There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

Power Aware Routing in Mobile Ad Hoc Networks

Network lifetime has become the key characteristic for evaluating sensor networks in an application-specific way. Especially the availability of nodes, the sensor coverage, and the connectivity have been included in discussions on network lifetime. Even quality of service measures can be reduced to lifetime considerations. A great number of algorithms and methods were proposed to increase the lifetime of a sensor network—while their evaluations were always based on a particular definition of network lifetime. Motivated by the great differences in existing definitions of sensor network lifetime that are used in relevant publications, we reviewed the state of the art in lifetime definitions, their differences, advantages, and limitations. This survey was the starting point for our work towards a generic definition of sensor network lifetime for use in analytic evaluations as well as in simulation models—focusing on a formal and concise definition of accumulated network lifetime and total network lifetime. Our definition incorporates the components of existing lifetime definitions, and introduces some additional measures. One new concept is the ability to express the service disruption tolerance of a network. Another new concept is the notion of time-integration: in many cases, it is sufficient if a requirement is fulfilled over a certain period of time, instead of at every point in time. In addition, we combine coverage and connectivity to form a single requirement called connected coverage. We show that connected coverage is different from requiring noncombined coverage and connectivity. Finally, our definition also supports the concept of graceful degradation by providing means of estimating the degree of compliance with the application requirements. We demonstrate the applicability of our definition based on the surveyed lifetime definitions as well as using some example scenarios to explain the various aspects influencing sensor network lifetime.

/pdf/on-the-lifetime-of-wireless-sensor-networks-59hdyqoqi3.pdf

On the lifetime of wireless sensor networks

Review: Coverage and connectivity issues in wireless sensor networks: A survey

In this paper we focus on characterizing the average end-to-end delay and maximum achievable per-node throughput in random access multihop wireless ad hoc networks with stationary nodes. We present an analytical model that takes into account the number of nodes, the random packet arrival process, the extent of locality of traffic, and the back off and collision avoidance mechanisms of random access MAC. We model random access multihop wireless networks as open G/G/1 queuing networks and use the diffusion approximation to evaluate closed form expressions for the average end-to-end delay. The mean service time of nodes is derived and used to obtain the maximum achievable per-node throughput. The analytical results obtained here from the queuing network analysis are discussed with regard to similarities and differences from the well established information-theoretic results on throughput and delay scaling laws in ad hoc networks. We perform extensive simulations and verify that the analytical results closely match the results obtained from simulations.

/pdf/queuing-network-models-for-delay-analysis-of-multihop-5do4seutgn.pdf

Queuing network models for delay analysis of multihop wireless ad hoc networks

Mobile sensors cover more area over a period of time than the same number of stationary sensors. However, the quality of coverage achieved by mobile sensors depends on the velocity, mobility pattern, number of mobile sensors deployed and the dynamics of the phenomenon being sensed. The gains attained by mobile sensors over static sensors and the optimal motion strategies for mobile sensors are not well understood. In this paper we consider the problem of event capture using mobile sensors. The events of interest arrive at certain points in the sensor field and fade away according to arrival and departure time distributions. An event is said to be captured if it is sensed by one of the mobile sensors before it fades away. For this scenario we analyze how the quality of coverage scales with the velocity, path and number of mobile sensors. We characterize the cases where the deployment of mobile sensors has no advantage over static sensors and find the optimal velocity pattern that a mobile sensor should adopt.We also present algorithms for two motion planning problems: (i) for a single sensor, what is the minimum speed and sensor trajectory required to satisfy a bound on event loss probability and (ii) for sensors with fixed speed, what is the minimum number of sensors required to satisfy a bound on event loss probability. When events occur only along a line or a closed curve our algorithms return optimal velocity for the minimum velocity problem. For the minimum sensor problem, the number of sensors used is within a factor two of the optimal solution. For the case where the events occur at arbitrary points on a plane we present heuristic algorithms for the above motion planning problems and bound their performance with respect to the optimal. The results of this paper have wide range of applications in areas like surveillance, wildlife monitoring, hybrid sensor networks and under-water sensor networks.

/pdf/stochastic-event-capture-using-mobile-sensors-subject-to-a-uya1v5rth3.pdf

Stochastic event capture using mobile sensors subject to a quality metric

In this paper we analyze the average end-to-end delay and maximum achievable per-node throughput in random access multihop wireless ad hoc networks with stationary nodes. We present an analytical model that takes into account the number of nodes, the random packet arrival process, the extent of locality of traffic, and the back off and collision avoidance mechanisms of random access MAC. We model random access multihop wireless networks as open G/G/1 queuing networks and use the diffusion approximation in order to evaluate closed form expressions for the average end-to-end delay. The mean service time of nodes is evaluated and used to obtain the maximum achievable per-node throughput. The analytical results obtained here from the queuing network analysis are discussed with regard to similarities and differences from the well established information-theoretic results on throughput and delay scaling laws in ad hoc networks. We also investigate the extent of deviation of delay and throughput in a real world network from the analytical results presented in this paper. We conduct extensive simulations in order to verify the analytical results and also compare them against NS-2 simulations.

/pdf/queuing-network-models-for-delay-analysis-of-multihop-4r42leyg8d.pdf

In this paper, we study the problem of designing motion strategies for a team of mobile agents, required to fulfill request for on-site service in a given planar region In our model, each service request is generated by a spatio-temporal stochastic process; once a service request has been generated, it remains active for a certain deterministic amount of time, and then expires An active service request is fulfilled when one of the mobile agents visits the location of the request Specific problems we investigate are the following: what is the minimum number of mobile agents needed to ensure that a certain fraction of service requests is fulfilled before expiration? What strategy should they use to ensure that this objective is attained? This problem can be viewed as the stochastic and dynamic version of the well-known vehicle routing problem with time windows We also extend our analysis to the case in which the time service requests remain active is itself a random variable, describing customer impatience The customers' impatience is only known to the mobile agents via prior statistics In this case, it is desired to minimize the fraction of service requests missed because of impatience Finally, we show how the routing strategies presented in the paper can be executed in a distributed fashion

/pdf/a-stochastic-and-dynamic-vehicle-routing-problem-with-time-3b3xbuxg9m.pdf

A Stochastic and Dynamic Vehicle Routing Problem with Time Windows and Customer Impatience

In this paper we develop a model for random walk search mechanism in unstructured P2P networks. Using the model we obtain analytical expressions for the performance metrics of random walk search in terms of the popularity of the resource being searched for and the parameters of random walk. We propose an equation based adaptive search mechanism that uses estimate of popularity of a resource in order to choose the parameters of random walk such that a targeted performance level is achieved by the search. We also propose a low-overhead method for maintaining an estimate of popularity that utilizes feedback (or lack there-off) obtained from previous searches. Simulation results show that the performance of the equation based adaptive search is significantly better than the non-adaptive random walk.

/pdf/modeling-and-analysis-of-random-walk-search-algorithms-in-560hex5pgs.pdf

Nabhendra Bisnik

Papers

Queuing network models for delay analysis of multihop wireless ad hoc networks

Stochastic event capture using mobile sensors subject to a quality metric

Queuing network models for delay analysis of multihop wireless ad hoc networks

A Stochastic and Dynamic Vehicle Routing Problem with Time Windows and Customer Impatience

Modeling and analysis of random walk search algorithms in P2P networks