scholarly journals On the Time to Buffer Overflow in a Queueing Model with a General Independent Input Stream and Power-Saving Mechanism Based on Working Vacations

Sensors ◽  
2021 ◽  
Vol 21 (16) ◽  
pp. 5507
Author(s):  
Martyna Kobielnik ◽  
Wojciech Kempa
Keyword(s):  
Distribution Functions ◽  
Cumulative Distribution ◽  
Buffer Overflow ◽  
Embedded Markov Chain ◽  
Total Probability ◽  
Single Server ◽  
Input Stream ◽  
Initial State ◽  
Transient Time ◽  
The Impact

A single server GI/M/1 queue with a limited buffer and an energy-saving mechanism based on a single working vacation policy is analyzed. The general independent input stream and exponential service times are considered. When the queue is empty after a service completion epoch, the server lowers the service speed for a random amount of time following an exponential distribution. Packets that arrive while the buffer is saturated are rejected. The analysis is focused on the duration of the time period with no packet losses. A system of equations for the transient time to the first buffer overflow cumulative distribution functions conditioned by the initial state and working mode of the service unit is stated using the idea of an embedded Markov chain and the continuous version of the law of total probability. The explicit representation for the Laplace transform of considered characteristics is found using a linear algebra-based approach. The results are illustrated using numerical examples, and the impact of the key parameters of the model is investigated.

Assessing the reliability of dynamical and historical climate forecasts in simulating hindcast pasture growth rates

2017 ◽  
Vol 57 (7) ◽  
pp. 1525 ◽  
Author(s):  
Matthew T. Harrison ◽  
Karen M. Christie ◽  
Richard P. Rawnsley
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Circulation Model ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Weather Data ◽  
Climate Data ◽  
Climate Forecasts ◽  
Farm Model ◽  
The Impact

A priori knowledge of seasonal pasture growth rates helps livestock farmers plan with pasture supply and feed budgeting. Longer forecasts may allow managers more lead time, yet inaccurate forecasts could lead to counterproductive decisions and foregone income. By using climate forecasts generated from historical archives or the global circulation model (GCM) called the Predictive Ocean Atmosphere Model for Australia (POAMA), we simulated pasture growth rates in a whole-farm model and compared growth-rate forecasts with growth-rate hindcasts (viz. retrospective forecasts). Hindcast pasture growth rates were generated using posterior weather data measured at two sites in north-western Tasmania, Australia. Forecasts were made on a monthly basis for durations of 30, 60 and 90 days. Across sites, forecasting approaches and durations, there were no significant differences between simulated growth-rate forecasts and hindcasts when our statistical inference was conducted using either the Kolmogorov–Smirnov statistic or empirical cumulative distribution functions. However, given that both of these tests were calculated by comparing growth-rate hindcasts with monthly distributions of forecasts, we also examined linear correlations between monthly hindcast values and median monthly growth-rate forecasts. Using this approach, we found a higher correlation between hindcasts and median monthly forecasts for 30 days than for 60 or 90 days, suggesting that monthly growth-rate forecasts provide more skilful predictions than forecast durations of 2 or 3 months. The range in monthly growth-rate forecasts at 30 days was less than that at 60 or 90 days, further reinfocing the aforementioned result. The strength of the correlation between growth-rate hindcasts and median monthly forecasts from the historical approach was similar to that generated using POAMA data. Overall, the present study found that (1) statistical methods of comparing forecast data with hindcast data are important, particularly if the former is a distribution whereas the latter is a single value, (2) 1-month growth-rate forecasts have less uncertainty than forecast durations of 2 or 3 months, and (3) there is little difference between pasture growth rates simulated using climate data from either historical records or from GCMs. To test the generality of these conclusions, the study should be extended to other dairy regions. Including more regions would both enable studies of sites with greater intra-seasonal climate variability, but also better highlight the impact of seasonal and regional variation in forecast skill of POAMA as applied in our forecasting methods.

scholarly journals THE IMPACT OF SPATIAL AND TEMPORAL RESOLUTIONS IN TROPICAL SUMMER RAINFALL DISTRIBUTION: PRELIMINARY RESULTS

2017 ◽  
Vol IV-4/W2 ◽  
pp. 183-191
Author(s):  
Q. Liu ◽  
L. S Chiu ◽  
X. Hao
Keyword(s):  
Climate Models ◽  
Hydrological Cycle ◽  
Probability Distributions ◽  
Summer Rainfall ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Statistical Parameters ◽  
Spatial And Temporal Scales ◽  
Gamma Distributions ◽  
The Impact

The abundance or lack of rainfall affects peoples’ life and activities. As a major component of the global hydrological cycle (Chokngamwong & Chiu, 2007), accurate representations at various spatial and temporal scales are crucial for a lot of decision making processes. Climate models show a warmer and wetter climate due to increases of Greenhouse Gases (GHG). However, the models’ resolutions are often too coarse to be directly applicable to local scales that are useful for mitigation purposes. Hence disaggregation (downscaling) procedures are needed to transfer the coarse scale products to higher spatial and temporal resolutions. The aim of this paper is to examine the changes in the statistical parameters of rainfall at various spatial and temporal resolutions. The TRMM Multi-satellite Precipitation Analysis (TMPA) at 0.25 degree, 3 hourly grid rainfall data for a summer is aggregated to 0.5,1.0, 2.0 and 2.5 degree and at 6, 12, 24 hourly, pentad (five days) and monthly resolutions. The probability distributions (PDF) and cumulative distribution functions(CDF) of rain amount at these resolutions are computed and modeled as a mixed distribution. Parameters of the PDFs are compared using the Kolmogrov-Smironov (KS) test, both for the mixed and the marginal distribution. These distributions are shown to be distinct. The marginal distributions are fitted with Lognormal and Gamma distributions and it is found that the Gamma distributions fit much better than the Lognormal.

Assessing the Impact of Soil Layer Depth Specification on the Observability of Modeled Soil Moisture and Brightness Temperature

2020 ◽  
Vol 21 (9) ◽  
pp. 2041-2060
Author(s):  
Peter J. Shellito ◽  
Sujay V. Kumar ◽  
Joseph A. Santanello ◽  
Patricia Lawston-Parker ◽  
John D. Bolten ◽  
...  
Keyword(s):  
Soil Moisture ◽  
Land Surface ◽  
Soil Column ◽  
Soil Layer ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
L Band ◽  
The Impact

AbstractThe utility of hydrologic land surface models (LSMs) can be enhanced by using information from observational platforms, but mismatches between the two are common. This study assesses the degree to which model agreement with observations is affected by two mechanisms in particular: 1) physical incongruities between the support volumes being characterized and 2) inadequate or inconsistent parameterizations of physical processes. The Noah and Noah-MP LSMs by default characterize surface soil moisture (SSM) in the top 10 cm of the soil column. This depth is notably different from the 5-cm (or less) sensing depth of L-band radiometers such as NASA’s Soil Moisture Active Passive (SMAP) satellite mission. These depth inconsistencies are examined by using thinner model layers in the Noah and Noah-MP LSMs and comparing resultant simulations to in situ and SMAP soil moisture. In addition, a forward radiative transfer model (RTM) is used to facilitate direct comparisons of LSM-based and SMAP-based L-band Tb retrievals. Agreement between models and observations is quantified using Kolmogorov–Smirnov distance values, calculated from empirical cumulative distribution functions of SSM and Tb time series. Results show that agreement of SSM and Tb with observations depends primarily on systematic biases, and the sign of those biases depends on the particular subspace being analyzed (SSM or Tb). This study concludes that the role of increased soil layer discretization on simulated soil moisture and Tb is secondary to the influence of component parameterizations, the effects of which dominate systematic differences with observations.

scholarly journals ON TIME-TO-BUFFER OVERFLOW DISTRIBUTION IN A SINGLE-MACHINE DISCRETE-TIME SYSTEM WITH FINITE CAPACITY

2020 ◽  
Vol 25 (2) ◽  
pp. 289-302
Author(s):  
Wojciech M. Kempa
Keyword(s):  
Single Machine ◽  
Geometric Distribution ◽  
Buffer Overflow ◽  
Embedded Markov Chain ◽  
Total Probability ◽  
Finite Capacity ◽  
Discrete Time System ◽  
Buffer Overflows ◽  
Processing Times ◽  
Initial Buffer

A model of a single-machine production system with finite magazine capacity is investigated. The input flow of jobs is organized according to geometric distribution of interarrival times, while processing times are assumed to be generally distributed. The closed-form formula for the generating function of the time to the first buffer overflow distribution conditioned by the initial buffer state is found. The analytical approach based on the idea of embedded Markov chain, the formula of total probability and linear algebra is applied. The corresponding result for next buffer overflows is also given. Numerical examples are attached as well.

Confidence Bounds for Fatigue Distribution Functions

2017 ◽  
Author(s):  
D. Gary Harlow
Keyword(s):  
Fatigue Life ◽  
Life Prediction ◽  
High Reliability ◽  
Distribution Functions ◽  
Fatigue Life Prediction ◽  
Cumulative Distribution ◽  
Low Carbon ◽  
Confidence Bounds ◽  
Cumulative Distribution Functions ◽  
The Impact

The effect of uncertainty is critical in the design of complex engineered systems, components, and structural materials subjected to fatigue. Uncertainty in fatigue life prediction is a combination of several factors. In fact, it cannot be eliminated from experimentation due to material and loading variability, manufacturing processing, and imprecise scientific modeling. Consequently, uncertainty must be characterized and managed. The impact of uncertainty is exacerbated especially when high reliability must be assured. One of the ways to estimate the effect of uncertainty is to consider confidence bounds for fatigue life prediction, specifically, for cumulative distribution functions associated with life. The purpose of this paper is to investigate the statistical variability and appropriately model that variability for life in fatigue using appropriate cumulative distribution functions, and subsequently, evaluate a variety of statistical methods to estimate confidence bounds. Specifically, the confidence bounds will be estimated using mean square error, Dvoretzky-Kiefer-Wolfowitz, and pointwise Normal approximation methods. Since high reliability and long life is typically desired, extra emphasis will be placed on estimation in the lower tails of the distribution functions. The ensuing analyses are based on data for a cold-rolled, low carbon, extra deep drawing steel, ASTM A969, and creep strengthened 9Cr-1Mo steel.

scholarly journals Flood risk trends in coastal watersheds in South Spain: direct and indirect impact of river regulation

2015 ◽  
Vol 370 ◽  
pp. 51-56 ◽  
Author(s):  
M. Egüen ◽  
M. J. Polo ◽  
Z. Gulliver ◽  
E. Contreras ◽  
C. Aguilar ◽  
...  
Keyword(s):  
Flood Risk ◽  
River Mouth ◽  
River Regulation ◽  
Annual Runoff ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Flood Events ◽  
Coastal Watersheds ◽  
Crop Area ◽  
The Impact

Abstract. Spain is one of the world's countries with a large number of reservoirs per inhabitant. This intense regulation of the fluvial network during the 20th century has resulted in a decrease in flood events, a higher availability of water resources, and a high development of the irrigated crop area, even in the drier regions. For decades, flood perception was reduced since the development of reservoirs protected the floodplains of river; this resulted in later occupation of soil by urban, agricultural and industrial uses. In recent years, an increasing perception of flood events is observed, associated to the higher damage associated to extreme events in the now occupied areas, especially in coastal watersheds. This work shows the change on flood risk in the coastal areas of three hydrographic basins in Andalusia (South Spain) during the reservoir expansion period: the Guadalete, Guadalquivir and Guadalhorce river basins. The results differentiate the impact of the regulation level on both the cumulative distribution functions of the fluvial discharge near the river mouth, for different time scales, and the associated damage related to the enhanced soil occupation during this period. The different impact on the final medium and long term flood risk is also assessed in terms of the storage capacity per unit area throughout the basins, the effective annual runoff/precipitation index, the frequency of sea storms, and the human factor (change in social perception of floods), for different intervals in the flood extreme regime. The implications for adaptation actions is also assessed.

scholarly journals Impact of Soil Moisture Assimilation on Land Surface Model Spinup and Coupled Land–Atmosphere Prediction

2016 ◽  
Vol 17 (2) ◽  
pp. 517-540 ◽  
Author(s):  
Joseph A. Santanello ◽  
Sujay V. Kumar ◽  
Christa D. Peters-Lidard ◽  
Patricia M. Lawston
Keyword(s):  
Soil Moisture ◽  
Land Surface ◽  
Initial Conditions ◽  
Weather Prediction ◽  
Wrf Model ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Satellite Monitoring ◽  
Surface Model ◽  
The Impact

Abstract Advances in satellite monitoring of the terrestrial water cycle have led to a concerted effort to assimilate soil moisture observations from various platforms into offline land surface models (LSMs). One principal but still open question is that of the ability of land data assimilation (LDA) to improve LSM initial conditions for coupled short-term weather prediction. In this study, the impact of assimilating Advanced Microwave Scanning Radiometer for EOS (AMSR-E) soil moisture retrievals on coupled WRF Model forecasts is examined during the summers of dry (2006) and wet (2007) surface conditions in the southern Great Plains. LDA is carried out using NASA’s Land Information System (LIS) and the Noah LSM through an ensemble Kalman filter (EnKF) approach. The impacts of LDA on the 1) soil moisture and soil temperature initial conditions for WRF, 2) land–atmosphere coupling characteristics, and 3) ambient weather of the coupled LIS–WRF simulations are then assessed. Results show that impacts of soil moisture LDA during the spinup can significantly modify LSM states and fluxes, depending on regime and season. Results also indicate that the use of seasonal cumulative distribution functions (CDFs) is more advantageous compared to the traditional annual CDF bias correction strategies. LDA performs consistently regardless of atmospheric forcing applied, with greater improvements seen when using coarser, global forcing products. Downstream impacts on coupled simulations vary according to the strength of the LDA impact at the initialization, where significant modifications to the soil moisture flux–PBL–ambient weather process chain are observed. Overall, this study demonstrates potential for future, higher-resolution soil moisture assimilation applications in weather and climate research.

scholarly journals Functioning of a technical system with an instantly replenished time reserve, taking into account preventive maintenance

2021 ◽  
pp. 258-264
Author(s):  
А.Л. Боран-Кешишьян ◽  
М.В. Заморёнов ◽  
П.Н. Флоря ◽  
А.А. Ярошенко ◽  
С.И. Кондратьев
Keyword(s):  
Transition Probabilities ◽  
Distribution Functions ◽  
Technical System ◽  
Embedded Markov Chain ◽  
State Graph ◽  
Total Probability ◽  
System Availability ◽  
Sojourn Times ◽  
Trajectory Method ◽  
Total Probability Theorem

В работе рассматривается функционирование технической системы с мгновенно пополняемым резервом времени с учетом профилактики. Приводится описание функционирования такой системы. При использовании аппарата полумарковских исследований производится построение аналитической модели системы с мгновенно пополняемым резервом времени при учете влияния профилактики на ее производительность. При построении полумарковской модели принимается ограничение на количество профилактик за время восстановления рабочего элемента. Описываются полумарковские состояния исследуемой системы, и приводится граф состояний. Определяются времена пребывания в состояниях системы, вероятности переходов и стационарное распределение вложенной цепи Маркова. Для определения функции распределения времени пребывания системы в подмножестве работоспособных состояний с использованием метода траекторий находятся все траектории переходов системы из этого подмножества в подмножество неработоспособных состояний и вероятности их реализации. Определяются времена пребывания системы в найденных траекториях. На основании теоремы полной вероятности определяются функции распределения времен пребывания системы в подмножествах работоспособных и неработоспособных состояний и коэффициент готовности системы. Приводится пример моделирования исследуемой системы. Проводится сравнение полученных результатов с результатами использования теоремы о среднестационарном времени пребывания системы в подмножестве состояний. The work examines the functioning of a technical system with an instantly replenished reserve of time, taking into account prevention. The description of the functioning of such a system is given. When using the apparatus of semi-Markov studies, an analytical model of the system is constructed with an instantly replenished reserve of time, taking into account the effect of prevention on its performance. When constructing a semi-Markov model, a limitation on the number of preventive measures during the restoration of a working element is adopted. The semi-Markov states of the system under study are described, and the state graph is given. The sojourn times in the states of the system, the transition probabilities, and the stationary distribution of the embedded Markov chain are determined. To determine the distribution function of the time spent by the system in a subset of operable states using the trajectory method, all trajectories of the system's transitions from this subset to the subset of inoperable states and the probability of their realization are found. The residence times of the system in the found trajectories are determined. On the basis of the total probability theorem, the distribution functions of the sojourn times of the system in subsets of the healthy and inoperable states and the system availability factor are determined. The modeling example of th system under study is given. The results obtained are compared with the results of using the theorem on the average stationary sojourn time of the system in a subset of states.

Comparative study of the impact of two mechanical perforation densities on the behavior of a sandy soil

2012 ◽  
Vol 8 (1) ◽  
pp. 37-48
Author(s):  
S. Chehaibi ◽  
K. Abrougui ◽  
F. Haouala
Keyword(s):  
Soil Water ◽  
Sandy Soil ◽  
Water Infiltration ◽  
Cone Penetration ◽  
Initial State ◽  
Soil Water Infiltration ◽  
Good Improvement ◽  
The Impact ◽  
Positive Effect ◽  
Resistance To Penetration

The effects of mechanical perforation densities by extracting soil cores through an aerator Vertidrain with a working width of 1.6 m and equipped with hollow tines spaced of 65 mm, were studied on a sandy soil of a grassy sward in the Golf Course El Kantaoui in Sousse (Tunisia). The mechanical aeration was performed at two densities: 250 and 350 holes/m2. The cone penetration resistance and soil water infiltration were measured. These parameters were performed at initial state before aeration (E0) and then on the 10th, 20th and 30th day after aeration. These results showed that perforation density of 350 holes/m2 had a positive effect on the soil by reducing its cone resistance to penetration compared to the initial state (Rp = 14.8 daN/cm2). At 5 cm depth the decrease in resistance to penetration was 34% and 43% on the 10th and 20th day after aeration, respectively. However, on the 30th day after aeration the soil resistance to penetration tended to grow and its value compared to the initial state decreased only by 21 and 26%, respectively, at 5 and 15 cm of depth only by 10% and 9% with 250 holes/m2 density. The soil water infiltration made a good improvement after aeration compared to the initial state. This parameter increased from 4.8 cm/h to 8.3, 10.9 and 13.1 cm/h with 250 holes/m2 density and to 10, 12.9 and 14.8 cm/h with 350 holes/m2 density on the 10th, 20th and 30th day following the aeration.

scholarly journals Do galactic bars depend on environment?: an information theoretic analysis of Galaxy Zoo 2

2020 ◽  
Vol 501 (1) ◽  
pp. 994-1001
Author(s):  
Suman Sarkar ◽  
Biswajit Pandey ◽  
Snehasish Bhattacharjee
Keyword(s):  
Spatial Distribution ◽  
Mutual Information ◽  
Local Density ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Host Galaxy ◽  
Data Sets ◽  
Data Set ◽  
Information Theoretic

ABSTRACT We use an information theoretic framework to analyse data from the Galaxy Zoo 2 project and study if there are any statistically significant correlations between the presence of bars in spiral galaxies and their environment. We measure the mutual information between the barredness of galaxies and their environments in a volume limited sample (Mr ≤ −21) and compare it with the same in data sets where (i) the bar/unbar classifications are randomized and (ii) the spatial distribution of galaxies are shuffled on different length scales. We assess the statistical significance of the differences in the mutual information using a t-test and find that both randomization of morphological classifications and shuffling of spatial distribution do not alter the mutual information in a statistically significant way. The non-zero mutual information between the barredness and environment arises due to the finite and discrete nature of the data set that can be entirely explained by mock Poisson distributions. We also separately compare the cumulative distribution functions of the barred and unbarred galaxies as a function of their local density. Using a Kolmogorov–Smirnov test, we find that the null hypothesis cannot be rejected even at $75{{\ \rm per\ cent}}$ confidence level. Our analysis indicates that environments do not play a significant role in the formation of a bar, which is largely determined by the internal processes of the host galaxy.

Sign in / Sign up

Export Citation Format

Share Document