scholarly journals Optimal Design of Bus Stop Locations Integrating Continuum Approximation and Discrete Models

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Xiaoling Luo ◽  
Wenbo Fan ◽  
Yangsheng Jiang ◽  
Jun Zhang
Keyword(s):  
Optimal Design ◽  
Location Problem ◽  
Real Data ◽  
Discrete Models ◽  
Continuum Approximation ◽  
Interior Point Algorithm ◽  
Nonlinear Minimization ◽  
Proposed Model ◽  
Before And After ◽  
Ca Model

Although transit stop location problem has been extensively studied, the two main categories of modeling methodologies, i.e., discrete models and continuum approximation (CA) ones, seem have little intersection. Both have strengths and weaknesses, respectively. This study intends to integrate them by taking the advantage of CA models’ parsimonious property and discrete models’ fine consideration of practical conditions. In doing so, we first employ the state-of-the-art CA models to yield the optimal design, which serves as the input to the next discrete model. Then, the stop location problem is formulated into a multivariable nonlinear minimization problem with a given number of stop location variables and location constraint. The interior-point algorithm is presented to find the optimal design that is ready for implementation. In numerical studies, the proposed model is applied to a variety of scenarios with respect to demand levels, spatial heterogeneity, and route length. The results demonstrate the consistent advantage of the proposed model in all scenarios as against its counterparts, i.e., two existing recipes that convert CA model-based solution into real design of stop locations. Lastly, a case study is presented using real data and practical constraints for the adjustment of a bus route in Chengdu (China). System cost saving of 15.79% is observed by before-and-after comparison.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

scholarly journals An adaptive social distancing SIR model for COVID-19 disease spreading and forecasting

2021 ◽  
Vol 10 (s1) ◽  
Author(s):  
Said Gounane ◽  
Yassir Barkouch ◽  
Abdelghafour Atlas ◽  
Mostafa Bendahmane ◽  
Fahd Karami ◽  
...  
Keyword(s):  
Mathematical Theory ◽  
Real Data ◽  
Sir Model ◽  
Epidemic Threshold ◽  
Social Distancing ◽  
Sir Epidemic ◽  
Proposed Model ◽  
Disease Spreading ◽  
The Government ◽  
The Impact

Abstract Recently, various mathematical models have been proposed to model COVID-19 outbreak. These models are an effective tool to study the mechanisms of coronavirus spreading and to predict the future course of COVID-19 disease. They are also used to evaluate strategies to control this pandemic. Generally, SIR compartmental models are appropriate for understanding and predicting the dynamics of infectious diseases like COVID-19. The classical SIR model is initially introduced by Kermack and McKendrick (cf. (Anderson, R. M. 1991. “Discussion: the Kermack–McKendrick Epidemic Threshold Theorem.” Bulletin of Mathematical Biology 53 (1): 3–32; Kermack, W. O., and A. G. McKendrick. 1927. “A Contribution to the Mathematical Theory of Epidemics.” Proceedings of the Royal Society 115 (772): 700–21)) to describe the evolution of the susceptible, infected and recovered compartment. Focused on the impact of public policies designed to contain this pandemic, we develop a new nonlinear SIR epidemic problem modeling the spreading of coronavirus under the effect of a social distancing induced by the government measures to stop coronavirus spreading. To find the parameters adopted for each country (for e.g. Germany, Spain, Italy, France, Algeria and Morocco) we fit the proposed model with respect to the actual real data. We also evaluate the government measures in each country with respect to the evolution of the pandemic. Our numerical simulations can be used to provide an effective tool for predicting the spread of the disease.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

scholarly journals Transition models for count data: a flexible alternative to fixed distribution models

2021 ◽  
Author(s):  
Moritz Berger ◽  
Gerhard Tutz
Keyword(s):  
Count Data ◽  
Regression Models ◽  
Negative Binomial ◽  
Real Data ◽  
Distribution Models ◽  
Explanatory Variables ◽  
Excess Zeros ◽  
Proposed Model ◽  
Transition Models ◽  
Fixed Distribution

AbstractA flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and Negative Binomial model, as well as to more general models accounting for excess zeros that are also based on fixed distributional assumptions. The model allows that the data itself determine the distribution of the response variable, but, in its basic form, uses a parametric term that specifies the effect of explanatory variables. In addition, an extended version is considered, in which the effects of covariates are specified nonparametrically. The proposed model and traditional models are compared in simulations and by utilizing several real data applications from the area of health and social science.

scholarly journals Assessing baseline dependency of anchor-based minimal important change (MIC): don’t stratify on the baseline score!

2021 ◽  
Author(s):  
Berend Terluin ◽  
Ewa M. Roos ◽  
Caroline B. Terwee ◽  
Jonas B. Thorlund ◽  
Lina H. Ingelsrud
Keyword(s):  
Real Data ◽  
Patient Reported Outcome ◽  
Health Condition ◽  
Important Change ◽  
Alternative Methods ◽  
Minimal Important Change ◽  
Baseline Score ◽  
Patient Reported ◽  
Before And After ◽  
Parallel Tests

Abstract Purpose The minimal important change (MIC) of a patient-reported outcome measure (PROM) is often suspected to be baseline dependent, typically in the sense that patients who are in a poorer baseline health condition need greater improvement to qualify as minimally important. Testing MIC baseline dependency is commonly performed by creating two or more subgroups, stratified on the baseline PROM score. This study’s purpose was to show that this practice produces biased subgroup MIC estimates resulting in spurious MIC baseline dependency, and to develop alternative methods to evaluate MIC baseline dependency. Methods Datasets with PROM baseline and follow-up scores and transition ratings were simulated with and without MIC baseline dependency. Mean change MICs, ROC-based MICs, predictive MICs, and adjusted MICs were estimated before and after stratification on the baseline score. Three alternative methods were developed and evaluated. The methods were applied in a real data example for illustration. Results Baseline stratification resulted in biased subgroup MIC estimates and the false impression of MIC baseline dependency, due to redistribution of measurement error. Two of the alternative methods require a second baseline measurement with the same PROM or another correlated PROM. The third method involves the construction of two parallel tests based on splitting the PROM’s item set. Two methods could be applied to the real data. Conclusion MIC baseline dependency should not be tested in subgroups based on stratification on the baseline PROM score. Instead, one or more of the suggested alternative methods should be used.

scholarly journals Remote Sensing Image Stripe Detecting and Destriping Using the Joint Sparsity Constraint with Iterative Support Detection

2019 ◽  
Vol 11 (6) ◽  
pp. 608 ◽  
Author(s):  
Yun-Jia Sun ◽  
Ting-Zhu Huang ◽  
Tian-Hui Ma ◽  
Yong Chen
Keyword(s):  
Remote Sensing ◽  
Real Data ◽  
Total Variation Regularization ◽  
Joint Sparsity ◽  
Alternating Direction ◽  
Proposed Model ◽  
Comparison Results ◽  
Wide Range ◽  
Image Edges ◽  
Full Consideration

Remote sensing images have been applied to a wide range of fields, but they are often degraded by various types of stripes, which affect the image visual quality and limit the subsequent processing tasks. Most existing destriping methods fail to exploit the stripe properties adequately, leading to suboptimal performance. Based on a full consideration of the stripe properties, we propose a new destriping model to achieve stripe detection and stripe removal simultaneously. In this model, we adopt the unidirectional total variation regularization to depict the directional property of stripes and the weighted ℓ 2 , 1 -norm regularization to depict the joint sparsity of stripes. Then, we combine the alternating direction method of multipliers and iterative support detection to solve the proposed model effectively. Comparison results on simulated and real data suggest that the proposed method can remove and detect stripes effectively while preserving image edges and details.

scholarly journals A Modified Cellular Automaton Model for Accounting for Traffic Behaviors during Signal Change Intervals

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Chih-Cheng Hsu ◽  
Yu-Chiun Chiou
Keyword(s):  
Microscopic Analysis ◽  
Traffic Signal ◽  
Traffic Signal Control ◽  
Fundamental Diagram ◽  
Macroscopic Fundamental Diagram ◽  
Proposed Model ◽  
Signal Change ◽  
Ca Model ◽  
Speed Adjustment ◽  
Diagram Analysis

Previous cellular automata (CA) models have been developed for simulating driver behaviors in response to traffic signal control. However, driver behaviors during traffic signal change intervals, including cross/stop decision and speed adjustment, have not yet been studied. Based on this, this paper aims to propose a change interval CA model for replicating driver’s perception and response to amber light based on stopping probability and speed adjusting functions. The proposed model has been validated by exemplified and field cases. To investigate the applicability of the proposed model, macroscopic and microscopic analyses are conducted. Although the macroscopic fundamental diagram analysis reveals only a small decrease in maximum traffic flow rates with considering driver behaviors in change intervals, in the microscopic analysis, the proposed model can present reasonable vehicular trajectories and deceleration rates during slowdown process.

scholarly journals Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
K. S. Sultan ◽  
A. S. Al-Moisheer
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Component Mixture ◽  
Data Set ◽  
Hazard Functions ◽  
Lognormal Distributions ◽  
Proposed Model ◽  
Estimation Of Model Parameters

We discuss the two-component mixture of the inverse Weibull and lognormal distributions (MIWLND) as a lifetime model. First, we discuss the properties of the proposed model including the reliability and hazard functions. Next, we discuss the estimation of model parameters by using the maximum likelihood method (MLEs). We also derive expressions for the elements of the Fisher information matrix. Next, we demonstrate the usefulness of the proposed model by fitting it to a real data set. Finally, we draw some concluding remarks.

scholarly journals Bivariate Nonlinear Diffusion Degradation Process Modeling via Copula and MCMC

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Huibing Hao ◽  
Chun Su
Keyword(s):  
Nonlinear Diffusion ◽  
Goodness Of Fit ◽  
Real Data ◽  
Degradation Process ◽  
Copula Function ◽  
Assessment Method ◽  
Unknown Parameters ◽  
Degradation Data ◽  
Proposed Model ◽  
Frank Copula

A novel reliability assessment method for degradation product with two dependent performance characteristics (PCs) is proposed, which is different from existing work that only utilized one dimensional degradation data. In this model, the dependence of two PCs is described by the Frank copula function, and each PC is governed by a random effected nonlinear diffusion process where random effects capture the unit to unit differences. Considering that the model is so complicated and analytically intractable, Markov Chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. A numerical example about LED lamp is given to demonstrate the usefulness and validity of the proposed model and method. Numerical results show that the random effected nonlinear diffusion model is very useful by checking the goodness of fit of the real data, and ignoring the dependence between PCs may result in different reliability conclusion.

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