JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. X, NO. Y, SEPTEMBER 2009 1 The availability and reliability of wireless multi-hop networks with stochastic link failures Geir Egeland, Member, IEEE, Paal E. Engelstad Senior Member, IEEE Abstract—The network reliability and availability in wireless multi-hop networks can be inadequate due to radio induced in- terference. It is therefore common to introduce redundant nodes. This paper provides a method to forecast how the introduction of redundant nodes increases the reliability and availability of such networks. For simplicity, it is assumed that link failures are stochastic and independent, and the network can be modelled as a random graph. First, the network reliability and availability of a static network with a planned topology is explored. This analysis is relevant to mesh networks for public access, but also provides insight into the reliability and availability behaviour of other categories of wireless multi-hop networks. Then, by extending the analysis to also consider random geometric graphs, networks with nodes that are randomly distributed in a metric space are also investigated. Unlike many other random graph analyses, our approach allows for advanced link models where the link failure probability is continuously decreasing with an increasing distance between the two nodes of the link. In addition to analysing the steady-state availability, the transient reliability behaviour of wireless multi-hop networks is also found. These results are supported by simulations. Index Terms—Random graphs, multi-hop mesh, IEEE 802.11s, reliability, availability, transient behaviour. I. I NTRODUCTION A wireless multi-hop network (typically with an ad hoc topology) is a network composed of a group of nodes interconnected via wireless links. The nodes in the network implements a routing protocol which enables them to com- municate with each other over multiple link hops. The nodes in these networks are often self-configured and self-organised. Examples of such networks include wireless mesh networks [1], mobile ad hoc networks (MANETs) [2] and wireless sensor networks (WSNs) [3]. This paper analyses two important classes of static wireless multi-hop networks. They will be referred to as: • Planned mesh networks • Random mesh networks Typically, in planned mesh networks the location of each node is carefully planned. These networks usually appear as a consequence of the high costs associated with interconnecting nodes in a network with wired links. For example, ad hoc technology can in a cost-efficient manner, extend the reach of a wired backbone through a wireless backhaul mesh network. Currently, there is a large number of commercial deployments G. Egeland is with the Department of Electrical and Computer Engineering, University of Stavanger, 4036 Stavanger, Norway e-mail: (geir.egeland@gmail.com). P. E. Engelstad is with UniK/UiO, Simula and Telenor, 1331 Fornebu, Norway e-mail: (paal.engelstad@telenor.com) Manuscript received August 15, 2008; revised January 31, 2009. of such solutions for public access in urban areas, where the nodes are often located on roof-tops. These networks are referred to as roof-top networks or backhaul mesh networks. Unlike a planned mesh, a random mesh network consists of nodes that are randomly distributed (i.e. geographically deployed in a random manner). They typically appear in situations where it is required that the network is set up in an ad hoc fashion. Such networks can be used to provide a self- formed temporary communication infrastructure for disaster recovery operations, for communication at conferences or conventions and in tactical military operations. Common for these two types of wireless networks, is that radio-links are vulnerable to failures caused by radio induced interference, which in most cases has a negative impact on the network reliability and availability. This represents a considerable barrier for wide deployment of planned and random mesh networks. In a planned mesh network it is therefore common to improve the network reliability and availability by introduc- ing redundant nodes. Typically, the possible location of a redundant node in a planned mesh network is known, e.g. the operator of a roof-top network is in contact with a property owner that is willing to offer a specific roof-top as a site for the redundant node. The site-acquisition and site-operation cost associated with each redundant node, is usually high. Therefore, the network planning phase should include a cost-benefit analysis, where the additional network reliability and availability of adding this redundant node is weighted against the additional costs. While the cost of adding a redundant node usually is easy to determine, it is more difficult to forecast the additional reliability and availability gained by adding the node. The main reason is that little have been published about network reliability and availability for mesh networks. By using the random graph analysis presented in this paper, however, it might be possible to estimate what will be the improved reliability and availability by adding one or more redundant nodes. Indeed, the main contribution of this paper is a method to forecast how the introduction of redundant nodes increases the network reliability and availability of planned mesh networks. By using the random graph analysis presented in this paper, the network reliability and availability of a planned mesh network can be found as a function of the number of redundant nodes. By applying the same method, it is possible to forecast how the introduction of redundant nodes will increase the network reliability for any given topology. (The possible topologies are given, since the location of the redundant node normally