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We consider large scale Peer-to-Peer Sensor Networks, which try to calculate and distribute the mean value of all sensor inputs. For this we design, simulate and evaluate distributed approximation algorithms which reduce the number of messages. The main difference of these algorithms is the underlying communication protocol which all use the random call model, where in discrete round model each node can call a random sensor node with uniform probability.The amount of data exchanged between sensor nodes and used in the calculation process affects the accuracy of the aggregation results leading to a trade-off situation. The key idea of our algorithms is to limit the sample size using the Finite Population Correction (FPC) method and collect the data using a distribution aggregation using Push-Pull Sampling, Pull Sampling, and Push Sampling communication protocols. It turns out that all methods show exponential improvement of Mean Squared Error (MSE) with the number of messages and rounds.
The interaction between agents in multiagent-based control systems requires peer to peer communication between agents avoiding central control. The sensor nodes represent agents and produce measurement data every time step. The nodes exchange time series data by using the peer to peer network in order to calculate an aggregation function for solving a problem cooperatively. We investigate the aggregation process of averaging data for time series data of nodes in a peer to peer network by using the grouping algorithm of Cichon et al. 2018. Nodes communicate whether data is new and map data values according to their sizes into a histogram. This map message consists of the subintervals and vectors for estimating the node joining and leaving the subinterval. At each time step, the nodes communicate with each other in synchronous rounds to exchange map messages until the network converges to a common map message. The node calculates the average value of time series data produced by all nodes in the network by using the histogram algorithm. The relative error for comparing the output of averaging time series data, and the ground truth of the average value in the network will decrease as the size of the network increases. We perform simulations which show that the approximate histograms method provides a reasonable approximation of time series data.
We consider the local group of agents for exchanging the time-series data value and computing the approximation of the mean value of all agents. An agent represented by a node knows all local neighbor nodes in the same group. The node has the contact information of other nodes in other groups. The nodes interact with each other in synchronous rounds to exchange the updated time-series data value using the random call communication model. The amount of data exchanged between agent-based sensors in the local group network affects the accuracy of the aggregation function results. At each time step, the agent-based sensor can update the input data value and send the updated data value to the group head node. The group head node sends the updated data value to all group members in the same group. Grouping nodes in peer-to-peer networks show an improvement in Mean Squared Error (MSE).