Routing dependent node density requirements for connectivity in multi-hop wireless networks

The problem of connectivity in multi-hop wireless networks has been extensively studied in the literature and general results for node density requirements have been obtained (P. Gupta and P.R. Kumar, Proc. 37th IEEE Conf. of Decision and Control, 1998). These results have been obtained based on the implicit assumption of a generic routing protocol, capable of exhaustively searching all possible routes, between all pairs of nodes. Hence these results would be too optimistic in several practical cases, where the routing protocols are not generic but optimized for specific applications. In this paper, we provide a framework for defining the appropriate notion of connectivity that reflects the underlying network architecture and protocols. Based on this framework, we define and analyze connectivity requirements for two network architectures proposed in the literature, namely, GAF (geographic adaptive fidelity) with Manhattan routing (Y. Xu et al., Proc. Int. Conf. on Mobile Comp. and Netw., 2001), proposed for ad-hoc networks and AIMRP (address-light integrated MAC and routing protocol) which employs tier-based routing in sensor networks (S.S. Kulkarni et al., submitted for publication in IEEE Trans. on Networking, Dec. 2003). By comparing the critical node density requirements for connectivity, obtained through our framework, with the results in Gupta and Kumar, we show that the earlier results are too optimistic and hence it is important to consider the underlying routing protocol to dimension the density of nodes appropriately.