We consider the k-barrier coverage problem, that is, the problem of deploying sensors on a border or perimeter to ensure that any intruder would be detected by at least k sensors. With random deployment of sensors, there is always a chance of gaps in coverage, thereby necessitating multiple rounds of deployment. In this paper, we study multi-round wireless sensor deployment on a border modeled as a line segment. We present two different classes of deployment strategies: complete and partial. In complete strategies, in every round, sensors are deployed over the entire border segment, while in partial strategies, sensors are deployed over only some part(s) of the border. First, we analyze the probability of k-coverage for any complete strategy as a function of parameters such as length of barrier to be covered, the width of the intruder, the sensing range of sensors, as well as the density of deployed sensors. Second, we propose two specific deployment strategies - Fixed-Density Complete and Fixed-Density Partial - and analyze the expected number of deployment rounds and expected total number of deployed sensors for each strategy. Next, we present a model for cost analysis of multi-round sensor deployment and calculate, for each deployment strategy, the expected total cost as a function of problem parameters and density of sensor deployment. Finally we find the optimal density of sensors in each round that minimizes the total expected cost of deployment for each deployment strategy. We validate our analysis by extensive simulation results.

We study the barrier coverage problem using relocatable sensor nodes. We assume each sensor can sense an intruder or event inside its sensing range. Sensors are initially located at arbitrary positions on the barrier and can move along the barrier. The goal is to find final positions for sensors so that the entire barrier is covered. In recent years, the problem has been studied extensively in the centralized setting. In this paper, we study the problem in the distributed setting. We assume each sensor repeatedly executes a Look-Compute-Move cycle: based on what it sees in its vicinity, it makes a decision on where to move, and moves to its next position. We make two strong but realistic restrictions on the capabilities of sensors: they have a constant visibility range and can move only a constant distance in every cycle. In this model, we give the first two distributed algorithms that achieve barrier coverage for a line segment barrier when there are enough nodes in the network to cover the entire barrier. Our algorithms are synchronous, and local in the sense that sensors make their decisions independently based only on what they see within their constant visibility range. One of our algorithms is oblivious whereas the other uses two bits of memory at each sensor to store the type of move made in the previous step. We show that our oblivious algorithm terminates within Θ(n2) steps with the barrier fully covered, while the constant-memory algorithm is shown to take Θ(n) steps to terminate in the worst case. Since any algorithm that can only move a constant distance in one step requires Ω(n) steps on some inputs, our second algorithm is asymptotically optimal. Finally, both our algorithms are self-stabilizing, and can be easily extended to the case of non-homogeneous sensors, and for the case when the barrier is a circle.

We study the load balancing aspect of routing algorithms in wireless ad hoc networks. We define a statistical measure called local coefficient of variance (lcv) to study the smoothness of the load distribution in the network. The importance of keeping lcv as low as possible in designing load balanced routing algorithms is demonstrated. We analyze how number of nodes, transmission range, network area and different routing algorithms can affect this metric. We introduce a class of algorithms called elliptic routing that reduce the maximum load of nodes in the network by avoiding the highly loaded network center at the same time as keeping the lcv of the load distribution low. Experimental results show that our algorithms outperform other existing algorithms in reducing the maximum load of the network. We also give a technique to reduce the lcv of the load distribution, and hence decrease the maximum load of the nodes in the network further. This technique can be combined with any location-based routing algorithm. We evaluate the performance gain obtained by this technique via simulations.