Stochastic heat conduction differential equation in spite of its complexity allows stationary solutions valid over a certain range of variables characterizing heat flow in multi-processor cores. Heat conduction equation is recast to account for anisotropy of a many core multi-processor in which heat generated at various locations depends on whether it is a cache, processor, bus controller, or memory controller: within the core generated heat depends on the hit rate, processor utilization, cache organization, and the technology used. Thermal conductivity of and heat generation in the core are treated as stochastic variables and influence of workloads, hitherto unrecognized, is explicitly accounted for in determining temperature distribution and its variation with processor clock frequency. Relationships derived from first principles indicate that rise in temperature with processor frequency for OLTP workload is not as catastrophic as predicted by some Industry brochures! A general framework for heat conduction in an orthotropic rectangular slab (representing a many core processor) with stochastic values of thermal conductivity and heat generation is developed; the theoretical trend is validated using published data for OLTP workloads to obtain temperature at the core surface as a function of clock frequency for the deterministic case. Transaction Processing Councils (TPC) openly available data from controlled, closely audited experiments for TPCC workloads during the period 2000–2011 were analyzed to determine the relation between throughput, clock frequency, main memory size, number of cores, and power consumed. Operating systems, compilers, linkers, processor architecture, cache, main memory, and storage sizes have changed drastically during this ten year period, not to mention hyper-threading was unknown in 2000! This analysis yields the following equations for throughput and power consumed, which for a specific case of 64 processors with a main memory of 32 GB and a million users, becomes W = 1075f0.22. For the isotropic case the temperature difference at the surface may be expressed for the case under study as ΔT = 71.1f0.22. This demonstrates that chip temperature for OLTP workloads does not increase to catastrophic values with increase in frequency. This behavior varies for other types of workloads.
A thermal resilient integration of many-core microprocessors and main memory by 2.5D TSI I/Os