# Communication Performance Assessment for Advanced Metering Infrastructure
## 2 Design of an Effective CPI  
Many communication quality parameters such as the link quality indicator, received signal strength indicator, signal-to-noise ratio, reading error rate etc. are commonly used to define the performance of a communication network. However, the response time of a smart meter is an essential factor to determine the response speed of the smart meter in the communication network. Besides, the reading success rate of a smart meter, used to make sure whether the reading process was successful, is also an important factor for observing the stability of a communication network. The response time and reading success rate are easily acquired from a smart meter and therefore are adopted in this paper to assess the communication performance. The CPI adopting those factors for a single smart meter is derived first, the CPIs for DCUs and AMI are then developed. Most smart meters in an AMI provide meter data every 15 min; therefore, the total reading number is 96 in a day. If the meter data are completely received by the meter data management system, then it will be counted as a successful reading. The reading success rate of a smart meter in a period of one day can be expressed as  
\[RSR(\%)=\frac{NRS}{96}\times 100\% \tag{1}\]  
where \(NRS\) is the number of reading successes. \(RSR(\%)\) is the reading success rate. If the number of reading successes is 95, the reading success rate is 98.96%. The average response time of a day can also be calculated by  
\[RT(ms)=\frac{\sum\limits_{i\in\Phi_{NRS}}RT(i)}{NRS}\times 100\% \tag{2}\]  
where \(RT(ms)\) is the average response time. \(RT(i)\) is the response time for the \(i^{th}\) reading success. \(\Phi_{NRS}\) is the set of reading success number in a day. Since at least daily response time and reading success rate acquired from a smart meter are adopted to assess the CPI and the absolute correlation between these two factors is difficult to undoubtedly determine, fuzzy logic is employed in this paper to integrate these two factors into the proposed CPI calculation. Fuzzy logic has been widely used in solving many industrial control and quality problems [27; 28; 29; 30]. Figure 1 shows the procedures of fuzzy logic realized for the proposed CPI. The reading success rate and response time of a smart meter are used as input variables and passed through the fuzzifier. The fuzzy rules and inference engine act like an expert to adjust the weightings between the input variables and then the defuzzifier scores the CPI for the meter. A triangular membership function with five levels, Negative Big (NB), Negative Small (NS), Zero (ZE), Positive Small (PS) and Positive Big (PB), is used in this paper. Figure 2 illustrates the membership functions used to fuzzify and defuzzify the input and the output variables. \(\mu_{RSR}\), \(\mu_{RT}\) and \(\mu_{CPI}\) in Figure 2 indicate the membership functions for reading success rate, response time and CPI of a meter, respectively. As an example, the membership functions of reading success rate and response time are in the range of 80% to 99% and in the range of 200 ms to 400 ms, respectively. Note that the ranges can be adjusted according to the actual communication network used. Variable membership functions including Gaussian, trapezoidal, polynomial etc. can also be adopted in calculating CPI without modifying the proposed procedures. Table 1 illustrates the fuzzy rules for the proposed CPI. The basic concept of fuzzy rules is that a higher reading success rate and lower response time should have a higher CPI. A minimum inference engine and center of gravity defuzzifier are used in this paper. Figure 3 shows the concept of a minimum inference engine. An example of this is if Rule 6 is activated and the values of \(\mu_{RSR}\) and \(\mu_{RT}\) are NS of 0.7 and NB of 0.3, respectively. The minimum inference engine picks the smaller of the two; therefore, the result of Rule 6 will be NS of 0.3.