Non-uniform Node Distribution Research Articles

ACO-Based Algorithm for Solving Energy Hole Problems in Wireless Sensor Networks

In a multi-hop wireless sensor network (WSN), the sensors closest to the sink tend to deplete their energy faster than other sensors, which is known as an energy hole around the sink. No more data can be delivered to the sink after an energy hole appears, while a considerable amount of energy is wasted and the network lifetime ends prematurely. This paper investigates the energy hole problem, and based on the improved corona model with levels, it concludes that the assignment of transmission ranges of nodes in different coronas is an effective approach for achieving energy-efficient network. It proves that the optimal transmission ranges for all areas is a multi-objective optimization problem (MOP), which is NP hard. The paper proposes an ACO (ant colony optimization)-based distributed algorithm to prolong the network lifetime, which can help nodes in different areas to adaptively find approximate optimal transmission range based on the node distribution. Furthermore, the simulation results indicate that the network lifetime under this solution approximates to that using the optimal list. Compared with existing algorithms, this ACO-based algorithm can not only make the network lifetime be extended more than two times longer, but also have good performance in the non-uniform node distribution.

The Energy Hole Problem of Nonuniform Node Distribution in Wireless Sensor Networks

The nonuniform node distribution strategy can be used to mitigate the energy hole problem in wireless sensor networks.In this paper,the authors investigate the theoretical aspects of the nonuniform node distribution strategy in multi-hop wireless sensor networks,and prove that in a circular sensor network with nonuniform node distribution and constant data reporting,the unbalanced energy depletion among the nodes in the whole network is unavoidable.In spite of this fact,suboptimal energy efficiency among the inner parts of the network is possible if the number of nodes in the network is quantified and meets some conditions.The authors propose a novel nonuniform node distribution strategy based on their analysis and a routing algorithm coupling with the proposed node distribution strategy for achieving the suboptimal energy efficiency.Simulation results show that when the network lifetime ends,the inner coronas nearly attain balanced energy depletion.

A Novel Cache Architecture and Placement Framework for Packet Forwarding Engines

Packet forwarding is a memory-intensive application requiring multiple accesses through a trie structure. With the requirement to process packets at line rates, high-performance routers need to forward millions of packets every second with each packet needing up to seven memory accesses. Earlier work shows that a single cache for the nodes of a trie can reduce the number of external memory accesses. It is observed that the locality characteristics of the level-one nodes of a trie are significantly different from those of lower level nodes. Hence, we propose a heterogeneously segmented cache architecture (HSCA) which uses separate caches for level-one and lower level nodes, each with carefully chosen sizes. Besides reducing misses, segmenting the cache allows us to focus on optimizing the more frequently accessed level-one node segment. We find that due to the nonuniform distribution of nodes among cache sets, the level-one nodes cache is susceptible to high conflict misses. We reduce conflict misses by introducing a novel two-level mapping-based cache placement framework. We also propose an elegant way to fit the modified placement function into the cache organization with minimal increase in access time. Further, we propose an attribute preserving trace generation methodology which emulates real traces and can generate traces with varying locality. Performance results reveal that our HSCA scheme results in a 32 percent speedup in average memory access time over a unified nodes cache. Also, HSCA outperforms IHARC, a cache for lookup results, with as high as a 10-fold speedup in average memory access time. Two-level mapping further enhances the performance of the base HSCA by up to 13 percent leading to an overall improvement of up to 40 percent over the unified scheme.

Comments on high-order integrators embedded within integral deferred correction methods

A class of novel deferred correction methods, integral deferred correction (IDC) methods, is studied. This class of methods is an extension of ideas introduced by Dutt, Greengard and Rokhlin on spectral deferred correction (SDC) methods for solving ordinary differential equations (ODEs). The novel nature of this class of defect correction methods is that the correction of the defect is carried out using an accurate integral form of the residual instead of the more familiar differential form. As a family of methods, these schemes are capable of matching the efficiency of popular high-order RK methods. The smoothness of the error vector associated with an IDC method is an important indicator of the order of convergence that can be expected from a scheme (Christlieb, Ong, and Qiu; Hansen and Strain; Skeel). It is demonstrated that embedding an r-th order integrator in the correction loop of an IDC method does not always result in an r-th order increase in accuracy. Examples include IDC methods constructed using non-self-starting multistep integrators, and IDC methods constructed using a nonuniform distribution of quadrature nodes. Additionally, the integral deferred correction concept is reposed as a framework to generate high-order Runge–Kutta (RK) methods; specifically, we explain how the prediction and correction loops can be incorporated as stages of a high-order RK method. This alternate point of view allows us to utilize standard methods for quantifying the performance (efficiency, accuracy and stability) of integral deferred correction schemes. It is found that IDC schemes constructed using uniformly distributed nodes and high-order integrators are competitive in terms of efficiency with IDC schemes constructed using Gauss–Lobatto nodes and forward Euler integrators. With respect to regions of absolute stability, however, IDC methods constructed with uniformly distributed nodes and high-order integrators are far superior. It is observed that as the order of the embedded integrator increases, the stability region of the IDC method increases.

Maximizing network lifetime based on transmission range adjustment in wireless sensor networks

In a wireless sensor network (WSN), the unbalanced distribution of communication loads often causes the problem of energy hole, which means the energy of the nodes in the hole region will be exhausted sooner than the nodes in other regions. This is a key factor which affects the lifetime of the networks. In this paper we propose an improved corona model with levels for analyzing sensors with adjustable transmission ranges in a WSN with circular multi-hop deployment (modeled as concentric coronas). Based on the model we consider that the right transmission ranges of sensors in each corona is the decision factor for optimizing the network lifetime after nodes deployment. We prove that searching optimal transmission ranges of sensors among all coronas is a multi-objective optimization problem (MOP), which is NP hard. Therefore, we propose a centralized algorithm and a distributed algorithm for assigning the transmission ranges of sensors in each corona for different node distributions. The two algorithms can not only reduce the searching complexity but also obtain results approximated to the optimal solution. Furthermore, the simulation results of our solutions indicate that the network lifetime approximates to that ensured by the optimal under both uniform and non-uniform node distribution.

Path unaware layered routing protocol (PULRP) with non‐uniform node distribution for underwater sensor networks

AbstractWe propose path unaware layered routing protocol (PULRP) for 2D underwater sensor networks (UWSNs) with mobile nodes. The steady‐state distribution of mobile nodes in UWSNs is nonuniform in general. Hence, we use a mobility model‐dependent node distribution. The proposed PULRP algorithm consists of two phases. In the first phase (layering phase), a layering structure is presented which is a set of concentric circles, around a sink node. The radii of the concentric circles are chosen based on equal distribution of nodes in every layer. A distributed power control mechanism is also introduced. The power level of nodes in a particular layer is chosen such that communication occurs only with nodes in the next layer. In PULRP, we consider multihop communication from source to sink. Therefore, in the second phase (communication phase), we propose a method to choose the intermediate relay nodes and an on the fly routing algorithm for packet delivery from source node to sink node across the chosen relay nodes. The proposed algorithm, PULRP finds the routing path on the fly and hence, it does not require any fixed routing table, localization, or time synchronization processes. We demonstrate the performance of PULRP using random waypoint (RWP) mobility model in a simulated underwater environment. Our findings show that the proposed algorithm has considerably better throughput (successful packet delivery rate) compared to the underwater diffusion (UWD) algorithm for various node densities as well as node velocities. In addition, the delay performance of PULRP is also better than that of UWD. Copyright © 2008 John Wiley & Sons, Ltd.

Avoiding Energy Holes in Wireless Sensor Networks with Nonuniform Node Distribution

In this paper, we investigate the theoretical aspects of the nonuniform node distribution strategy used to mitigate the energy hole problem in wireless sensor networks (WSNs). We conclude that in a circular multihop sensor network (modeled as concentric coronas) with nonuniform node distribution and constant data reporting, the unbalanced energy depletion among all the nodes in the network is unavoidable. Even if the nodes in the inner coronas of the network have used up their energy simultaneously, the ones in the outermost corona may still have unused energy. This is due to the intrinsic many-to-one traffic pattern of WSNs. Nevertheless, nearly balanced energy depletion in the network is possible if the number of nodes increases in geometric progression from the outer coronas to the inner ones except the outermost one. Based on the analysis, we propose a novel nonuniform node distribution strategy to achieve nearly balanced energy depletion in the network. We regulate the number of nodes in each corona and derive the ratio between the node densities in the adjacent (i + 1)th and ith coronas by the strategy. Finally, we propose (q-switch routing, a distributed shortest path routing algorithm tailored for the proposed nonuniform node distribution strategy. Extensive simulations have been performed to validate the analysis.

Utilizing Voronoi Cells of Location Data Streams for Accurate Computation of Aggregate Functions in Sensor Networks

Sensor networks are unattended deeply distributed systems whose database schema can be conceptualized using the relational model. Aggregation queries on the data sampled at each sensor node are the main means to extract the abstract characteristics of the surrounding environment. However, the non-uniform distribution of the sensor nodes in the environment leads to inaccurate results generated by the aggregation queries. In this paper, we introduce “spatial aggregations” that take into consideration the spatial location of each measurement generated by the sensor nodes. We propose the use of spatial interpolation methods derived from the fields of spatial statistics and computational geometry to answer spatial aggregations. In particular, we study Spatial Moving Average (SMA), Voronoi Diagram and Triangulated Irregular Network (TIN). Investigating these methods for answering spatial average queries, we show that the average value on the data samples weighted by the area of the Voronoi cell of the corresponding sensor node, provides the best precision. Consequently, we introduce an algorithm to compute and maintain the accurate Voronoi cell at each sensor node while the location of the others arrive on data stream. We also propose AVC-SW, a novel algorithm to approximate this Voronoi cell over a sliding window that supports dynamism in the sensor network. To demonstrate the performance of in-network implementation of our aggregation operators, we have developed prototypes of two different approaches to distributed spatial aggregate processing.

Utilizing Voronoi Cells of Location Data Streams for Accurate Computation of Aggregate Functions in Sensor Networks

Sensor networks are unattended deeply distributed systems whose database schema can be conceptualized using the relational model. Aggregation queries on the data sampled at each sensor node are the main means to extract the abstract characteristics of the surrounding environment. However, the non-uniform distribution of the sensor nodes in the environment leads to inaccurate results generated by the aggregation queries. In this paper, we introduce "spatial aggregations" that take into consideration the spatial location of each measurement generated by the sensor nodes. We propose the use of spatial interpolation methods derived from the fields of spatial statistics and computational geometry to answer spatial aggregations. In particular, we study Spatial Moving Average (SMA), Voronoi Diagram and Triangulated Irregular Network (TIN). Investigating these methods for answering spatial average queries, we show that the average value on the data samples weighted by the area of the Voronoi cell of the corresponding sensor node, provides the best precision. Consequently, we introduce an algorithms to compute and maintain the accurate Voronoi cell at each sensor node while the location of the others arrive on data stream. We also propose AVC-SW, a novel algorithm to approximate this Voronoi cell over a sliding window that supports dynamism in the sensor network. To demonstrate the performance of in-network implementation of our aggregation operators, we have developed prototypes of two different approaches to distributed spatial aggregate processing.

Connected fixed node degree based topologies in ad hoc networks

Topology control in an ad hoc network can provide better spatial reuse of the wireless channel and assist in conserving the power usage. A number of distributed topology control algorithms have been proposed to remove the need of a centralised controller. Distributed algorithms such as location information no topology (LINT), location information link state topology (LILT), MobileGrid (MG) and K-Neigh, aim to achieve overall network connectivity and low transmission range by maintaining a fixed node degree value. In the case of a non-uniform node distribution, maintaining a fixed node degree can unnecessarily partition a network. In this paper, we identify cases where a fixed node degree approach may result in a disconnected network and lead to isolated nodes and disjointed clusters. We propose two distributed algorithms that utilise one hop neighbours and their location information to improve the connectivity of the fixed node degree approaches, by incorporating unidirectional link information in topology control decisions and maintaining a number of critical links. A distributed mechanism to construct and maintain a network topology is proposed, which can be integrated with a neighbour discovery protocol. Furthermore, we identify and investigate the convergence issue related to LINT, MG and LILT as a result of independent direct power control decisions. We compare the performance of such algorithms with the graph based approaches. A worked example and a simulation based analysis of the proposed algorithms are provided for a number of node degree values. Simulations and analysis indicate that that the proposed algorithms are able to achieve higher connectivity for different node distributions and provide a more fault tolerant topology.

Highly nonlinear standing water waves with small capillary effect

We calculate spatially and temporally periodic standing waves using a spectral boundary integral method combined with Newton iteration. When surface tension is neglected, the non-monotonic behaviour of global wave properties agrees with previous computations by Mercer & Roberts (1992). New accurate results near the limiting form of gravity waves are obtained by using a non-uniform node distribution. It is shown that the crest angle is smaller than 90° at the largest calculated crest curvature. When a small amount of surface tension is included, the crest form is changed significantly. It is necessary to include surface tension to numerically reproduce the steep standing waves in Taylor's (1953) experiments. Faraday-wave experiments in a large-aspect-ratio rectangular container agree with our computations. This is the first time such high-amplitude, periodic waves appear to have been observed in laboratory conditions. Ripple formation and temporal symmetry breaking in the experiments are discussed.

Mass Distribution and Frequencies of a Vertical Spring

A vertical spring in a gravitational field has a density increase from top to bottom. The density variation, which is often not noticeable, depends on the ratio of the spring weight to the quantity kz0, the spring constant k times the unstretched length z0. Two springs prepared by prestretch-ing 78 and 23 turn portions of a “Slinky” showed density increases by factors of about 10 and 4, respectively. The detailed density distribution of the smaller spring agrees very well with the results of an analysis based on Hooke's law behavior. The heavier spring shows non-Hookean effects. The lowest few frequencies can be measured by driving the spring in resonance by hand, and for the lighter spring these also agree well with calculated values. The predicted nonuniform distribution of nodes is observable. This simple apparatus may provide stimulating experiments for intermediate laboratories.