All-Terminal Reliability Analysis of Wireless Networks of Redundant Radio Modules

Due to the low cost of easy-to-use components of open-source hardware and software, the Internet of Things may be pervading through everything everywhere. The dependability of the Internet of Things is critical because the services will be concerned with real life. However, the inexpensive hardware provides limited resources for communication. In this paper, we present exact all-terminal reliability of the wireless networks of which the number of links of each node is bounded. First, we analyze the all-terminal reliability of the regular wireless network, where any two nodes are connected by a wireless link consisting of a pair of radio modules. The reliability polynomial is derived from the Tutte polynomial that is the seminal work of the algebraic graph theory. Second, we analyze the all-terminal reliability of the wireless network including the random mesh network under the assumption that if the module fails, all radio links connected through a radio module are cut off. We consider both the fault of the communication module and the fading of the wireless channel in the indoor channel condition. For improving the reliability, we also propose a fault-tolerant method giving redundant radio modules into each node. We also analyze cost-effectiveness. We also calculate the mean-time-to-failure (MTTF) for wireless networks. We show that the random mesh network of which each node includes three or more the radio-broadcast modules is more dependable than any other regular network of which each node comprises four point-to-point modules if it is the connected graph in the static environment.