The stochastic model assumed to govern the mobility of nodes in a mobile ad hoc network has been shown to significantly affect the network's coverage, maximum throughput, and achievable throughput-delay trade-offs. In this paper, we compare several mobility models, including the random walk, random waypoint, and Manhattan models on the basis of the number of states visited in a fixed time, the time to visit every state in a region, and the effect of the number of wandering nodes on the time to first enter a set of states. These metrics for a mobility model are useful for assessing the achievable event detection rates in surveillance applications where wireless-sensor-equipped vehicles are used to detect events of interest in a city. We also consider mobility models based on Correlated Random Walks, which can account for time dependency, geographical restrictions, and nonzero drift. We demonstrate that these models are analytically tractable by using a matrix-analytic approach to derive new, closed-form results in both the time and transform-domains for the probability that a node is at any location at any time for both semi-infinite and finite 1D lattices. We also derive first entrance time distributions for these walks. We find that a correlated random walk 1) covers more ground in a given amount of time and takes a smaller amount of time to cover an area completely than a random walk with the same average transition rate, 2) has a smaller first entrance time to small sets of states than the random waypoint and random walk models, and 3) leads to a uniform distribution of nodes (except at the boundaries) in steady state.

In a sensor cluster, a large number of geographically distributed sensor nodes each make local measurements and transmit them toward the clusterhead. The clusterhead may schedule simultaneous transmissions from nodes within the cluster by identifying non-interfering areas in the cluster. Directional antennas that are oriented toward the clusterhead may increase spatial reuse and thus increase the number of simultaneous transmissions. On the other hand, the antennas' narrower coverage areas may reduce connectivity, thus reducing the number of sensors from which data can be collected. In this paper, we investigate this tradeoff between spatial reuse and connectivity in the context of the spatiotemporal sampling rate that can be achieved by the cluster. We also propose a simple analytical approach to optimizing the antennas beam width in order to improve the spatiotemporal sampling rate by maximizing the transport capacity of the network

To enable proper functioning of wireless ad hoc networks, all nodes in the network are expected to cooperate in forwarding each other's packet. But relaying other nodes' packets involves spending energy without getting any immediate revenue. Hence, due to the constraints on available energy the nodes usually have in such networks, from an individual node's point of view, the best response is always not to cooperate. We model this problem as a repeated game and show analytically that given a suitable punishment mechanism, individual nodes can be deterred from their selfish behavior, and cooperation can emerge as the best response. We also show that generosity by other nodes cannot be part of a credible deterrent mechanism.

A multi-hop network of wireless sensors can be used to gather spatio-temporal samples of a physical phenomenon and transmit these samples to a processing center. This paper addresses an important issue in the design of such networks: determining the spatio-temporal sampling rate of the network under conditions of minimum energy usage. A new collision-free protocol for gathering sensor data is-used to obtain analytical results that characterize the tradeoffs among sensor density, energy usage, throughput, delay, temporal sampling rates and spatial sampling rates in wireless sensor networks. We also show that the lower bound on the delay incurred in gathering data is O(k(2)n) in a clustered network of n sensors with at most k hops between any sensor and its clusterhead (CH). Simulation results on the tradeoff between the achievable spatial sampling rates and the achievable temporal sampling rates when IEEE 802.11 distributed coordination function (DCF) is used as the media access scheme are provided and compared with the analytical results obtained in this paper.

A multihop network of wireless sensors can be used to gather spatio-temporal samples of a physical phenomenon and transmit these samples to a processing center. This paper addresses an important issue in the design of such networks: determining the spatio-temporal sampling rate of the network under conditions of minimum energy usage. Prior results on the design of energy-minimizing clustering algorithms and a new collision-free protocol for gathering sensor data are used to obtain analytical results that characterize the tradeoffs among sensor density, energy usage, temporal sampling rates and spatial sampling rates in wireless sensor networks. We also show that the lower bound on delay incurred in gathering data is O(k/sup 2/n) in a clustered network of n sensors with at most k hops between any sensor and its CH.

A wireless network consisting of a large number of small sensors with low-power 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 limited 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.

This paper develops a technique for quantifying and minimizing the energy required to gather data from all sensors in a multi-hop wireless sensor network The technique combines analytical results from stochastic geometry with a distributed, randomized algorithm for generating clusters. The minimum communication energy achieved by this approach is significantly lower than the energy costs incurred in non-clustered networks and in clustered networks produced by such algorithms as the max-min d-cluster algorithm.