Distributed Network Size Estimation Executed by Average Consensus Bounded by Stopping Criterion for Wireless Sensor Networks

Abstract

The exact information about the network size is crucial for the proper functioning of many distributed algorithms. In this paper, we analyze the average consensus algorithm for a distributed network size estimation bounded by the stopping criterion proposed for the wireless sensor networks. We analyze its four initial configurations over random geometric graphs of different connectivity under various parameters of the implemented stopping criterion. The performance is evaluated by the mean square error and the convergence rate expressed as the iteration number for the consensus. Finally, the results obtained under various conditions are compared to find the best performing configuration of both the average consensus algorithm and the implemented stopping criterion. Also, the results are compared to the distributed summing functionality.

Applicability of Generalized Metropolis-Hastings Algorithm to Estimating Aggregate Functions in Wireless Sensor Networks

“…For counter threshold = 100, accuracy = 10 −6 , and ensuring the highest performance, the convergence rate of GMH is greater than the convergence rate of the average consensus algorithm by 139.5 iterations in Scenario 2, by 87.3 iterations in Scenario 3, and by 52.5 iterations in Scenario 4. Also, like in the previous analysis, the value of the mixing parameter has only a marginal impact on the convergence rate in contrast to the average consensus algorithm examined in [8,28].…”

“…In this case, the values of MSE are from 3 only MSE for = 0 are provided -see Table 2 for the results obtained for the other values of the mixing parameter ), proving that multiplying the initial inner states with the graph order n ensures higher precision of the algorithm than multiplying the final estimates. As mentioned earlier, we analyze the average consensus algorithm for distributed summing and distributed graph order estimation in our previous work [8,28]. Compared to those results, it can be seen that GMH outperforms the average consensus algorithms for estimating both examined aggregate functions.…”

“…For counter threshold = 100, accuracy = 10 −6 , and ensuring the highest performance, GMH outperforms the average consensus algorithm by 12.78 dB in Scenario 2, by 77.31 dB in Scenario 3, and by 104.469 dB in Scenario 4. Moreover, an important fact identified in [8] is that the average consensus achieves a very low estimation precision for lower values of counter threshold and higher values of accuracy in the case of graph order estimation, making the algorithm unusable with these configurations of the stopping criterion. However, in this paper, we identify that this phenomenon is not visible in the case of GMH; therefore, this algorithm is much more appropriate for graph order estimation than the average consensus algorithm when the stopping criterion [27] is implemented.…”

“…Over the last years, WSNs have found the application in various areas such as industrial monitoring, health care, localization, security, structural monitoring, military monitoring, etc. [8].…”

“…Thus, the experimental section consists of four scenarios. Finally, GMH for distributed summing and distributed graph order estimation is compared to our previous work where the average consensus algorithm is analyzed [8,28].…”