Phase Transitions for Controlled Mobility in Wireless Ad Hoc Networks
Cory Dixon, Daniel P. Henkel, Timothy M. Brown, Eric W. Frew · AIAA Guidance, Navigation, and Control Conference and Exhibit · 2006
In this paper we investigate the phase transitions between different modes of controlled mobility in wireless ad hoc networks. The transmission of data between two nodes can be performed by one of three methods in a mobile ad hoc network: direct transmission between nodes; multi-hop relaying through intermediate nodes; and data ferrying through a node that physically moves between sources and destinations. Assuming the source and destination nodes are stationary, the best choice of transmission mode through the network is a function of several variables including the separation distance between nodes, the required average data throughput, the maximum tolerable delay, and the data ferry speed and buffer capacity. This paper presents the notion of a phase diagram relating separation distance to average data throughput. Contours of maximum packet delay are specified on this phase plot and are used to identify the optimal mode under various configurations. The creation and maintenance of communication channels of specified performance in a mobile ad hoc network can be viewed as a hybrid control problem. Calculation of the boundaries between phases corresponds to determining the transition conditions of the hybrid controller. Nomenclature D = source and destination separation distance d = distance between any two communicating nodes B = buffer size P = packet size K = RF power coefficient ε = RF power loss exponent R = long term average communication rate SNR = signal-to-noise ratio C = Shannon channel capacity (instantaneous communication rate) W = Shannon bandwidth coefficient τ = time delay for delivery of a packet T = required throughput M = hybrid control mode V = ferry speed C I.