Wireless Netw (2008) 14: 87–102 DOI 10.1007/s11276-006-7831-4 On stability analysis of virtual backbone in mobile ad hoc networks ∗ ˙ Ibrahim H ¨ okelek · M. ¨ Umit Uyar · Mariusz A. Fecko Published online: 9 June 2006 C  Springer Science + Business Media, LLC 2006 Abstract Service discovery architectures and cluster- assisted routing protocols in mobile ad-hoc networks (MANETs) heavily use formation and maintenance of a vir- tual backbone (VB), where the most stable mobile nodes with higher node degree are dynamically selected as the backbone nodes. In this paper we present a novel analytic model for VB stability in MANETs. The model employs the dynamics of node movements, where link creation/failure is modeled via a random walk with probabilistic state-transition matrix. The backbone formation algorithm gives preference to the nodes with the smaller number of link changes and the higher de- gree. Therefore, the link arrivals and departures determine the probability (and thus the expected time) for a mobile node to leave, join, or remain in the backbone, i.e., the stability of a dynamic structure of VB. 1. Introduction Mobile ad hoc networks (MANETs) (RFC2501) [8] suffer from a harsh communication environment due to node mobil- ity and peculiarities of the wireless medium such as fading, ∗ Prepared through collaborative participation in the Communications & Networks Consortium sponsored by the U.S. Army Research Lab under the Collaborative Technology Alliance Program, Cooperative Agreement DAAD19-01-2-0011. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. ˙ I. H ¨ okelek . M. ¨ U. Uyar ( ) Electrical Engineering Dept., CCNY, The City University of New York, USA e-mail: uyar@ccny.cuny.edu M. A. Fecko Applied Research Area, Telcordia Technologies, Inc., Piscataway, NJ, USA interference, and asymmetric links. Since mobile nodes are often subject to random movement, the network topology may change rapidly and unpredictably. Reliability of ser- vices is critical but difficult to provide in such networks, es- pecially when applications (e.g., military communications, real-time transactions, videoconferencing, and disaster re- covery) require survivability from the underlying network infrastructure. A related issue is the scalability of ad hoc networks, which is often addressed by abstracting the network topology through clustering: creating clusters that can be collapsed in higher levels. A virtual backbone (VB) [6] is one common clustering substructure that is exploited mostly in (reliable) service discovery in ad hoc networks [10, 16, 18, 19]. A VB consists of a subset of nodes such that the backbone nodes are able to discover and communicate with one an- other. The VB nodes are dynamically selected in a distributed fashion. To handle frequent topology changes that may hap- pen due to the node mobility, most backbone formation al- gorithms [15, 17, 22] include the maintenance feature that dynamically reassigns nodes to either join or leave the VB according to the number and stability of their links. We present an analytic model to study the stability of virtual backbones. This new model allows the computation of two important metrics characterizing the dynamics of a node’s random movement in an ad hoc network: (1) aver- age time for the number of link changes of the node (i.e., instances of link creation and failure) to either drop below or exceed a given threshold, and, analogously, (2) average time for the number of active links of the node to either drop below or exceed a given threshold. The former defines the stability of the node’s links and the latter is the node’s de- gree (the number of active neighbors). Our model will help analyze the performance of various paradigms that rely on such link-based mobility metrics [6, 14, 15, 16, 28] includ- Springer