribution of hotspot temperatures is derived based on the assumption that IPCs of all cores follow the same normal distribution. Thirdly and lastly, the probabilistic distribution of the set of discrete frequencies is determined. It can be seen from the experimental results that hotspot temperatures of multicore processors are not deterministic and have significant variations, and the number of active cores and running frequency simultaneously determine the probabilistic distribution of hotspot temperatures. The number of active cores not only results in different probabilistic distribution of frequencies, but also leads to different probabilities for triggering DFS (dynamic frequency scaling).

Probabilistic Analysis of Steady-State Temperature and Maximum Frequency of Multicore Processors considering Workload Variation