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Journal articles on the topic 'STEADY STATE PROBABILITY'

Author: Grafiati

Published: 11 September 2023

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1

Murphy, Ryan H. "Steady state economic freedom." Economics and Business Letters 12, no. 2 (July 13, 2023): 132–36. http://dx.doi.org/10.17811/ebl.12.2.2023.132-136.

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This note projects forward into the distant future the number of countries existing under regimes of different levels of economic liberalism by deriving a transition probability matrix from Economic Freedom of the World data. Naively extrapolating trends from 1970-2020 suggests a modest majority of 165 countries will be economically free in the long-run steady state, with results driven by improvements in variables associated with the freedom to trade internationally and especially the quality of the legal system and property rights.

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2

Gotoh, Toshiyuki. "Probability density functions in steady-state Burgers turbulence." Physics of Fluids 11, no. 8 (August 1999): 2143–48. http://dx.doi.org/10.1063/1.870106.

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3

MADAN, DILIP B., MARTIJN PISTORIUS, and WIM SCHOUTENS. "CONIC TRADING IN A MARKOVIAN STEADY STATE." International Journal of Theoretical and Applied Finance 20, no. 02 (March 2017): 1750010. http://dx.doi.org/10.1142/s0219024917500108.

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Trading strategies are valued using nonlinear conditional expectations based on concave probability distortions. They are also referred to as expectation with respect to a nonadditive probability. The nonadditive probability attains conservatism by exaggerating upwards the probabilities of tail loss events and simultaneously deflating the probabilities of tail gain events. Fixed points for value and policy iterations are obtained when probabilities are distorted and they fail to exist for classical linear or additive expectations. Illustrations are provided for Markovian systems in one, two and five dimensions. Trading positions are seen to balance prediction rewards against the demands for hedging value functions.

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Chełminiak, Przemysław, and Michał Kurzyński. "Steady-state distributions of probability fluxes on complex networks." Physica A: Statistical Mechanics and its Applications 468 (February 2017): 540–51. http://dx.doi.org/10.1016/j.physa.2016.10.070.

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5

Samawi, Hani M., Martin Dunbar, and Ding-Geng (Din) Chen. "Steady-state ranked Gibbs sampler." Journal of Statistical Computation and Simulation 82, no. 8 (August 2012): 1223–38. http://dx.doi.org/10.1080/00949655.2011.575378.

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6

Noh, Jae Dong, and Joongul Lee. "On the steady-state probability distribution of nonequilibrium stochastic systems." Journal of the Korean Physical Society 66, no. 4 (February 2015): 544–52. http://dx.doi.org/10.3938/jkps.66.544.

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7

ZHANG Jian-ye, 张建业, and 朴. 燕. PIAO Yan. "Stereo matching algorithm based on improved steady-state matching probability." Chinese Journal of Liquid Crystals and Displays 33, no. 4 (2018): 357–64. http://dx.doi.org/10.3788/yjyxs20183304.0357.

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8

Arizono, I., and A. Yamamoto. "A simplified graphical method for deriving system steady-state probability." IEEE Transactions on Reliability 42, no. 2 (June 1993): 307–13. http://dx.doi.org/10.1109/24.229507.

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9

Carlevaro, Carlos M., and Luis A. Pugnaloni. "Steady state of tapped granular polygons." Journal of Statistical Mechanics: Theory and Experiment 2011, no. 01 (January 6, 2011): P01007. http://dx.doi.org/10.1088/1742-5468/2011/01/p01007.

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10

LIM, JAE-HAK, SANG WOOK SHIN, DAE KYUNG KIM, and DONG HO PARK. "BOOTSTRAP CONFIDENCE INTERVALS FOR STEADY-STATE AVAILABILITY." Asia-Pacific Journal of Operational Research 21, no. 03 (September 2004): 407–19. http://dx.doi.org/10.1142/s021759590400031x.

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Steady-state availability, denoted by A, has been widely used as a measure to evaluate the reliability of a repairable system. In this paper, we develop new confidence intervals for steady-state availability based on four bootstrap methods; standard bootstrap confidence interval, percentile bootstrap confidence interval, bootstrap-t confidence interval, and bias-corrected and accelerated confidence interval. We also investigate the accuracy of these bootstrap confidence intervals by calculating the coverage probability and the average length of intervals.

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11

Zhai, Y., J. Liu, and L. Liu. "MATHEMATICAL ANALYSIS OF VEHICLE DELIVERY SCALE OF BIKE-SHARING RENTAL NODES." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-3 (April 30, 2018): 2229–35. http://dx.doi.org/10.5194/isprs-archives-xlii-3-2229-2018.

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Aiming at the lack of scientific and reasonable judgment of vehicles delivery scale and insufficient optimization of scheduling decision, based on features of the bike-sharing usage, this paper analyses the applicability of the discrete time and state of the Markov chain, and proves its properties to be irreducible, aperiodic and positive recurrent. Based on above analysis, the paper has reached to the conclusion that limit state (steady state) probability of the bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then this paper analyses the difficulty of the transition probability matrix parameter statistics and the linear equations group solution in the traditional solving algorithm of the bike-sharing Markov chain. In order to improve the feasibility, this paper proposes a "virtual two-node vehicle scale solution" algorithm which considered the all the nodes beside the node to be solved as a virtual node, offered the transition probability matrix, steady state linear equations group and the computational methods related to the steady state scale, steady state arrival time and scheduling decision of the node to be solved. Finally, the paper evaluates the rationality and accuracy of the steady state probability of the proposed algorithm by comparing with the traditional algorithm. By solving the steady state scale of the nodes one by one, the proposed algorithm is proved to have strong feasibility because it lowers the level of computational difficulty and reduces the number of statistic, which will help the bike-sharing companies to optimize the scale and scheduling of nodes.

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12

Pollak, Moshe, and Tom Hope. "Sequential detection of a steady state." Sequential Analysis 35, no. 1 (January 2, 2016): 2–29. http://dx.doi.org/10.1080/07474946.2016.1131565.

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13

Cordero, Patricio, Dino Risso, and Rodrigo Soto. "Steady quasi-homogeneous granular gas state." Physica A: Statistical Mechanics and its Applications 356, no. 1 (October 2005): 54–60. http://dx.doi.org/10.1016/j.physa.2005.05.012.

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14

Xia, Chengjun, Xiaotian Zheng, Lin Guan, and Sobia Baig. "Probability analysis of steady-state voltage stability considering correlated stochastic variables." International Journal of Electrical Power & Energy Systems 131 (October 2021): 107105. http://dx.doi.org/10.1016/j.ijepes.2021.107105.

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15

Hong, L. Jeff, and Guangwu Liu. "Pathwise Estimation of Probability Sensitivities Through Terminating or Steady-State Simulations." Operations Research 58, no. 2 (April 2010): 357–70. http://dx.doi.org/10.1287/opre.1090.0739.

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16

Attard, Phil. "Statistical mechanical theory for steady state systems. V. Nonequilibrium probability density." Journal of Chemical Physics 124, no. 22 (June 14, 2006): 224103. http://dx.doi.org/10.1063/1.2203069.

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17

DUBKOV, ALEXANDER. "STEADY-STATE DISTRIBUTIONS FOR HARMONIC OSCILLATOR WITH VERY FAST FREQUENCY FLUCTUATIONS." Fluctuation and Noise Letters 11, no. 03 (September 2012): 1242009. http://dx.doi.org/10.1142/s0219477512420096.

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The moment and probability steady-state characteristics of harmonic oscillator with frequency fluctuations in the form of white noise are investigated. Based on well-known functional approach, we derive integro-differential Kolmogorov equation for the joint probability density function of oscillator coordinate and velocity. For white Gaussian noise, using a set of equations for joint moments, we reconstruct the approximate form of coordinate and velocity distributions in the limit of small friction. As shown, these probability density functions do not exist for zero friction because they cannot be normalized.

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18

Šurda, A. "Statistical mechanics of steady state traffic flow." Journal of Statistical Mechanics: Theory and Experiment 2008, no. 04 (April 14, 2008): P04017. http://dx.doi.org/10.1088/1742-5468/2008/04/p04017.

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19

Glasserman, Paul, Jian-Qiang Hu, and Stephen G. Strickland. "Strongly Consistent Steady-State Derivative Estimates." Probability in the Engineering and Informational Sciences 5, no. 4 (October 1991): 391–413. http://dx.doi.org/10.1017/s0269964800002199.

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We establish strong consistency (i.e., almost sure convergence) of infinitesimal perturbation analysis (IPA) estimators of derivatives of steady-state means for a broad class of systems. Our results substantially extend previously available results on steady-state derivative estimation via IPA.Our basic assumption is that the process under study is regenerative, but our analysis uses regenerative structure in an indirect way: IPA estimators are typically biased over regenerative cycles, so straightforward differentiation of the regenerative ratio formula does not necessarily yield a valid estimator of the derivative of a steady-state mean. Instead, we use regeneration to pass from unbiasedness over fixed, finite time horizons to convergence as the time horizon grows. This provides a systematic way of extending results on unbiasedness to strong consistency.Given that the underlying process regenerates, we provide conditions under which a certain augmented process is also regenerative. The augmented process includes additional information needed to evaluate derivatives; derivatives of time averages of the original process are time averages of the augmented process. Thus, through this augmentation we are able to apply standard renewal theory results to the convergence of derivatives.

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20

Mangeat, Matthieu, Thomas Guérin, and David S. Dean. "Steady state of overdamped particles in the non-conservative force field of a simple non-linear model of optical trap." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 11 (November 1, 2021): 113205. http://dx.doi.org/10.1088/1742-5468/ac3907.

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Abstract Optically trapped particles are often subject to a non-conservative scattering force arising from radiation pressure. In this paper, we present an exact solution for the steady state statistics of an overdamped Brownian particle subjected to a commonly used force field model for an optical trap. The model is the simplest of its kind that takes into account non-conservative forces. In particular, we present the exact results for certain marginals of the full three-dimensional steady state probability distribution, in addition to results for the toroidal probability currents that are present in the steady state, as well as for the circulation of these currents. Our analytical results are confirmed by numerical solution of the steady state Fokker–Planck equation.

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21

Al-Saleh, Mohammad Fraiwan. "Steady-state ranked set sampling and parametric estimation." Journal of Statistical Planning and Inference 123, no. 1 (June 2004): 83–95. http://dx.doi.org/10.1016/s0378-3758(03)00139-3.

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22

Sharma, S. D. "On a non-Markovian time-dependent queueing system." Journal of Applied Probability 26, no. 1 (March 1989): 142–51. http://dx.doi.org/10.2307/3214324.

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This paper studies the transient and steady-state behaviour of a continuous and discrete-time queueing system with non-Markovian type of departure mechanism. The Laplace transforms of the probability generating function of the time-dependent queue length distribution in the transient state are obtained and the probability generating function of the queue length distribution in the steady state is derived therefrom. Finally, some particular cases are discussed.

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23

Sharma, S. D. "On a non-Markovian time-dependent queueing system." Journal of Applied Probability 26, no. 01 (March 1989): 142–51. http://dx.doi.org/10.1017/s0021900200041875.

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This paper studies the transient and steady-state behaviour of a continuous and discrete-time queueing system with non-Markovian type of departure mechanism. The Laplace transforms of the probability generating function of the time-dependent queue length distribution in the transient state are obtained and the probability generating function of the queue length distribution in the steady state is derived therefrom. Finally, some particular cases are discussed.

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24

Sun, J. Q., and C. S. Hsu. "The Generalized Cell Mapping Method in Nonlinear Random Vibration Based Upon Short-Time Gaussian Approximation." Journal of Applied Mechanics 57, no. 4 (December 1, 1990): 1018–25. http://dx.doi.org/10.1115/1.2897620.

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A short-time Gaussian approximation scheme is proposed in the paper. This scheme provides a very efficient and accurate way of computing the one-step transition probability matrix of the previously developed generalized cell mapping (GCM) method in nonlinear random vibration. The GCM method based upon this scheme is applied to some very challenging nonlinear systems under external and parametric Gaussian white noise excitations in order to show its power and efficiency. Certain transient and steady-state solutions such as the first-passage time probability, steady-state mean square response, and the steady-state probability density function have been obtained. Some of the solutions are compared with either the simulation results or the available exact solutions, and are found to be very accurate. The computed steady-state mean square response values are found to be of error less than 1 percent when compared with the available exact solutions. The efficiency of the GCM method based upon the short-time Gaussian approximation is also examined. The short-time Gaussian approximation renders the overhead of computing the one-step transition probability matrix to be very small. It is found that in a comprehensive study of nonlinear stochastic systems, in which various transient and steady-state solutions are obtained in one computer program execution, the GCM method can have very large computational advantages over Monte Carlo simulation.

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25

Piasecki, Jarosław, and Rodrigo Soto. "Approach to a non-equilibrium steady state." Physica A: Statistical Mechanics and its Applications 369, no. 2 (September 2006): 379–86. http://dx.doi.org/10.1016/j.physa.2005.12.045.

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26

PAMUK, SERDAL. "QUALITATIVE ANALYSIS OF A MATHEMATICAL MODEL FOR CAPILLARY FORMATION IN TUMOR ANGIOGENESIS." Mathematical Models and Methods in Applied Sciences 13, no. 01 (January 2003): 19–33. http://dx.doi.org/10.1142/s0218202503002362.

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Qualitative analysis of a mathematical model for capillary formation is presented under assumptions that enzyme and fibronectin concentrations are in quasi-steady state. The aim of this paper is to prove mathematically that the long-time tendency of endothelial cells will be towards the transition probability density function of enzyme and fibronectin. Endothelial cell steady-state solution is obtained and a numerical simulation is provided to show that there is a close agreement between the steady-state solution obtained analytically and the numerically calculated steady-state of the related initial value problem, which provides strong evidence for the stability of this steady-state.

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27

Willie, Helmut. "Periodic steady state of loss systems with periodic inputs." Advances in Applied Probability 30, no. 1 (March 1998): 152–66. http://dx.doi.org/10.1239/aap/1035227997.

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The input of a multiserver loss system is assumed to be a periodic random marked point process which has, with probability one, infinitely many construction points. It is shown that, independently of the initial distribution, there exists a unique periodic process modeling the periodic steady-state behaviour of the loss system. In addition, practical sufficient conditions for the existence of enough construction points are derived.

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28

Willie, Helmut. "Periodic steady state of loss systems with periodic inputs." Advances in Applied Probability 30, no. 01 (March 1998): 152–66. http://dx.doi.org/10.1017/s0001867800008132.

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The input of a multiserver loss system is assumed to be a periodic random marked point process which has, with probability one, infinitely many construction points. It is shown that, independently of the initial distribution, there exists a unique periodic process modeling the periodic steady-state behaviour of the loss system. In addition, practical sufficient conditions for the existence of enough construction points are derived.

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29

Hallen, Mark, Bochong Li, Yu Tanouchi, Cheemeng Tan, Mike West, and Lingchong You. "Computation of Steady-State Probability Distributions in Stochastic Models of Cellular Networks." PLoS Computational Biology 7, no. 10 (October 13, 2011): e1002209. http://dx.doi.org/10.1371/journal.pcbi.1002209.

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30

Zhang, Jianye, and Yan Piao. "Research on Stereo Matching Algorithm Based on Improved Steady-State Matching Probability." Journal of Physics: Conference Series 1004 (April 2018): 012009. http://dx.doi.org/10.1088/1742-6596/1004/1/012009.

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31

Utkin, Lev V., and Sergey V. Gurov. "Steady-state reliability of repairable systems by combined probability and possibility assumptions." Fuzzy Sets and Systems 97, no. 2 (July 1998): 193–202. http://dx.doi.org/10.1016/s0165-0114(96)00362-4.

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32

Choi, Yeontaek, and Sang Gyu Jo. "Steady-state probability density function in wave turbulence under large volume limit." Chinese Physics B 20, no. 5 (May 2011): 050501. http://dx.doi.org/10.1088/1674-1056/20/5/050501.

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33

ROSEN, G. "Existence of steady-state probability distributions in multilocus models for genotype evolution." Bulletin of Mathematical Biology 48, no. 1 (1986): 87–95. http://dx.doi.org/10.1016/s0092-8240(86)90022-4.

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34

Rosen, Gerald. "Existence of steady-state probability distributions in multilocus models for genotype evolution." Bulletin of Mathematical Biology 48, no. 1 (January 1986): 87–95. http://dx.doi.org/10.1007/bf02460064.

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35

Chang, H.-C., A. Karch, and A. Yarom. "An ansatz for one dimensional steady state configurations." Journal of Statistical Mechanics: Theory and Experiment 2014, no. 6 (June 30, 2014): P06018. http://dx.doi.org/10.1088/1742-5468/2014/06/p06018.

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36

Schmidt, Gunter N., Petra Bischoff, Thomas Standl, Kai Jensen, Moritz Voigt, and Jochen Schulte am Esch. "Narcotrend® and Bispectral Index® Monitor Are Superior to Classic Electroencephalographic Parameters for the Assessment of Anesthetic States during Propofol-Remifentanil Anesthesia." Anesthesiology 99, no. 5 (November 1, 2003): 1072–77. http://dx.doi.org/10.1097/00000542-200311000-00012.

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Background A new electroencephalogram monitor, the Narcotrend, was developed to measure anesthetic depth. The authors compared the Narcotrend, the Bispectral Index, and classic electroencephalographic and hemodynamic parameters during anesthesia with propofol and remifentanil. Methods The authors investigated 25 patients undergoing laminectomy at different anesthetic states: awake, steady state anesthesia, first reaction during emergence, and extubation. Narcotrend value; BIS; relative power (percent) in delta, theta, alpha, and beta; median frequency; spectral edge frequency; and hemodynamic parameters were recorded simultaneously. The ability of the classic and processed electroencephalographic and hemodynamic parameters to predict the clinically relevant anesthetic states of awake, steady state anesthesia, first reaction, and extubation was tested using prediction probability. Results Only the Narcotrend was able to differentiate between awake versus steady state anesthesia and steady state anesthesia versus first reaction/extubation with a prediction probability value of more than 0.90. Conclusions Modern electroencephalographic parameters, especially Narcotrend, are more reliable indicators for the clinical assessment of anesthetic states than classic parameters.

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37

Zhai, Liu, Du, and Wu. "Fleet Size and Rebalancing Analysis of Dockless Bike-Sharing Stations Based on Markov Chain." ISPRS International Journal of Geo-Information 8, no. 8 (July 29, 2019): 334. http://dx.doi.org/10.3390/ijgi8080334.

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In order to improve the dynamic optimization of fleet size and standardized management of dockless bike-sharing, this paper focuses on using the Markov stochastic process and linear programming method to solve the problem of bike-sharing fleet size and rebalancing. Based on the analysis of characters of bike-sharing, which are irreducible, aperiodic and positive-recurrence, we prove that the probability limits the state (steady-state) of bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then a new “Markov chain dockless bike-sharing fleet size solution” algorithm is proposed. The process includes three parts. Firstly, the irreducibility of the bike-sharing transition probability matrix is analyzed. Secondly, the rank-one updating method is used to construct the transition probability random prime matrix. Finally, an iterative method for solving the steady-state probability vector is therefore given and the convergence speed of the method is analyzed. Furthermore, we discuss the dynamic solution of the bike-sharing steady-state fleet size according to the time period, so as improving the practicality of the algorithm. To verify the efficiency of this algorithm, we adopt the linear programming method for bicycle rebalancing analysis. Experiment results show that the algorithm could be used to solve the disordered deployment of dockless bike-sharing.

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38

Ridder, Ad. "Stochastic ordering of conditional steady-state probabilities." Stochastic Processes and their Applications 26 (1987): 224–25. http://dx.doi.org/10.1016/0304-4149(87)90153-0.

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39

Shongwe, S. C., J. C. Malela-Majika, and E. M. Rapoo. "One-Sided and Two-Sided w-of-w Runs-Rules Schemes: An Overall Performance Perspective and the Unified Run-Length Derivations." Journal of Probability and Statistics 2019 (February 19, 2019): 1–20. http://dx.doi.org/10.1155/2019/6187060.

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The one-sided and two-sided Shewhart w-of-w standard and improved runs-rules monitoring schemes to monitor the mean of normally distributed observations from independent and identically distributed (iid) samples are investigated from an overall performance perspective, i.e., the expected weighted run-length (EWRL), for every possible positive integer value of w. The main objective of this work is to use the Markov chain methodology to formulate a theoretical unified approach of designing and evaluating Shewhart w-of-w standard and improved runs-rules for one-sided and two-sided X- schemes in both the zero-state and steady-state modes. Consequently, the main findings of this paper are as follows: (i) the zero-state and steady-state ARL and initial probability vectors of some of the one-sided and two-sided Shewhart w-of-w standard and improved runs-rules schemes are theoretically similar in design; however, their empirical performances are different and (ii) unlike previous studies that use ARL only, we base our recommendations using the zero-state and steady-state EWRL metrics and we observe that the steady-state improved runs-rules schemes tend to yield better performance than the other considered competing schemes, separately, for one-sided and two-sided schemes. Finally, the zero-state and steady-state unified approach run-length equations derived here can easily be used to evaluate other monitoring schemes based on a variety of parametric and nonparametric distributions.

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40

DEAN, DAVID S., and ALEXANDRE LEFEVRE. "THE STEADY STATE OF THE TAPPED ISING MODEL." Advances in Complex Systems 04, no. 04 (December 2001): 333–43. http://dx.doi.org/10.1142/s0219525901000255.

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We consider a tapping dynamics, analogous to that in experiments on granular media, on the simple one-dimensional ferromagnetic Ising model. When unperturbed, the system undergoes a single spin flip falling dynamics where only energy lowering moves occur. With this dynamics the system has an exponentially large number of metastable states and gets stuck in blocked or jammed configurations as do granular media. When stuck, the system is tapped, in order to make it evolve, by flipping in parallel each spin with probability p (corresponding to the strength of the tapping). Under this dynamics the system reaches a steady state regime characterized by an asymptotic energy per spin E(p), which is determined analytically. Within the steady state regime we compare certain time averaged quantities with the ensemble average of Edwards based on a canonical measure over metastable states of fixed average energy. The ensemble average yields results in excellent agreement with the dynamical measurements.

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41

Grigorescu, Ilie, and Min Kang. "Steady state and scaling limit for a traffic congestion model." ESAIM: Probability and Statistics 14 (2010): 271–85. http://dx.doi.org/10.1051/ps:2008029.

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42

Khlifi, Y., S. Seddik, and A. El Allati. "Steady state entanglement behavior between two quantum refrigerators." Physica A: Statistical Mechanics and its Applications 596 (June 2022): 127199. http://dx.doi.org/10.1016/j.physa.2022.127199.

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43

Dubkov, Alexander A., Pavel N. Makhov, and Bernardo Spagnolo. "Nonequilibrium steady-state distributions in randomly switching potentials." Physica A: Statistical Mechanics and its Applications 325, no. 1-2 (July 2003): 26–32. http://dx.doi.org/10.1016/s0378-4371(03)00179-1.

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44

Gelenbe, Erol. "Network of interacting synthetic molecules in steady state." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2096 (April 3, 2008): 2219–28. http://dx.doi.org/10.1098/rspa.2008.0001.

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In this paper, we study the steady-state behaviour of a reaction network of interacting molecules using the chemical master equation (CME). The model considers a set of base species from which further compounds are created via binary reactions, as well as by monomolecular and dissipation reactions. The model includes external arrivals of molecules into the reaction volume and assumes that the reaction rates are proportional to the number of molecules of the reactants that are present. We obtain an explicit expression for the solution of the CME in equilibrium under the assumption that the system obeys a mass conservation law for the overall rate of incoming and outgoing molecules. This closed-form solution shows that the joint probability distribution of the number of molecules of each species is in ‘product form’, i.e. it is the product of the marginal distributions for the number of molecules of each species. We also show that the steady-state distribution of the number of molecules of each base and synthesized species follows a Poisson distribution.

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45

Liberzon, D., and R. W. Brockett. "Nonlinear feedback systems perturbed by noise: steady-state probability distributions and optimal control." IEEE Transactions on Automatic Control 45, no. 6 (June 2000): 1116–30. http://dx.doi.org/10.1109/9.863596.

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46

Vallejos C., R. A., and J. M. Martinez V. "A Fast Transformation of Markov Chains and Their Respective Steady-State Probability Distributions." Computer Journal 57, no. 1 (June 27, 2012): 1–11. http://dx.doi.org/10.1093/comjnl/bxs086.

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47

Zhai, Y., J. Liu, J. Du, and J. Chen. "SOLUTION TO FLEET SIZE OF DOCKLESS BIKE-SHARING STATION BASED ON MATRIX ANALYSIS." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences IV-4 (September 19, 2018): 255–62. http://dx.doi.org/10.5194/isprs-annals-iv-4-255-2018.

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<p><strong>Abstract.</strong> Aiming at the problems of the lack of reasonable judgment of fleet size and non-optimization of rebalancing for dockless bike-sharing station, based on the usage characteristics of dockless bike-sharing, this paper demonstrates that the Markov chain is suitable for the analysis of the fleet size of station. It is concluded that dockless bike-sharing Markov chain probability limit state (steady-state) only exists and is independent of the initial probability distribution. On that basis, this paper analyses the difficulty of the transition probability matrix parameter statistics and the power method of the bike-sharing Markov chain, and constructs the transition probability sparse matrix in order to reduce computational complexity. Since the sparse matrices may be reducible, the rank-one updating method is used to construct the transition probability random prime matrix to meet the requirements of steady-state size calculation. An iterative method for solving the steady-state probability is therefore given and the convergence speed of the method is analysed. In order to improve the practicability of the algorithm, the paper further analyses the construction methods of the initial values of the dockless bike-sharing and the transition probability matrices at different time periods in a day. Finally, the algorithm is verified with practical and simulation data. The results of the algorithm can be used as a baseline reference data to dynamically optimize the fleet size of dockless bike-sharing station operated by bike-sharing companies for strengthening standardized management.</p>

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Su, Jie, and Xu Guang Wang. "A Chi-Square Distribution Based Steady-State Data Judgment Criterion." Applied Mechanics and Materials 80-81 (July 2011): 724–29. http://dx.doi.org/10.4028/www.scientific.net/amm.80-81.724.

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The acquisition of steady-state data is the premise for optimizing the boiler combustion parameters. Assuming the measuring parameters obey the Gaussion distribution, this paper uses the large-probability distribution interval to approximate the variation range of random variable, constructs appropriate working condition matrix whose column quadratic sum approximately obeys the Chi-square distribution, and then obtains the Chi-square distribution based steady-state data judgment criterion. The judgment threshold of this criterion could be self-adaptive. This judgment criterion has been validated by an experiment.

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Sakthi, R., V. Vidhya, and T. Dhiki. "A Simple Tool for Solving Queuing Model with Erlang Distribution." Asian Journal of Engineering and Applied Technology 4, no. 1 (May 5, 2015): 5–7. http://dx.doi.org/10.51983/ajeat-2015.4.1.752.

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In this paper we use the online tool to find the performance measures of the steady-state behavior of the queuing model where inter arrival and service times are Erlang distributions with parameters k and m respectively. The suggested tool has a simple graphical interface, based on a recently published simple recurrence method[1], it provides the performance measures of the queuing system (i.e., average number in the system, average waiting time, the system utilization, probability of loss, probability of waiting time), also the steady-state distribution of the system.

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Balakrishnan, A. V. "An Infinite-Dimensional Gaussian Markov Process with Nonnuclear Steady State Covariance." Theory of Probability & Its Applications 38, no. 3 (September 1994): 516–20. http://dx.doi.org/10.1137/1138048.

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