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60
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 256 (7 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.
Movementbased location update and selective paging for PCS networks
 IEEE/ACM Transactions on Networking
, 1996
"... Abstract This paper introduces a mobility tracking mechanism that combines a movementbased location update policy with a selective paging scheme. Movementbased location update is selected for its simplicity. It does not require ea & mobile terminal to store information about the arrangement and t ..."
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Cited by 128 (9 self)
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Abstract This paper introduces a mobility tracking mechanism that combines a movementbased location update policy with a selective paging scheme. Movementbased location update is selected for its simplicity. It does not require ea & mobile terminal to store information about the arrangement and the distance relationship of all cells. In fact, each mobile terminal only keeps a counter of the number of cells visited. A location update is performed when this counter exceeds a predefined threshold value. This scheme allows the dynamic selection of the movement threshold on a peruser basis. This is desirable as different users may have very different mobility patterns. Selective paging reduces the cost for locating a mobile terminal in the expense of an increase in the paging delay. In this paper, we propose a selective paging scheme which significantly decreases the location tracking cost under a small increase in the allowable paging delay. We introduce an analytical model for the proposed location tracking mechanism which captures the mobility and the incoming call arrival patterns of each mobile terminal. Analytical results are provided to demonstrate the costeffectiveness of the proposed scheme under various parameters. Index TermsPersonal communication networks, location update, terminal paging, mobile terminal. I.
Delay and Capacity Tradeoffs for Wireless Ad Hoc Networks with Random Mobility
, 2005
"... In this paper, we study the delay and capacity tradeoffs for wireless ad hoc networks with random mobility. We consider some simple distributed scheduling and relaying protocols that are motivated by the 2hop relaying protocol proposed by Grossglauser and Tse (2001). We consider a model in which t ..."
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Cited by 31 (3 self)
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In this paper, we study the delay and capacity tradeoffs for wireless ad hoc networks with random mobility. We consider some simple distributed scheduling and relaying protocols that are motivated by the 2hop relaying protocol proposed by Grossglauser and Tse (2001). We consider a model in which the nodes are placed uniformly on a sphere, and move in accordance with an i.i.d. mobility model. We consider two i.i.d mobility models: Brownian mobility model and random waypoint mobility model. We show that under a distributed GrossglauserTse 2hop relaying protocol, the delay scales as Θ(T_p(n)n) for random waypoint mobility model, and O(T_p(n)log²n) for Brownian mobility model, where T_p(n) is the transmission time of the packet. In the case, where only nearest neighbor transmissions are allowed, the delay is shown to scale as &Omega(T_p(n)√n), for all possible scheduling and relaying protocols. In the case of random waypoint mobility model, we show that delay/capacity ≥ Θ(T_p(n)n) is a necessary tradeoff. Two protocols which achieve the lower bound of Θ(T_p(n)n) are considered, and their relative performance in terms of delay/capacity tradeoff is established. Our results indicate that significant improvement in the delay can be achieved by reducing the packet size, at high node speeds.
Degenerate DelayCapacity Tradeoffs in AdHoc Networks with Brownian Mobility
 IEEE/ACM Trans. Netw
, 2006
"... Abstract — There has been significant recent interest within the networking research community to characterize the impact of mobility on the capacity and delay in mobile ad hoc networks. In this paper, we study the fundamental tradeoff between the capacity and delay for a mobile ad hoc network unde ..."
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Cited by 29 (1 self)
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Abstract — There has been significant recent interest within the networking research community to characterize the impact of mobility on the capacity and delay in mobile ad hoc networks. In this paper, we study the fundamental tradeoff between the capacity and delay for a mobile ad hoc network under the Brownian motion model. We show that the 2hop relaying scheme proposed by Grossglauser and Tse (2001), while capable of achieving Θ(1) pernode capacity, incurs an expected packet delay of Ω(log n/σ 2 n), where σ 2 n is the variance parameter of the Brownian motion model. We then show that in order to reduce the delay by any significant amount, one must be ready to accept a pernode capacity close to static ad hoc networks. In particular, we show that under a large class of scheduling and relaying schemes, if the mean packet delay is O(n α /σ 2 n), for any α < 0, then the pernode capacity must be O(1 / √ n). This result is in sharp contrast to other results that have recently been reported in the literature. I.
Survey of decision field theory
, 2002
"... This article summarizes the cumulative progress of a cognitivedynamical approach to decision making and preferential choice called decision field theory. This review includes applications to (a) binary decisions among risky and uncertain actions, (b) multiattribute preferential choice, (c) multia ..."
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Cited by 28 (5 self)
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This article summarizes the cumulative progress of a cognitivedynamical approach to decision making and preferential choice called decision field theory. This review includes applications to (a) binary decisions among risky and uncertain actions, (b) multiattribute preferential choice, (c) multialternative preferential choice, and (d) certainty equivalents such as prices. The theory provides natural explanations for violations of choice principles including strong stochastic transitivity, independence of irrelevant alternatives, and regularity. The theory also accounts for the relation between choice and decision time, preference reversals between choice and certainty equivalents, and preference reversals under time pressure. Comparisons with other dynamic models of decisionmaking and other random utility models of preference are discussed.
A particle migrating randomly on a sphere
 J. Theoretical Prob
, 1997
"... Consider a particle moving on the surface of the unit sphere in R 3 and heading towards a specific destination with a constant average speed, but subject to random deviations. The motion is modeled as a diffusion with drift restricted to the surface of the sphere. Expressions are set down for variou ..."
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Cited by 21 (11 self)
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Consider a particle moving on the surface of the unit sphere in R 3 and heading towards a specific destination with a constant average speed, but subject to random deviations. The motion is modeled as a diffusion with drift restricted to the surface of the sphere. Expressions are set down for various characteristics of the process including expected travel time to a cap, the limiting distribution, the likelihood ratio and some estimates for parameters appearing in the model. KEY WORDS: Drift; great circle path; likelihood ratio; poleseeking; skew product; spherical Brownian motion; stochastic differential equation; travel time. 1.
THE MARKOV CHAIN MONTE CARLO REVOLUTION
"... Abstract. The use of simulation for highdimensional intractable computations has revolutionized applied mathematics. Designing, improving and understanding the new tools leads to (and leans on) fascinating mathematics, from representation theory through microlocal analysis. 1. ..."
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Cited by 18 (1 self)
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Abstract. The use of simulation for highdimensional intractable computations has revolutionized applied mathematics. Designing, improving and understanding the new tools leads to (and leans on) fascinating mathematics, from representation theory through microlocal analysis. 1.
Quantitative bounds for convergence rates of continuous time Markov processes
, 1996
"... We develop quantitative bounds on rates of convergence for continuoustime Markov processes on general state spaces. Our methods involve coupling and shiftcoupling, and make use of minorization and drift conditions. In particular, we use auxiliary coupling to establish the existence of small (or pseu ..."
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Cited by 16 (6 self)
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We develop quantitative bounds on rates of convergence for continuoustime Markov processes on general state spaces. Our methods involve coupling and shiftcoupling, and make use of minorization and drift conditions. In particular, we use auxiliary coupling to establish the existence of small (or pseudosmall) sets. We apply our method to some diffusion examples. We are motivated by interest in the use of Langevin diffusions for Monte Carlo simulation.
Quantum dynamics of human decisionmaking
, 2006
"... A quantum dynamic model of decisionmaking is presented, and it is compared with a previously established Markov model. Both the quantum and the Markov models are formulated as random walk decision processes, but the probabilistic principles differ between the two approaches. Quantum dynamics descri ..."
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Cited by 14 (4 self)
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A quantum dynamic model of decisionmaking is presented, and it is compared with a previously established Markov model. Both the quantum and the Markov models are formulated as random walk decision processes, but the probabilistic principles differ between the two approaches. Quantum dynamics describe the evolution of complex valued probability amplitudes over time, whereas Markov models describe the evolution of real valued probabilities over time. Quantum dynamics generate interference effects, which are not possible with Markov models. An interference effect occurs when the probability of the union of two possible paths is smaller than each individual path alone. The choice probabilities and distribution of choice response time for the quantum model are derived, and the predictions are contrasted with the Markov model.
A cascade decomposition theory with applications to Markov and exchangeable cascades, T rans
 Amer. Math. Soc
, 1996
"... Abstract. A multiplicative random cascade refers to a positive Tmartingale in the sense of Kahane on the ultrametric space T = {0, 1,...,b−1} N. Anew approach to the study of multiplicative cascades is introduced. The methods apply broadly to the problems of: (i) nondegeneracy criterion, (ii) dime ..."
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Cited by 13 (2 self)
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Abstract. A multiplicative random cascade refers to a positive Tmartingale in the sense of Kahane on the ultrametric space T = {0, 1,...,b−1} N. Anew approach to the study of multiplicative cascades is introduced. The methods apply broadly to the problems of: (i) nondegeneracy criterion, (ii) dimension spectra of carrying sets, and (iii) divergence of moments criterion. Specific applications are given to cascades generated by Markov and exchangeable processes, as well as to homogeneous independent cascades. 1. Positive Tmartingales Positive Tmartingales were introduced by JeanPierre Kahane as the general framework for independent multiplicative cascades and random coverings. Although originating in statistical theories of turbulence, the general framework also includes certain spinglass and random polymer models as well as various other spatial distributions of interest in both probability theory and the physical sciences. For basic definitions, let T be a compact metric space with Borel sigmafield B, and let (Ω, F,P) be a probability space together with an increasing sequence Fn,n =1,2,..., of subsigmafields of F. A positive Tmartingale is a sequence {Qn} of B×F−measurable nonnegative functions on T × Ω such that (i) For each t ∈ T,{Qn(t, ·):n=0,1,...} is a martingale adapted to Fn,n =0,1,...; (ii) For Pa.s. ω ∈ Ω, {Qn(·,ω):n=0,1,...} is a sequence of Borel measurable nonnegative realvalued functions on T. Let M +(T) denote the space of positive Borel measures on T and suppose that {Qn(t)} is a positive Tmartingale. For σ ∈ M +(T) such that q(t):=EQn(t) ∈ L1 (σ), let σn ≡ Qnσ denote the random measure defined by Qnσ << σ and dQnσ dσ (t):=Qn(t),t∈T. Then, essentially by the martingale convergence theorem, one obtains a random Borel measure σ ∞ ≡ Q∞σ such that for f ∈ C(T), (1.1) lim f(t)Qn(t, ω)σ(dt) = f(t)Q∞σ(dt, ω) a.s. n→∞