Quantifying Link Stability in Ad Hoc Wireless Networks Subject to Ornstein-Uhlenbeck Mobility

The performance of mobile ad hoc networks in general and that of the routing algorithm, in particular, can be heavily affected by the intrinsic dynamic nature of the underlying topology. In this paper, we build a new analytical/numerical framework that characterizes nodes' mobility and the evolution of links between them. This formulation is based on a stationary Markov chain representation of link connectivity. The existence of a link between two nodes depends on their distance, which is governed by the mobility model. In our analysis, nodes move randomly according to an Ornstein-Uhlenbeck process using one tuning parameter to obtain different levels of randomness in the mobility pattern. Finally, we propose an entropy-rate-based metric that quantifies link uncertainty and evaluates its stability. Numerical results show that the proposed approach can accurately reflect the random mobility in the network and fully captures the link dynamics. It may thus be considered a valuable performance metric for the evaluation of the link stability and connectivity in these networks.Comment: 6 pages, 4 figures, Submitted to IEEE International Conference on Communications 201

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

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, modelled 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

Quantifying Link Stability in Ad Hoc Wireless Networks Subject to Ornstein-Uhlenbeck Mobility

The performance of mobile ad hoc networks in general and that of the routing algorithm, in particular, can be heavily affected by the intrinsic dynamic nature of the underlying topology. In this paper, we build a new analytical/numerical framework that characterizes nodes' mobility and the evolution of links between them. This formulation is based on a stationary Markov chain representation of link connectivity. The existence of a link between two nodes depends on their distance, which is governed by the mobility model. In our analysis, nodes move randomly according to an Ornstein-Uhlenbeck process using one tuning parameter to obtain different levels of randomness in the mobility pattern. Finally, we propose an entropy-rate-based metric that quantifies link uncertainty and evaluates its stability. Numerical results show that the proposed approach can accurately reflect the random mobility in the network and fully captures the link dynamics. It may thus be considered a valuable performance metric for the evaluation of the link stability and connectivity in these networks

Anticipating Critical Transitions in Psychological Systems using Early Warning Signals: Theoretical and Practical Considerations

Many real-world systems can exhibit tipping points and multiple stable states, creating the potential for sudden and difficult to reverse transitions into a less desirable regime. The theory of dynamical systems points to the existence of generic early warning signals that may precede these so-called critical transitions. Recently, psychologists have begun to conceptualize mental disorders such as depression as an alternative stable state, and suggested that early warning signals based on the phenomenon of critical slowing down might be useful for predicting transitions into depression or other psychiatric disorders. Harnessing the potential of early warning signals requires us to understand their limitations as well as the factors influencing their performance in practice. In this paper, we (a) review limitations of early warning signals based on critical slowing down to better understand when they can and cannot occur, and (b) study the conditions under which early warning signals may anticipate critical transitions in online-monitoring settings by simulating from a bistable dynamical system, varying crucial features such as sampling frequency, noise intensity, and speed of approaching the tipping point. We find that, in sharp contrast to their reputation of being generic or model-agnostic, whether early warning signals occur or not strongly depends on the specifics of the system. We also find that they are very sensitive to noise, potentially limiting their utility in practical applications. We discuss the implications of our findings and provide suggestions and recommendations for future research