Random ID Model for a Computer Network

For peer-to-peer networks on the Internet, there are many searching algorithms. We introduce a random model for one of these types of algorithms and study how many steps it takes to search for a target node by using the searching algorithm. The nodes are labeled with random IDs, which we call the Random ID Model, was only briefly mentioned. Our analysis shows that with high probability it takes about clogn steps to locate any node, where n is the total number of nodes in the network and c is a constant that does not depend on n