**5.2. Models**

This work adopts a hierarchical methodology for conducting dependability evaluation of data center architectures. In general, the methodology aims at grouping related components in order to generate subsystem models, which are adopted to mitigate the complexity of the final system model evaluation. Thus, the final model is an approximation, but rather simpler, of a more intricate system model. One should bear in mind that the detailed model could be adopted instead, but at the expenses of complexity.

Following the adopted methodology, systems with no failure dependencies between components have been evaluated through RBD models. For instance, Figure 20 depicts the RBD model that represents the architecture A1.

332 Petri Nets – Manufacturing and Computer Science A Petri Net-Based Approach to the Quantification of Data Center Dependability <sup>21</sup> A Petri Net-Based Approach to the Quanti cation of Data Center Dependability 333

**Figure 21.** SPN of Architectures A2.

20 Petri Nets

This work adopts a hierarchical methodology for conducting dependability evaluation of data center architectures. In general, the methodology aims at grouping related components in order to generate subsystem models, which are adopted to mitigate the complexity of the final system model evaluation. Thus, the final model is an approximation, but rather simpler, of a more intricate system model. One should bear in mind that the detailed model could be

Following the adopted methodology, systems with no failure dependencies between components have been evaluated through RBD models. For instance, Figure 20 depicts the

**Figure 19.** Data Center Power Architectures.

**Figure 20.** RBD of Architecture A1.

adopted instead, but at the expenses of complexity.

RBD model that represents the architecture A1.

**5.2. Models**

**Figure 22.** RBD of Architectures A2.

In architecture A2, the generator is only activated when both AC sources are not available. Therefore, a model that deal with dependencies must be adopted. Figure 21 shows the SPN model considering cold standby redundance to represent the subsystem composed of generator and two AC sources. Besides, we assume that UPS' batteries support the system during the generator activation. The reliability or availability is computed by the probability *P*{#*ACSource*1\_*ON* = OR #*ACSource*2\_*ON* = 1 OR #*Generator*\_*ON* = 1}.

The other components of the architecture A2 are modeled using RBD as shown in Figure 22. Once obtained the results of both models (RBD and the SPN model with dependencies), a RBD model with two blocks (considering the results of those models) in a serial arrangement is created. The RBD evaluation provides the dependability results of the architecture A2 system.

The adopted MTTF and MTTR values for the power devices were obtained from [21] [29] [19] and are shown in Table 3.

#### **5.3. Results**

Figure 23 depicts a graphical comparison between the reliability results (in number of 9's) of those two data center power architectures. The respective number of nines (-*log*[1 - A/100]) and the period of 8760 hours (1 year) are adopted. As the reader should note, the reliability of both architectures decreases when the time increases. Besides, it is also possible to notice that


Dietmar Tutsch

**7. References**

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**Table 3.** MTTF and MTTR values for power devices.

the generator has increased the reliability of the architecture A2. Considering the availability results, similar behavior happened. The availability has increased from 5.47 to 7.96 (in number of 9's).

**Figure 23.** Reliability Comparison of Architectures A1 and A2.

## **6. Conclusion**

This work considers the advantages of both Stochastic Petri Nets (SPN) and Reliability Block Diagrams (RBD) formalisms to analyze data center infrastructures. Such approach is supported by an integrated environment, ASTRO, which allows data center designers to estimate the dependability metrics before implementing the architectures. The methodology proposes that the system should be evaluated piecewisely to allow the composition of simpler models representing a data center infrastructure appropriately. Moreover, experiments demonstrate the feasibility of the environment, in which different architectures for a data center power infrastructures have been adopted.
