Optimal sequential wireless relay placement on a random lattice path

Our work is motivated by impromptu (or ``as-you-go'') deployment of wireless relay nodes along a path, a need that arises in many situations. In this paper, the path is modeled as starting at the origin (where there is the data sink, e.g., the control center), and evolving randomly over a lattice in the positive quadrant. A person walks along the path deploying relay nodes as he goes. At each step, the path can, randomly, either continue in the same direction or take a turn, or come to an end, at which point a data source (e.g., a sensor) has to be placed, that will send packets to the data sink. A decision has to be made at each step whether or not to place a wireless relay node. Assuming that the packet generation rate by the source is very low, and simple link-by-link scheduling, we consider the problem of sequential relay placement so as to minimize the expectation of an end-to-end cost metric (a linear combination of the sum of convex hop costs and the number of relays placed). This impromptu relay placement problem is formulated as a total cost Markov decision process. First, we derive the optimal policy in terms of an optimal placement set and show that this set is characterized by a boundary (with respect to the position of the last placed relay) beyond which it is optimal to place the next relay. Next, based on a simpler one-step-look-ahead characterization of the optimal policy, we propose an algorithm which is proved to converge to the optimal placement set in a finite number of steps and which is faster than value iteration. We show by simulations that the distance threshold based heuristic, usually assumed in the literature, is close to the optimal, provided that the threshold distance is carefully chosen. (C) 2014 Elsevier B.V. All rights reserved.

A shortest path tree based algorithm for relay placement in a wireless sensor network and its performance analysis

In this paper, we study a problem of designing a multi-hop wireless network for interconnecting sensors (hereafter called source nodes) to a Base Station (BS), by deploying a minimum number of relay nodes at a subset of given potential locations, while meeting a quality of service (QoS) objective specified as a hop count bound for paths from the sources to the BS. The hop count bound suffices to ensure a certain probability of the data being delivered to the BS within a given maximum delay under a light traffic model. We observe that the problem is NP-Hard. For this problem, we propose a polynomial time approximation algorithm based on iteratively constructing shortest path trees and heuristically pruning away the relay nodes used until the hop count bound is violated. Results show that the algorithm performs efficiently in various randomly generated network scenarios; in over 90% of the tested scenarios, it gave solutions that were either optimal or were worse than optimal by just one relay. We then use random graph techniques to obtain, under a certain stochastic setting, an upper bound on the average case approximation ratio of a class of algorithms (including the proposed algorithm) for this problem as a function of the number of source nodes, and the hop count bound. To the best of our knowledge, the average case analysis is the first of its kind in the relay placement literature. Since the design is based on a light traffic model, we also provide simulation results (using models for the IEEE 802.15.4 physical layer and medium access control) to assess the traffic levels up to which the QoS objectives continue to be met. (C) 2014 Elsevier B.V. All rights reserved.

As-You-Go Deployment of a 2-Connected Wireless Relay Network for Sensor-Sink Interconnection

A person walks along a line (which could be an idealisation of a forest trail, for example), placing relays as he walks, in order to create a multihop network for connecting a sensor at a point along the line to a sink at the start of the line. The potential placement points are equally spaced along the line, and at each such location the decision to place or not to place a relay is based on link quality measurements to the previously placed relays. The location of the sensor is unknown apriori, and is discovered as the deployment agent walks. In this paper, we extend our earlier work on this class of problems to include the objective of achieving a 2-connected multihop network. We propose a network cost objective that is additive over the deployed relays, and accounts for possible alternate routing over the multiple available paths. As in our earlier work, the problem is formulated as a Markov decision process. Placement algorithms are obtained for two source location models, which yield a discounted cost MDP and an average cost MDP. In each case we obtain structural results for an optimal policy, and perform a numerical study that provides insights into the advantages and disadvantages of multi-connectivity. We validate the results obtained from numerical study experimentally in a forest-like environment.

Uncertainty Quantification in Ultrasonic Wave Based Detection of Delamination in Composite Structures

In this paper we consider the problem of guided wave scattering from delamination in laminated composite and further the problem of estimating delamination size and layer-wise location from the guided wave measurement. Damage location and region/size can be estimated from time of flight and wave packet spread, whereas depth information can be obtained from wavenumber modulation in the carrier packet. The key challenge is that these information are highly sensitive to various uncertainties. Variation in reflected and transmitted wave amplitude in a bar due to boundary/interface uncertainty is studied to illustrate such effect. Effect of uncertainty in material parameters on the time of flight are estimated for longitudinal wave propagation. To evaluate the effect of uncertainty in delamination detection, we employ a time domain spectral finite element (tSFEM) scheme where wave propagation is modeled using higher-order interpolation with shape function have spectral convergence properties. A laminated composite beam with layer-wise placement of delamination is considered in the simulation. Scattering due to the presence of delamination is analyzed. For a single delamination, two identical waveforms are created at the two fronts of the delamination, whereas waves in the two sub-laminates create two independent waveforms with different wavelengths. Scattering due to multiple delaminations in composite beam is studied.