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The capacity of wireless networks
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2000
"... When n identical randomly located nodes, each capable of transmitting at bits per second and using a fixed range, form a wireless network, the throughput @ A obtainable by each node for a randomly chosen destination is 2 bits per second under a noninterference protocol. If the nodes are optimally p ..."
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Cited by 3243 (42 self)
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When n identical randomly located nodes, each capable of transmitting at bits per second and using a fixed range, form a wireless network, the throughput @ A obtainable by each node for a randomly chosen destination is 2 bits per second under a noninterference protocol. If the nodes are optimally placed in a disk of unit area, traffic patterns are optimally assigned, and each transmission’s range is optimally chosen, the bit–distance product that can be transported by the network per second is 2 @ A bitmeters per second. Thus even under optimal circumstances, the throughput is only 2 bits per second for each node for a destination nonvanishingly far away. Similar results also hold under an alternate physical model where a required signaltointerference ratio is specified for successful receptions. Fundamentally, it is the need for every node all over the domain to share whatever portion of the channel it is utilizing with nodes in its local neighborhood that is the reason for the constriction in capacity. Splitting the channel into several subchannels does not change any of the results. Some implications may be worth considering by designers. Since the throughput furnished to each user diminishes to zero as the number of users is increased, perhaps networks connecting smaller numbers of users, or featuring connections mostly with nearby neighbors, may be more likely to be find acceptance.
HEED: A Hybrid, EnergyEfficient, Distributed Clustering Approach for Ad Hoc Sensor Networks
 IEEE TRANS. MOBILE COMPUTING
, 2004
"... Topology control in a sensor network balances load on sensor nodes and increases network scalability and lifetime. Clustering sensor nodes is an effective topology control approach. In this paper, we propose a novel distributed clustering approach for longlived ad hoc sensor networks. Our proposed ..."
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Cited by 590 (1 self)
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Topology control in a sensor network balances load on sensor nodes and increases network scalability and lifetime. Clustering sensor nodes is an effective topology control approach. In this paper, we propose a novel distributed clustering approach for longlived ad hoc sensor networks. Our proposed approach does not make any assumptions about the presence of infrastructure or about node capabilities, other than the availability of multiple power levels in sensor nodes. We present a protocol, HEED (Hybrid EnergyEfficient Distributed clustering), that periodically selects cluster heads according to a hybrid of the node residual energy and a secondary parameter, such as node proximity to its neighbors or node degree. HEED terminates in Oð1Þ iterations, incurs low message overhead, and achieves fairly uniform cluster head distribution across the network. We prove that, with appropriate bounds on node density and intracluster and intercluster transmission ranges, HEED can asymptotically almost surely guarantee connectivity of clustered networks. Simulation results demonstrate that our proposed approach is effective in prolonging the network lifetime and supporting scalable data aggregation.
An Energy Efficient Hierarchical Clustering Algorithm for Wireless Sensor Networks
, 2003
"... A wireless network consisting of a large number of small sensors with lowpower transceivers can be an effective tool for gathering data in a variety of environments. The data collected by each sensor is communicated through the network to a single processing center that uses all reported data to de ..."
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Cited by 390 (1 self)
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A wireless network consisting of a large number of small sensors with lowpower transceivers can be an effective tool for gathering data in a variety of environments. The data collected by each sensor is communicated through the network to a single processing center that uses all reported data to determine characteristics of the environment or detect an event. The communication or message passing process must be designed to conserve the Hmited energy resources of the sensors. Clustering sensors into groups, so that sensors communicate information only to clusterheads and then the clusterheads communicate the aggregated information to the processing center, may save energy. In this paper, we propose a distributed, randomized clustering algorithm to organize the sensors in a wireless sensor network into clusters. We then extend this algorithm to generate a hierarchy of clusterheads and observe that the energy savings increase with the number of levels in the hierarchy. Results in stochastic geometry are used to derive solutions for the values of parameters of our algorithm that minimize the total energy spent in the network when all sensors report data through the clusterheads to the processing center.
The Node Distribution of the Random Waypoint Mobility Model for Wireless Ad Hoc Networks
, 2003
"... The random waypoint model is a commonly used mobility model in the simulation of ad hoc networks. It is known that the spatial distribution of network nodes moving according to this model is, in general, nonuniform. However, a closedform expression of this distribution and an indepth investigation ..."
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Cited by 377 (10 self)
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The random waypoint model is a commonly used mobility model in the simulation of ad hoc networks. It is known that the spatial distribution of network nodes moving according to this model is, in general, nonuniform. However, a closedform expression of this distribution and an indepth investigation is still missing. This fact impairs the accuracy of the current simulation methodology of ad hoc networks and makes it impossible to relate simulationbased performance results to corresponding analytical results. To overcome these problems, we present a detailed analytical study of the spatial node distribution generated by random waypoint mobility. More specifically, we consider a generalization of the model in which the pause time of the mobile nodes is chosen arbitrarily in each waypoint and a fraction of nodes may remain static for the entire simulation time. We show that the structure of the resulting distribution is the weighted sum of three independent components: the static, pause, and mobility component. This division enables us to understand how the models parameters influence the distribution. We derive an exact equation of the asymptotically stationary distribution for movement on a line segment and an accurate approximation for a square area. The good quality of this approximation is validated through simulations using various settings of the mobility parameters. In summary, this article gives a fundamental understanding of the behavior of the random waypoint model.
On the Minimum Node Degree and Connectivity of a Wireless Multihop Network
 ACM MobiHoc
, 2002
"... This paper investigates two fundamental characteristics of a wireless multihop network: its minimum node degree and its k–connectivity. Both topology attributes depend on the spatial distribution of the nodes and their transmission range. Using typical modeling assumptions — a random uniform distri ..."
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Cited by 318 (4 self)
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This paper investigates two fundamental characteristics of a wireless multihop network: its minimum node degree and its k–connectivity. Both topology attributes depend on the spatial distribution of the nodes and their transmission range. Using typical modeling assumptions — a random uniform distribution of the nodes and a simple link model — we derive an analytical expression that enables the determination of the required range r0 that creates, for a given node density ρ, an almost surely k–connected network. Equivalently, if the maximum r0 of the nodes is given, we can find out how many nodes are needed to cover a certain area with a k–connected network. We also investigate these questions by various simulations and thereby verify our analytical expressions. Finally, the impact of mobility is discussed. The results of this paper are of practical value for researchers in this area, e.g., if they set the parameters in a network–level simulation of a mobile ad hoc network or if they design a wireless sensor network. Categories and Subject Descriptors C.2 [Computercommunication networks]: Network architecture and design—wireless communication, network communications, network topology; G.2.2 [Discrete mathematics]: Graph theory; F.2.2 [Probability and statistics]: Stochastic processes
Topology Control in Wireless Ad Hoc and Sensor Networks
 ACM Computing Surveys
, 2005
"... Topology Control (TC) is one of the most important techniques used in wireless ad hoc and sensor networks to reduce energy consumption (which is essential to extend the network operational time) and radio interference (with a positive effect on the network traffic carrying capacity). The goal of thi ..."
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Cited by 304 (4 self)
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Topology Control (TC) is one of the most important techniques used in wireless ad hoc and sensor networks to reduce energy consumption (which is essential to extend the network operational time) and radio interference (with a positive effect on the network traffic carrying capacity). The goal of this technique is to control the topology of the graph representing the communication links between network nodes with the purpose of maintaining some global graph property (e.g., connectivity), while reducing energy consumption and/or interference that are strictly related to the nodes ’ transmitting range. In this article, we state several problems related to topology control in wireless ad hoc and sensor networks, and we survey stateoftheart solutions which have been proposed to tackle them. We also outline several directions for further research which we hope will motivate researchers to undertake additional studies in this field.
Efficient routing in intermittently connected mobile networks: The multiplecopy case
, 2008
"... Intermittently connected mobile networks are wireless networks where most of the time there does not exist a complete path from the source to the destination. There are many real networks that follow this model, for example, wildlife tracking sensor networks, military networks, vehicular ad hoc net ..."
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Cited by 303 (18 self)
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Intermittently connected mobile networks are wireless networks where most of the time there does not exist a complete path from the source to the destination. There are many real networks that follow this model, for example, wildlife tracking sensor networks, military networks, vehicular ad hoc networks, etc. In this context, conventional routing schemes fail, because they try to establish complete endtoend paths, before any data is sent. To deal with such networks researchers have suggested to use floodingbased routing schemes. While floodingbased schemes have a high probability of delivery, they waste a lot of energy and suffer from severe contention which can significantly degrade their performance. Furthermore, proposed efforts to reduce the overhead of floodingbased schemes have often been plagued by large delays. With this in mind, we introduce a new family of routing schemes that “spray ” a few message copies into the network, and then route each copy independently towards the destination. We show that, if carefully designed, spray routing not only performs significantly fewer transmissions per message, but also has lower average delivery delays than existing schemes; furthermore, it is highly scalable and retains good performance under a large range of scenarios. Finally, we use our theoretical framework proposed in our 2004 paper to analyze the performance of spray routing. We also use this theory to show how to choose the number of copies to be sprayed and how to optimally distribute these copies to relays.
PowerAware Localized Routing in Wireless Networks
, 2000
"... Recently, a cost aware metric for wireless networks based on remaining battery power at nodes was proposed for shortestcost routing algorithms, assuming constant transmission power. Power aware metrics where transmission power depends on distance between nodes, and corresponding shortestpower algo ..."
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Cited by 298 (33 self)
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Recently, a cost aware metric for wireless networks based on remaining battery power at nodes was proposed for shortestcost routing algorithms, assuming constant transmission power. Power aware metrics where transmission power depends on distance between nodes, and corresponding shortestpower algorithms were also recently proposed. We define a new powercost metric based on the combination of both node's lifetime and distance based power metrics. We investigate some properties of power adjusted transmissions, and show that, if additional nodes can be placed at desired locations between two nodes at distance d, the transmission power can be made linear in d as opposed to d a dependence for a2. This provides basis for power, cost, and powercost localized routing algorithms, where nodes make routing decisions solely on the basis of location of their neighbors and destination. Power aware routing algorithm attempts to minimize the total power needed to route a message between a source...
Stochastic Geometry and Random Graphs for the Analysis and Design of Wireless Networks
"... Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, mathematical techniques have been developed in the last decade to provide communicationtheoretic results accoun ..."
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Cited by 240 (42 self)
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Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, mathematical techniques have been developed in the last decade to provide communicationtheoretic results accounting for the network’s geometrical configuration. Often, the location of the nodes in the network can be modeled as random, following for example a Poisson point process. In this case, different techniques based on stochastic geometry and the theory of random geometric graphs – including point process theory, percolation theory, and probabilistic combinatorics – have led to results on the connectivity, the capacity, the outage probability, and other fundamental limits of wireless networks. This tutorial article surveys some of these techniques, discusses their application to model wireless networks, and presents some of the main results that have appeared in the literature. It also serves as an introduction to the field for the other papers in this special issue.