Design Guidelines for Maximizing Lifetime and Avoiding Energy Holes in Sensor Networks with Uniform Distribution and Uniform Reporting

This paper investigates theoretical aspects of the uneven energy depletion phenomenon recently noticed in sink-based wireless sensor networks. We consider uniformly distributed sensors, each sending roughly the same number of reports toward the closest sink. We assume an energy consumption model governed by the relation E = d +c where d, (d ≤ tx), is the transmission distance, α ≥ 2 is the power attenuation, c is a technology-dependent positive constant, and tx is the maximum transmission range of sensors. Our results are multifold. First, we show that for α > 2, all sensors whose distance to the sink is min{tx, ( 2c α−2 ) 1 α } should transmit directly to the sink. Interestingly, this limit does not depend on the size of the network, expressed as the largest distance R from a sensor to the closest sink. Next, we prove that in order to minimize the total amount of energy spent on routing along a path originating at a sensor in a corona and ending at the sink, all the coronas must have the same width, equal to the above expression. This choice, however, leads to uneven energy depletion and to the creation of energy holes. We show that for α > 2 the uneven energy depletion can be prevented by judicious system design, resulting in balanced energy expenditure across the network. We describe an iterative process for determining the sizes of coronas. Their optimal sizes (and corresponding transmission radii) and the number of coronas depend on R. As expected, the width of coronas in energy-balanced sensor network increases. Finally, we show that for α = 2, the uneven energy depletion phenomenon is intrinsic to the system and no routing strategy can avoid the creation of an energy hole around the sink.