Probability Distribution Of Duration Research Articles

Contention aware mobility prediction routing for intermittently connected mobile networks

This paper introduces a novel multi-copy routing protocol, called predict and forward (PF), for delay tolerant networks, which aims to explore the possibility of using mobile nodes as message carriers for end-to-end delivery of the messages. With PF, the message forwarding decision is made by manipulating the probability distribution of future inter-contact and contact durations based on the network status, including wireless link condition and nodal buffer availability. In particular, PF is based on the observations that the node mobility behavior is semi-deterministic and could be predicted once there is sufficient mobility history information. We implemented the proposed protocol and compared it with a number of existing encounter-based routing approaches in terms of delivery delay, delivery ratio, and the number of transmissions required for message delivery. The simulation results show that PF outperforms all the counterpart multi-copy encounter-based routing protocols considered in the study.

Statistical analysis and modeling of occupancy patterns in open-plan offices using measured lighting-switch data

Occupancy profile is one of the driving factors behind discrepancies between the measured and simulated energy consumption of buildings. The frequencies of occupants leaving their offices and the corresponding durations of absences have significant impact on energy use and the operational controls of buildings. This study used statistical methods to analyze the occupancy status, based on measured lighting-switch data in five-minute intervals, for a total of 200 open-plan (cubicle) offices. Five typical occupancy patterns were identified based on the average daily 24-hour profiles of the presence of occupants in their cubicles. These statistical patterns were represented by a one-square curve, a one-valley curve, a two-valley curve, a variable curve, and a flat curve. The key parameters that define the occupancy model are the average occupancy profile together with probability distributions of absence duration, and the number of times an occupant is absent from the cubicle. The statistical results also reveal that the number of absence occurrences decreases as total daily presence hours decrease, and the duration of absence from the cubicle decreases as the frequency of absence increases. The developed occupancy model captures the stochastic nature of occupants moving in and out of cubicles, and can be used to generate a more realistic occupancy schedule. This is crucial for improving the evaluation of the energy saving potential of occupancy based technologies and controls using building simulations. Finally, to demonstrate the use of the occupancy model, weekday occupant schedules were generated and discussed.

Integration between neuro-fuzzy system and Monte Carlo simulation for duration estimation of the bored piles

Traditional methods of duration prediction of the bored pile projects are far from accurate and consistent. This can be attributed to the fact that the problem in estimating the construction duration is very complex and not yet precisely understood. Neuro-fuzzy system (NFS) has been proposed to deal with several problems associated with cognitive uncertainty caused by human subjectivity. Despite the relative merits of the NFS, it cannot determine non-cognitive caused by factors such as constant change of site conditions, low technical competence of workers, material unavailability, and bad weather conditions. These factors result in the variation in activity duration. An alternative stochastic approach is necessary for providing more rational estimation of activity duration. In this paper, the probability distribution of activity duration is obtained by integrating the NFS with Monte Carlo simulation. The estimators can make a decision regarding risk factors and their impacts on the estimated duration by employing the proposed method. As a result, a more realistic estimation of the actual duration can be provided.

Large Scale Probabilistic Drought Characterization Over Europe

A reliable assessment of drought return periods is essential to help decision makers in setting effective drought preparedness and mitigation measures. However, often an inferential approach is unsuitable to model the marginal or joint probability distributions of drought characteristics, such as drought duration and accumulated deficit, due to the relatively limited number of drought events that can be observed in the historical records of the hydrological variables of interest. As an alternative, the marginal and multivariate probability cdf’s of drought characteristics can be derived as functions of the parameters of the cdf of the underlying variable (e.g. precipitation), whose sample series is usually long enough to obtain trustworthy estimates in a statistical sense. In this study, the latter methodology is applied to investigate space-time variability of drought occurrences over Europe by using the CRU TS3.10.01 precipitation dataset for the period 1901–2009. In particular, a methodology able to take into account autocorrelation in the underlying precipitation series is adopted. First, a spatial analysis of historical droughts at European level is carried out. Then, the joint probability distributions of drought duration and accumulated deficit are derived for each cell, with reference to both historical and design drought events. Finally, the corresponding bivariate drought return periods are computed, as the expected values of the interarrival time between consecutive critical droughts.Results show that several heavy drought episodes have widely affected the continent. Among the most recent events, drought occurred during the period 1985–1995 was the worst in terms of extent of the regions characterized by return periods greater than 250 years. Besides Euro-Mediterranean regions, North Western and Central Eastern regions appear more drought prone than the rest of Europe, in terms of low values of return periods.

Linking On-State Memory and Distributed Kinetics in Single Nanocrystal Blinking

Memory effects in single nanocrystal fluorescence blinking are investigated as a function of the on-state kinetics for CdSe/ZnS quantum dots and CdSe nanorods. The on-state duration probability distributions for single nanocrystal blinking traces are characterized by an inverse power law, which crosses over to exponential decay for long on-state durations. The correlations of subsequent on-state durations (Rlog,on) are found to decrease for nanocrystals that display earlier crossover times and smaller power law coefficients. Specifically, Rlog,on increases from 0.14 ± 0.02 to a saturation value of 0.44 ± 0.01 for nanocrystals with average crossover times of ~100 ms to more than 5.0 s, respectively. The results represent the first link between memory effects and blinking kinetics and are interpreted in the framework of two competing charge trapping mechanisms. A slow fluctuation-based trapping mechanism leads to power-law-distributed on durations and significant memory effects; however, the additional contribution of an ionization-induced trapping pathway is found to induce crossover to exponential decay and decreased memory. Monte Carlo simulations of nanocrystal blinking based on the two trapping mechanisms reproduce the experimental results, suggesting that the power law component and the memory effects correlate with a fluctuation-based mechanism. This effect is found to be universal, occurring for two nanocrystal morphologies and in blinking data measured using a wide range of continuous and pulsed excitation conditions.

Technical Note—A Sampling-Based Approach to Appointment Scheduling

We consider the problem of appointment scheduling with discrete random durations but under the more realistic assumption that the duration probability distributions are not known and only a set of independent samples is available, e.g., historical data. For a given sequence of appointments (jobs, tasks), the goal is to determine the planned starting time of each appointment such that the expected total underage and overage costs due to the mismatch between allocated and realized durations is minimized. We use the convexity and subdifferential of the objective function of the appointment scheduling problem to determine bounds on the number of independent samples required to obtain a provably near-optimal solution with high probability.

When perceptual time stands still: Long percept-memory in binocular rivalry

We have carried out binocular rivalry experiments with a large number of subjects to obtain high quality statistics on probability distribution of dominance duration (PDDD) for two cases where (a) the rival stimulus is continuously presented and (b) the rival stimulus is periodically removed, with stimulus-on and stimulus-off intervals Ton and Toff respectively. In the present study we have chosen to study the regime of relatively long stimulus-on time, i.e., Ton> 1s, where the stimulus presentation duration is significantly longer than the human reaction and recognition time. In the case of periodically removed stimulus, the total probability for percept reversal during each of the successive stimulus-on intervals Ton can be predicted using the PDDD for continuous viewing. More importantly, this total probability for percept reversal during any stimulus-on interval is independent of the length Toff of the preceding blank time, which can be quite long. We argue that this suggests that, in the regime of long Ton and Toff considered here, the variables representing the perceptual state do not change significantly during long blank intervals. We discuss that these findings impose challenges to theoretical models which aim at describing visual perception.

Assessing Performance Risk for Complex Product Development: A Simulation‐Based Model

Assessing and managing performance risk is important for complex product development projects. The performance risk of complex product development can be defined as the probability failing to achieve desired performance level subject to cost and time constraints. This article presents a simulation model based on the graphical evaluation and review technique (GERT) and analyzes the complex product development project using simulation data. The model computes the probability distribution of project duration and cost in a GERT network with multifeedback branches considering activities rework that is caused by probabilistic failure to meet the planned design objective. A simulation strategy is designed to assess the performance risk in both subsystems and system development. With the performance risk assessment methodology, project managers can make a better decision and then minimize the performance risk of product development project. Finally, an obstacle clearance armored vehicle development project is used to illustrate the effectiveness of the proposed model. Copyright © 2012 John Wiley & Sons, Ltd.

A probabilistic description of rain storms incorporating peak intensities

Summary Design storms with standardized hyetograph shapes and selected combinations of storm depths and durations are widely used in engineering hydrology. The key distinguishing feature between equal-duration design storms is their distinct intensity distributions. Differences in design storm hyetographs do not affect storm frequency, since only the frequency of the combination of storm depth and duration are determined through the use of Depth–Duration–Frequency curves. Probability distributions of peak intensity within rainfall events are not determined in current practice. Some current research applies copulas to joint distributions of rainstorm variables, but most of these are limited to bivariate distributions, and those that are developed for trivariate distributions do not address key variables important to everyday practice, or are limited by complexity of analysis. An alternative approach to characterizing peak storm intensity, intensity peak factor, together with its probability distribution is developed in this paper. An Archimedean copula is applied to describe the joint probability distribution of storm duration with intensity peak factor. That joint distribution is combined with the probability distribution of storm depth, to produce a joint probability distribution for storm depth, duration, and peak intensity. The result is a simple approach to fully characterizing the storm variables of direct interest to practitioners, thereby providing a complete probabilistic description of the return period or frequency of a selected design storm.

Incident Duration Prediction Based on Latent Gaussian Naive Bayesian classifier

The probability distribution of duration is a critical input for predicting the potential impact of traffic incidents. Most of the previous duration prediction models are discrete, which divide duration into several intervals. However, sometimes the continuous probability distribution is needed. Therefore a continuous model based on latent Gaussian naive Bayesian (LGNB) classifier is developed in this paper, assuming duration fits a lognormal distribution. The model is calibrated and tested by incident records from the Georgia Department of Transportation. The results show that LGNB can describe the continuous probability distribution of duration well. According to the evidence sensitivity analysis of LGNB, the four classes of incidents classified by LGNB can be interpreted by the level of severity and complexity.

How the Contact-Probing Mechanism Affects the Transmission Capacity of Delay-Tolerant Networks

Link duration is a main factor in determining the transmission capacity between two encounter nodes in delay-tolerant networks (DTNs). Existing research on DTN transmission capacity usually assumes that a node can immediately discover the nodes that move into its transmission range. Under this assumption, the link duration in DTNs is determined by the moving speed and transmission distance of encounter nodes. However, this assumption may be invalid in realistic DTNs, where the nodes use a contact-probing protocol to detect their neighbors. In this paper, we investigate the impact of contact-probing mechanisms on link duration and, thus, the transmission capacity of DTNs. We first derive the probability distribution of link duration and analyze the impact of contact-probing mechanisms on the total link durations. Based on this approach, we derive the theoretical node throughput and energy consumption and explore their tradeoff. In addition, we provide a framework for computing the optimal contact-probing frequency under energy limitations and adjust the probing frequency according to the node-encountering rate. Simulation experiments based on the Opportunistic Network Environment simulator validates the correctness and the accuracy of our analytical model. Our analytical results provide insights into how contact probing affects the DTN transmission capacity and energy consumption.

A hybrid approach of HMM and grey model for age-dependent health prediction of engineering assets

This paper presents a hybrid prognosis approach of age-dependent hidden Markov model (HMM) and grey model (GM) for prediction of engineering asset health. Age-dependent HMM allows modeling the time duration of the hidden states and therefore is capable of prognosis. The estimated state duration probability distributions can be used to predict the remaining useful life (RUL) of the assets. The previous HMM based prognosis method assumed that the transition probabilities are only state-dependent. That is, the probability of making transition to a less healthy state does not increase with the age. In the proposed method, in order to characterize a deteriorating asset, an aging factor that discounts the probabilities of staying at current state while increasing the probabilities of transitions to less healthy states will be introduced. After the estimation of the aging factor, a grey model is used to compute the expected residual life (ERL) by redefining the hazard rate. With the asset health prognosis, the behavior of the asset condition can be predicted.

Fractal analysis reveals pernicious stress levels related to boat presence and type in the Indo–Pacific bottlenose dolphin, Tursiops aduncus

The stress induced in the Indo–Pacific bottlenose dolphin, Tursiops aduncus, by boat presence and type was investigated in a highly urbanized coastal environment, the Port Adelaide River-Barker Inlet Estuary, South Australia. The level of stress experienced by bottlenose dolphins was inferred from the distribution patterns of their dive durations. Dive duration has previously been shown to increase under boat traffic conditions, and is considered as a typical avoidance behavior. Dive durations were opportunistically recorded from land-based stations between January 2008 and October 2010 in the absence of boat traffic, and in the presence of kayaks, inflatable motor boats, powerboats and fishing boats. Subsequent analyses were based on nearly 6000 behavioral observations. No significant differences in dive durations were found between control observations (i.e. absence of boats) and boat interferences, which could erroneously lead to conclude that boat traffic did not induce any stress in T. aduncus. In contrast, the scaling exponents of the cumulative probability distribution of dive durations obtained in the absence of boat traffic and under different conditions of boat interferences show (i) that the presence of boats affected the complexity of dive duration patterns and (ii) that stress levels were a function of boat type. Specifically, the complexity of dive duration patterns (estimated by the scaling exponent ϕ ) did not significantly differ between control behavioral observations and behavioral observations conducted in the presence of kayaks. A significant increased in behavioral stress (i.e. decreasing values of ϕ ) was, however, induced by the presence of fishing boats, motorized inflatable boats and powerboats. This demonstrates that traditional approaches based on the analysis of averaged behavioral metrics may not be sensitive enough to detect changes in the distribution pattern of behavioral sequences, hence underestimate the potential consequences of e.g. chronic exposure to low levels of stress. It is finally emphasized that fractal analyses of behavioral variables, and in particular the analysis of their cumulative probability distribution function, may provide a non-invasive, objective and quantitative framework that can be used to assess the changes in stress response, and subsequently evaluate the welfare status of organisms under various conditions of abiotic and/or biotic stress.

Equipment PHM using non-stationary segmental hidden semi-Markov model

Health monitoring and prognostics of equipment is a basic requirement for condition-based maintenance (CBM) in many application domains where safety, reliability, and availability of the systems are considered mission critical. As a key complement to CBM, prognostics and health management (PHM) is an approach to system life-cycle support that seeks to reduce/eliminate inspections and time-based maintenance through accurate monitoring, incipient faults. Conducting successful prognosis, however, is more difficult than conducting fault diagnosis. A much broader range of asset health related data, especially those related to the failures, shall be collected. The asset health progression can then be possibly extracted from the congregated data, which has proved to be very challenging. This paper presents a non-stationary segmental hidden semi-Markov model (NSHSMM) based prognosis method to predict equipment health. Unlike previous HSMMs, the proposed NSHSMM no longer assumes that the state-dependent transition probabilities keep the same value all the time. That is, the probability of transiting to a less healthy state does not increase with the age. ''Non-stationary'' means the transition probabilities will change with time. In the proposed method, in order to characterize a deteriorating equipment, three kinds of aging factor that discount the probabilities of staying at current state while increasing the probabilities of transitions to less healthy states are introduced. The performances of these aging factors are compared by using historical data colleted from three hydraulic pumps. The hazard function (h.f.) has been introduced to analyze the distribution of lifetime with a combination of historical failure data and on-line condition monitoring data. Using h.f., PHM is based on a failure rate that is a function of both the equipment age and the equipment conditions. The state values of the equipment condition considered in PHM, however, are limited to those stochastically increasing over time and those having non-decreasing effect on the hazard rate. The estimated state duration probability distributions can be used to predict the remaining useful life of the systems. With the equipment PHM, the behavior of the equipment condition can be predicted.

Facts and Artifacts in the Blinking Statistics of Semiconductor Nanocrystals

Since its initial discovery just over a decade ago, blinking of semiconductor nanocrystals has typically been described in terms of probability distributions for durations of bright, or "on," states and dark, or "off," states. These distributions are obtained by binning photon counts in order to construct a time series for emission intensity and then applying a threshold to distinguish on states from off states. By examining experimental data from CdSe/ZnS core/shell nanocrystals and by simulating this data according to a simple, two-state blinking model, we find that the apparent truncated power-law distributions of on times can depend significantly on the choices of binning time and threshold. For example, increasing the binning time by a factor of 10 can double the apparent truncation time and change the apparent power-law exponent by 30%, even though the binning time is only 3% of the truncation time. Our findings indicate that stringent experimental conditions are needed to accurately determine blinking-time probability distributions. Similar considerations should apply to any phenomenon characterized by time series data that displays telegraph noise.

Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm

This study aims to model the joint probability distribution of drought duration, severity and inter-arrival time using a trivariate Plackett copula. The drought duration and inter-arrival time each follow the Weibull distribution and the drought severity follows the gamma distribution. Parameters of these univariate distributions are estimated using the method of moments (MOM), maximum likelihood method (MLM), probability weighted moments (PWM), and a genetic algorithm (GA); whereas parameters of the bivariate and trivariate Plackett copulas are estimated using the log-pseudolikelihood function method (LPLF) and GA. Streamflow data from three gaging stations, Zhuangtou, Taian and Tianyang, located in the Wei River basin, China, are employed to test the trivariate Plackett copula. The results show that the Plackett copula is capable of yielding bivariate and trivariate probability distributions of correlated drought variables.

Scheduling projects with stochastic activity duration to maximize expected net present value

Abstract Although uncertainty is rife in many project management contexts, little is known about adaptively optimizing project schedules. We formulate the problem of adaptively optimizing the expected present value of a project’s cash flow, and we show that it is practical to perform the optimization. The formulation includes randomness in activity durations, costs, and revenues, so the optimization leads to a recursion with a large state space even if the durations are exponentially distributed. We present an algorithm that partially exercises the “curse of dimensionality” as computational results demonstrate. Most of the paper is restricted to exponentially distributed task durations, but we sketch the adaptation of the algorithm to approximate any probability distribution of task duration.

Quantum formalism to describe binocular rivalry

On the basis of the general character and operation of the process of perception, a formalism is sought to mathematically describe the subjective or abstract/mental process of perception. It is shown that the formalism of orthodox quantum theory of measurement, where the observer plays a key role, is a broader mathematical foundation which can be adopted to describe the dynamics of the subjective experience. The mathematical formalism describes the psychophysical dynamics of the subjective or cognitive experience as communicated to us by the subject. Subsequently, the formalism is used to describe simple perception processes and, in particular, to describe the probability distribution of dominance duration obtained from the testimony of subjects experiencing binocular rivalry. Using this theory and parameters based on known values of neuronal oscillation frequencies and firing rates, the calculated probability distribution of dominance duration of rival states in binocular rivalry under various conditions is found to be in good agreement with available experimental data. This theory naturally explains an observed marked increase in dominance duration in binocular rivalry upon periodic interruption of stimulus and yields testable predictions for the distribution of perceptual alteration in time.

The Effects of Thermal Stratification on Clustering Properties of Canopy Turbulence

The intermittent structure of turbulence within the canopy sublayer (CSL) is sensitive to the presence of foliage and to the atmospheric stability regime. How much of this intermittency originates from amplitude variability or clustering properties remains a vexing research problem for CSL flows. Using a five-level set of measurements collected within a dense hardwood canopy, the clustering properties of CSL turbulence and their dependence on atmospheric stability are explored using the telegraphic approximation (TA). The binary structure of the TA removes any amplitude variability from turbulent excursions but retains their zero-crossing behaviour, and thereby isolating the role of clustering in intermittency. A relationship between the spectral exponents of the actual and the TA series is derived across a wide range of atmospheric stability regimes and for several flow variables. This relationship is shown to be consistent with a relationship derived for long-memory and monofractal processes such as fractional Brownian motion (fBm). Moreover, it is demonstrated that for the longitudinal and vertical velocity components, the vegetation does not appreciably alter fine-scale clustering but atmospheric stability does. Stable atmospheric stability conditions is characterized by more fine scale clustering when compared to other atmospheric stability regimes. For scalars, fine-scale clustering above the canopy is similar to its velocity counterpart but is significantly increased inside the canopy, especially under stable stratification. Using simplified scaling analysis, it is demonstrated that clustering is much more connected to space than to time within the CSL. When comparing intermittency for flow variables and their TA series, it is shown that for velocity, amplitude variations modulate intermittency for all stability regimes. However, amplitude variations play only a minor role in scalar intermittency. Within the crown region of the canopy, a ‘double regime’ emerges in the inter-pulse duration probability distributions not observed in classical turbulence studies away from boundaries. The double regime is characterized by a power-law distribution for shorter inter-pulse periods and a log-normal distribution for large inter-pulse periods. The co-existence of these two regimes is shown to be consistent with near-field/far-field scaling arguments. In the near-field, short inter-pulse periods are controlled by the source strength, while in the far-field long inter-pulse periods are less affected by the precise source strength details and more affected by the transport properties of the background turbulence.

A Fully Consistent Hidden Semi-Markov Model-Based Speech Recognition System

In a hidden Markov model (HMM), state duration probabilities decrease exponentially with time, which fails to adequately represent the temporal structure of speech. One of the solutions to this problem is integrating state duration probability distributions explicitly into the HMM. This form is known as a hidden semi-Markov model (HSMM). However, though a number of attempts to use HSMMs in speech recognition systems have been proposed, they are not consistent because various approximations were used in both training and decoding. By avoiding these approximations using a generalized forward-backward algorithm, a context-dependent duration modeling technique and weighted finite-state transducers (WFSTs), we construct a fully consistent HSMM-based speech recognition system. In a speaker-dependent continuous speech recognition experiment, our system achieved about 9.1% relative error reduction over the corresponding HMM-based system.