[show abstract][hide abstract] ABSTRACT: In wireless networks, the channels are often subject to random variations that limit the reliability of communications between any two radios. Geographic transmission strategies can improve the performance in such networks, by allowing any of a transmitter's neighbors that success- fully receive a transmission and are in the direction of the packet's destination to forward the packet on to the destination. However, requiring all of the radios in a network to keep their receivers on to receive geographic transmissions will significantly shorten the network lifetime by depleting the energy of the radios in the network. In this work, we investigate an optimal strategy for deciding which neighbors of a transmitter should activate to try to recover a transmission. We find a solution to this problem by solving for a related measure in a constrained optimization problem. We present results that compare the performance of the optimal approach, our previous suboptimal eorts, and a conventional approach. time to deploy such resources. Such scenarios typically arise in tactical military communications and during disaster- recovery operations. The communication signals in wireless MANETs usually experi- ence significant losses from both electromagnetic attenuation over distance and mul- tipath fading. Multipath fading, often just called fading, is a random phenomenon caused when the transmitted signal reflects o objects in the environment. The sig-
SIAM Journal of Applied Mathematics. 01/2011; 71:586-604.
[show abstract][hide abstract] ABSTRACT: In multi-hop packet radio networks with low mobility, forwarding strategies based on the location of the radios are considered to be quite robust and scalable since they consume less network resources for the exchange and storage of network state information than conventional routing. When such geographical forwarding strategies are used over fading channels, the presence of multiple potential forwarding agents provides multi-user diversity. However, the number of radios that should keep their receivers active during a transmission may need to be limited to conserve the energy of mobile devices. Since receivers at different distances from the transmitter have different probabilities of recovering a message, we have previously proposed node activation based on link distance (NA-BOLD) schemes to increase the transmission distance and/or transport capacity, with a constraint on the energy used in reception (which depends on the number of nodes that activate to receive a transmission). In this work, we consider a total energy constraint, i.e., a constraint on the sum of the energies used in transmission and reception. We optimize the allocation of energy between transmission and reception when nodes activate using NA-BOLD approaches.
[show abstract][hide abstract] ABSTRACT: In earlier works, the gauge theorem was proved for additive functionals of Brownian motion of the form
)ds, whereq is a function in the Kato class. Subsequently, the theorem was extended to additive functionals with Revuz measures in the Kato class. We prove that the gauge theorem holds for a large class of additive functionals of zero energy which are, in general, of unbounded variation. These additive functionals may not be semi-martingales, but correspond to a collection of distributions that belong to the Kato class in a suitable sense. Our gauge theorem generalizes the earlier versions of the gauge theorem.
Probability Theory and Related Fields 02/1993; 97(1):195-210. · 1.39 Impact Factor
[show abstract][hide abstract] ABSTRACT: Let (X(t),P
x) and (X(t))},PP}x) be two Hunt processes in duality with respect to an excessive measure ξ and having resolvents that commute. The main result of this article is that if there is an ε with 0<ε<1 so that (U
1f‖2 for everyf in ℒ2(ξ), thenX(t) satisfies Hunt's hypothesis (H): every set that is semipolar forX(t) is polar forX(t).
Journal of Theoretical Probability 10/1988; 1(4). · 0.55 Impact Factor
[show abstract][hide abstract] ABSTRACT: Two methods for symmetrizing Markov processes are discussed. Letu
a(x, y) be the potential density of a Lvy process on a compact Abelian groupG. A general condition is given that guarantees thatv(x, y)=ua(x, y)+ua(y, x) is the potential density of a symmetric Lvy process onG. The second method arises by considering the linear space of one-potentialsU
f, withf inL
2, endowed with the inner product (U
f. If the semigroup ofX(t) is normal, then the completionH of this space is the Dirichlet space of a symmetric processY(t). A set that is semipolar forX(t) is polar forY(t).
Journal of Theoretical Probability 06/1988; 1(3):305-325. · 0.55 Impact Factor
[show abstract][hide abstract] ABSTRACT: A large class of Markov processes satisfying Hunt's hypothesis (H) is displayed. In particular, if $\Phi$ is a Levy-Khinchin exponent, then the Levy process with exponent $\Phi^\alpha (0 < \alpha < 1)$ satisfies (H). That is, every semipolar set is polar.
The Annals of Probability 07/1986; · 1.38 Impact Factor
[show abstract][hide abstract] ABSTRACT: We consider a collection of battery-operated, low- power sensors randomly deployed within a geographic region for the purpose of sensing/monitoring the environment. We assume that a transmitting sensor broadcasts messages to receiver nodes over a randomly varying(fading) wireless channel. With the intention of maximizing overall network lifetime in such a setting, we propose a protocol that allows the receivers to sleep (power off) most of the time and turn on (activate) according to a function that depends on their link distance from the transmitter. We first derive the optimum density of link distances assuming N (fixed) nodes to be awake such that the distance to the farthest successful receiver is maximized. We then extend our analysis to networks where the number of nodes are distributed according to the Poisson distribution. In particular, we utilize this optimal density function to derive a simple expression for the conditional probability that a node turns on, given its distance from the transmitter. We also derive the minimum node density and scaling constant that meets the constraint on the average number of nodes that are awake to listen to a transmission. We compare the performance of our protocol with a simpler protocol that turns on all the nodes around the transmitter upto a certain distance. For fairness in comparison, the average number of nodes that activate is kept the same in both the protocols.