Phase transition phenomena in wireless ad hoc networks

Abstract

Abstract-There are many contexts in distributed wireless networks where there is a critical threshold, corresponding to a minimum amount of the communication effort or power expenditure by individual nodes, above which a desirable global property exists with high probability. When this individual node effort is below the threshold the desired global property exists with a low probability. This "phase transition" is typically seen to become sharper as the number of nodes in the network increases. We discuss in this paper some examples of properties that exhibit such critical behavior: node reachability with probabilistic flooding, ad-hoc network connectivity, and sensor network coordination. We discuss the connections between these phenomena and the phase transitions that have been shown to arise in random graphs. We argue that a good understanding of these phase transition phenomena can provide useful design principles for engineering distributed wireless networks.

A Theory of Network Localization

“…We formally analyzed the performance of network localization in networks of randomly placed nodes. Even though some researchers have studied random graphs in sensor networks, e.g., [14], [15], [20], [34], the focus is mainly on routing but not on localization. In [14], Díaz, Petit and Serna analyzed the performance of localization for optical sensor networks.…”

Probabilistic Broadcasting in Wireless Ad Hoc Networks

“…The analysis of this scheme presents to us a very new direction. The idea of phase transitions in wireless ad hoc networks was first presented by B. Krishnamachari et al in (Krishnamachari et al, 2001). Phase transitions are characterized by an abrupt emergence or disappearence of a property beyond a critical value of a parameter.…”

“…In probabilistic flooding each node decides to rebroadcast with a probability p. In (Krishnamachari et al, 2001) authors present that reachability in such probabilistic flooding schemes show a phase transition. The parameter that this property depends upon is the broadcast proabability p. Thus for a p > p c 6 ,…”

“…Phase transitions are characterized by an abrupt emergence or disappearence of a property beyond a critical value of a parameter. In (Krishnamachari et al, 2001), the authors have shown that some properties of a wireless ad hoc network(node reachability with probabilistic flooding, ad hoc network connectivity and sensor network coordination) exhibit this phase transition and the critical behaviour. Though this idea of phase transitions happen to be new to the field of wireless communications, such behavior has been known to mathematicians for several decades in the form of zero-one laws in Random Graphs 5 .…”

TDMA scheduling algorithms for wireless sensor networks

“…Each topology corresponds to a different configuration of the sensor nodes with respect to the base station: The locations of the sensor nodes depends on the locations that requires sensing by the application whereas the density of the nodes depends on the number of locations to be sensed in a certain area or the accuracy the application requires, i.e., the higher accuracy required, the higher the density of the nodes. The transmission range, denoted r s , is chosen to be slightly larger than the threshold necessary for network connectivity [25].…”