Connectivity Times for Mobile D2D Networks

Smith, Peter J.; Coon, Justin P.

doi:10.1109/icc.2018.8422587

Cited by 5 publications

(5 citation statements)

References 10 publications

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“…The best known special case is the two-dimensional OU process where v(x) = αx for some positive constant, α. In this case, the processes, X 1 (t), X 2 (t) R(t) are well known, see for example [26, p.234] and [29], and extensive transient as well as steady state results are available since, in this case, X 1 (t), X 2 (t) are Gaussian. In most other cases the transient solution is not available but steady state results on the displacement PDF, connectivity probability, MFHT and kinetic energy are given in Secs.…”

Section: Special Casesmentioning

confidence: 99%

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Control Mechanisms for Mobile Devices

Smith

Singh

Dmochowski

et al. 2023

IEEE Trans. Veh. Technol.

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In this paper we consider control mechanisms for mobile devices in a stochastic environment. In particular, we consider a device in n-dimensional space subject to Brownian perturbations where a control mechanism moves the device towards its target location at a speed which is a function of its displacement. For this scenario, we construct stochastic differential equations for the mobility process and solve for the steady state probability density function of displacement. From this we are able to give general solutions to key metrics such as displacement outage (the long term probability of exceeding a given distance from the target), connectivity probability (derived from the SNR distribution in a Rayleigh channel with pathloss), the mean time at which the device first exceeds a given distance from the target, and the mean kinetic energy required by the control mechanism. We evaluate these metrics for important special cases of the control mechanism and also study the optimization problem of minimizing kinetic energy over the parameters of the control function.

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Section: Special Casesmentioning

confidence: 99%

“…) Hence, using the recursion in (29), I m can be solved in terms of I 0 which is given in [30,Eq. 3.322.1].…”

Section: A Ramp Control (Rc) and On-off Control (Oc)mentioning

confidence: 99%

Control Mechanisms for Mobile Devices

Smith

Singh

Dmochowski

et al. 2023

IEEE Trans. Veh. Technol.

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“…Proof: To obtain the pdf, apply the principle of random variable transformation to (7) and the result follows. The cdf, instead, is obtained by integrating the pdf in (15).…”

Section: Corollary 3 the Density Function Of The Link Snr Ismentioning

confidence: 99%

“…The link performance is fundamentally determined by the instantaneous SNR and, hence, it has been extensively analyzed in the literature. Authors in [7] used the link SNR to evaluate the mean proportion of time that two mobile devices are connected for five different types of mobility (including Ornstein-Uhlenbeck mobility). In [8], the authors characterized variations in the SNR process to study the coverage and outage durations experienced by mobile users, while, in [9] they studied the time variations of the SNR in the absence of fading experienced when a mobile user moves across a Poisson cellular network.…”

Section: Introductionmentioning

confidence: 99%

Statistical Properties of Transmissions Subject to Rayleigh Fading and Ornstein-Uhlenbeck Mobility

Cika¹,

Badiu²,

Coon³

2019

Preprint

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In this paper, we derive closed-form expressions for significant statistical properties of the link signal-to-noise ratio (SNR) and the separation distance in mobile ad hoc networks subject to Ornstein-Uhlenbeck (OU) mobility and Rayleigh fading. In these systems, the SNR is a critical parameter as it directly influences link performance. In the absence of signal fading, the distribution of the link SNR depends exclusively on the squared distance between nodes, which is governed by the mobility model. In our analysis, nodes move randomly according to an Ornstein-Uhlenbeck process, using one tuning parameter to control the temporal dependency in the mobility pattern. We derive a complete statistical description of the squared distance and show that it forms a stationary Markov process. Then, we compute closed-form expressions for the probability density function (pdf), the cumulative distribution function (cdf), the bivariate pdf, and the bivariate cdf of the link SNR. Next, we introduce small-scale fading, modeled by a Rayleigh random variable, and evaluate the pdf of the link SNR for rational path loss exponents. The validity of our theoretical analysis is verified by extensive simulation studies. The results presented in this work can be used to quantify link uncertainty and evaluate stability in mobile ad hoc wireless systems.

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“…Each of these synthetic models, while allowing analysis, possesses undesirable features, such as piecewise motion for waypoint models and unbounded wandering in Brownian motion. Critically, they lack the ability to explicitly model the control mechanism which attempts to return the node to the desired location [9]. Hence, in this paper, we are motivated to create a family of 3D mobility models based on stochastic differential equations (SDEs) which explicitly allow the use of different control mechanisms and lead to tractable steady state solutions.…”

Section: Introductionmentioning

confidence: 99%

3D Mobility Models and Analysis for UAVs

Smith

Dmochowski

Singh

et al. 2020

2020 IEEE 31st Annual International Symposium on Personal, Indoor and Mobile Radio Communications

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We present a flexible family of 3D mobility models suitable for unmanned aerial vehicles (UAV). Based on stochastic differential equations, the models offer a unique property of explicitly incorporating the mobility control mechanism and environmental perturbation, while enabling tractable steady state solutions for properties such as position and connectivity. Specifically, motivated by UAV flight data, for a symmetric mobility model with an arbitrary control mechanism, we derive the steady state distribution of the distance from the target position. We provide closed form expressions for the special cases of the Ornstein-Uhlenbeck (OU) process and on-off control (OC). We extend the model to incorporate imperfect positioning and asymmetric control. For a practically relevant scenario of partial symmetry (such as in the x-y plane), we present steady state position results for the OU control. Building on these results, we derive UAV connectivity probability results based on a SNR criterion in a Rayleigh fading environment.

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Connectivity Times for Mobile D2D Networks

Cited by 5 publications

References 10 publications

Control Mechanisms for Mobile Devices

Control Mechanisms for Mobile Devices

Statistical Properties of Transmissions Subject to Rayleigh Fading and Ornstein-Uhlenbeck Mobility

3D Mobility Models and Analysis for UAVs

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