Accurate Event Distribution Monitoring for Very Large Wireless Systems

In a network of large number of devices, we address the problem of estimation of the probability distribution of quantities measured by the set of nodes in a geographical area. Queries are sent to the nodes by the network with the reporting condition and reporting probability. Nodes that satisfy the reporting condition report the measurement with the specified probability. It is shown that the probability distribution of the measurement can be estimated accurately with bounded number of reports, by careful selection of reporting conditions and reporting probability. A general framework for designing the report rates is developed. Simple expressions for distance measures between the estimated and the true distribution is provided. Based on the concepts that are developed, we present a two-phase process and an iterative process for inferring the measurements' distribution in the cases of one time querying as well as periodic querying.