Theoretical Analysis of Route Expected Transmission Count in Multi-Hop Wireless Networks

In multi-hop wireless networks, communication quality depends on the route from a source to a destination. In this paper, we consider a one-dimensional multi-hop wireless network where nodes are distributed randomly and theoretically analyze the relation between communication quality and routing policy using a measure called the Expected Transmission Count (ETX), which is the predicted number of data transmissions required to send a packet over that link, including retransmissions. First, we theoretically analyze the mean length of links, the mean number of hops, and the mean route ETX, which is the sum of the ETXs of all links in a route, of Longest Path Routing (LPR), and Shortest Path Routing (SPR). Second, we propose Adjustable Routing (AR), an approximation to Optimum Routing (OR), which minimizes route ETX. We theoretically compute the above characteristic values of AR. We also theoretically compute a lower bound of the mean route ETX of OR. We compare LPR, SPR, and OR using the results of analyses and show differences between these algorithms in the route ETX. key words: multi-hop wireless networks, Expected Transmission Count, theoretical analysis