## Measurement and Management Technologies for Data Centers - Statistical Modeling

**A Statistical Model for Data-Center Temperatures**

In the statistical work we use knowledge based models and trends and combine them with kriging techniques. For example, a comprehensive knowledge base of thermal profiles has been generated from MMT data of over 80 DCs showing s-shaped, vertical temperature profiles across the server inlets of a rack. Research and statistical analysis has shown that the form of s-shape is governed by physical parameter such as air flow supply and demand, discharge temperatures of the neighboring ACUs, the relative location with respect to ACUs and other servers (location with an aisle etc). The dynamic models will be further furbished using statistical forecasting techniques

Figure 1: a typical S-curve pattern for the vertical temperature profiles for ten different air conditioner settings. Ten solid curves are the MMT observations at ten settings and the dashed curves are the statistical model estimations given air flow inputs and temperatures at plenum and ceiling levels.

Figure 2: images of temperature fitting for different heights under certain air conditioner setting. The top panel is the MMT temperature measurements compared to the fitted temperature values at the bottom panel.

**A Statistical Approach to Thermal Zone Mapping**

A statistical method, which leverages temperature measurements from a real-time sensing system, is developed for assigning dynamically thermal zones. Such thermal zones are generally defined as the region of influence of a particular cooling unit or cooling "source" (such as an air condition unit (ACU)) and can provide valuable decision support for optimizing cooling. In order to characterize ACU thermal zones, a statistical method is investigated to model the correlations between temperatures observed from sensors located at the discharge of an ACU and the other sensors located in the room. Outputs from the statistical solution can be used to optimize the placement of equipment in a data center, investigate failure scenarios, and make sure that a proper cooling solution has been achieved.

Figure 3: an example of thermal zones characterized by the correlation between each of the four ACU discharge temperatures and the temperatures in the room. It shows that ACU#1 has the largest impact in its closer vicinity and ACU#1 and ACU#4 have significant larger thermal zones than ACU#2 and ACU#3.

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