Critical Transmission Range for Channel Allocation in Multi-hop Wireless Networks
Bhaskar Krishnamachari, Stephen B. Wicker · 2002
As in other large-scale complex systems, many global properties of interest in multihop wireless networks undergo phase transitions as the local interaction parameter – the common transmission range of nodes – exceeds a critical value. It is now well-established in the literature that there exists such a critical range for network connectivity. We show that critical transmission range thresholds are also associated with conflict free channel allocation in wireless networks. When the common communication radius of nodes exceeds this value, the probability that k channels suffice drops sharply from nearly one to nearly zero. The analysis of these phase transitions provides useful lessons about energy-efficient and bandwidth-efficient operating points as well as feasible regions for such networks. Other results presented in this paper include a polynomial algorithm for one-dimensional conflict-free channel allocation (which is an NP-hard problem in the general case), and an analysis of maximum throughput in channelized wireless networks.