Path reachability including distance-constrained detours

When nodes and/or links are down in a network, the network may not function normally. Most of the existing work focuses on the reachability between two nodes along a path, that is, path reliability, and that through arbitrary paths, that is, network reliability. However, in case of wireless multi-hop networks and road networks, it may be inefficient or difficult to recalculate a path from the source to the destination when a failure occurs at an intermediate link in the path. In such cases, we can expect that the reachability between two nodes will improve by taking a detour from the entry of the failure link (i.e. failure point) to the destination without traversing the failure link. Since the detour may also increase the communication/travel delay, in this paper, we propose a new path metric (i.e. path reachability including distance-constrained detours), which consists of the conventional path reachability and the reachability along distance-constrained detours under arbitrary link failures in the original path. We first prove the two important characteristics: (1) the proposed metric is exactly the same as the network reliability in case of no distance constraint and (2) it is upper bounded by the diameter constrained network reliability. Through numerical results using a grid network and more realistic networks (i.e. wireless networks and a road network), we show the fundamental characteristics of the proposed metric and analyze the goodness of several representative paths in terms of the proposed metric as well as the conventional metrics (i.e. path length and path reachability).