Refined Approximate Algorithm for Steady-State Probabilities of the Large Scale Queuing Systems with Instantaneous and Delayed Feedback

In this paper, models of unreliable multi-server retrial queues with delayed feedback are examined. The Bernoulli retrial is allowed upon the arrival of both primary (from outside) and feedback customers (from orbit), as well as the Bernoulli feedback that may occur after each service in this system. Servers can break down both during the service of customers and when they are idle. If a server breaks down during the service of a customer, then the interrupted customer, in accordance with the Bernoulli scheme, decides either to leave the system or join a common orbit of retrial and feedback customers. An approximate method, based on the space merging approach of three-dimensional Markov chains, is proposed for the calculation of the steady-state probabilities, as well as performance measures of the system. The results of the numerical experiments are demonstrated.

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Cyclic Breathing Simulations in Large Scale Models of the Lung Airway From the Oronasal Opening to the Terminal Bronchioles

Volume 2: Biomedical and Biotechnology ◽

10.1115/imece2012-88901 ◽

2012 ◽

Author(s):

D. Keith Walters ◽

Greg W. Burgreen ◽

Robert L. Hester ◽

David S. Thompson ◽

David M. Lavallee ◽

...

Keyword(s):

Steady State ◽

Boundary Conditions ◽

Large Scale ◽

Whole Body ◽

Patient Specific ◽

Cfd Simulations ◽

Reduced Order ◽

Scale Models ◽

Steady State Simulation ◽

Conducting Zone

Computational fluid dynamics (CFD) simulations were performed for unsteady periodic breathing conditions, using large-scale models of the human lung airway. The computational domain included fully coupled representations of the orotracheal region and large conducting zone up to generation four (G4) obtained from patient-specific CT data, and the small conducting zone (to G16) obtained from a stochastically generated airway tree with statistically realistic geometrical characteristics. A reduced-order geometry was used, in which several airway branches in each generation were truncated, and only select flow paths were retained to G16. The inlet and outlet flow boundaries corresponded to the oronasal opening (superior), the inlet/outlet planes in terminal bronchioles (distal), and the unresolved airway boundaries arising from the truncation procedure (intermediate). The cyclic flow was specified according to the predicted ventilation patterns for a healthy adult male at three different activity levels, supplied by the whole-body modeling software HumMod. The CFD simulations were performed using Ansys FLUENT. The mass flow distribution at the distal boundaries was prescribed using a previously documented methodology, in which the percentage of the total flow for each boundary was first determined from a steady-state simulation with an applied flow rate equal to the average during the inhalation phase of the breathing cycle. The distal pressure boundary conditions for the steady-state simulation were set using a stochastic coupling procedure to ensure physiologically realistic flow conditions. The results show that: 1) physiologically realistic flow is obtained in the model, in terms of cyclic mass conservation and approximately uniform pressure distribution in the distal airways; 2) the predicted alveolar pressure is in good agreement with previously documented values; and 3) the use of reduced-order geometry modeling allows accurate and efficient simulation of large-scale breathing lung flow, provided care is taken to use a physiologically realistic geometry and to properly address the unsteady boundary conditions.

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Stochastic ordering of conditional steady-state probabilities

Stochastic Processes and their Applications ◽

10.1016/0304-4149(87)90153-0 ◽

1987 ◽

Vol 26 ◽

pp. 224-225

Author(s):

Ad Ridder

Keyword(s):

Steady State ◽

Stochastic Ordering ◽

Steady State Probabilities

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The Research of Production Process Statistical Steady-State Based on the Hypothesis Test

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.314-316.2433 ◽

2011 ◽

Vol 314-316 ◽

pp. 2433-2438

Author(s):

Wei Zhi Wang

Keyword(s):

Quality Control ◽

Steady State ◽

Production Process ◽

Quantitative Method ◽

Large Scale ◽

Hypothesis Test ◽

Influence Factors ◽

Normal Operation ◽

Scale Production ◽

Large Scale Production

By only applying a after the event exam in the quality control of the batch production is not enough to meet the needs of modern large-scale production. To a certain extent, modern quality control is a dynamic process of the steady-state judge and adjustment. A simple and reliable steady-state judge rule and method is the premise to guarantee the normal operation. This paper provides a quantitative method to evaluate production process steady-state by analyzing influence factors based on mathematical statistics. The method is both suitable for simple production process and complex production process with sub-processes.

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Nonlinear Steady-State Optimization of Large-Scale Gas Transmission Networks

Energies ◽

10.3390/en14102832 ◽

2021 ◽

Vol 14 (10) ◽

pp. 2832

Author(s):

Andrzej J. Osiadacz ◽

Małgorzata Kwestarz

Keyword(s):

Steady State ◽

Large Scale ◽

Optimization Problem ◽

Operating Cost ◽

Network Efficiency ◽

Major Objective ◽

Transmission Networks ◽

Sqp Method ◽

Gas Network ◽

Compressor Power

The major optimization problem of the gas transmission system is to determine how to operate the compressors in a network to deliver a given flow within the pressure bounds while using minimum compressor power (minimum fuel consumption or maximum network efficiency). Minimization of fuel usage is a major objective to control gas transmission costs. This is one of the problems that has received most of the attention from both practitioners and researchers because of its economic impact. The article describes the algorithm of steady-state optimization of a high-pressure gas network of any structure that minimizes the operating cost of compressors. The developed algorithm uses the “sequential quadratic programming (SQP)” method. The tests carried out on the real network segment confirmed the correctness of the developed algorithm and, at the same time, proved its computational efficiency. Computational results obtained with the SQP method demonstrate the viability of this approach.

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A single server Markovian queuing system with limited buffer and reverse balking

Independent Journal of Management & Production ◽

10.14807/ijmp.v12i7.1471 ◽

2021 ◽

Vol 12 (7) ◽

pp. 1774-1784

Author(s):

Girin Saikia ◽

Amit Choudhury

Keyword(s):

Steady State ◽

Performance Measures ◽

Mutual Fund ◽

System Size ◽

Queuing System ◽

Single Server ◽

Insurance Company ◽

Number Of Customers ◽

Steady State Probabilities

The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance company, Mutual Fund Company, banks etc.). As the number of customers in the firm goes up, it creates trust among potential investors. Fewer customers would like to balk as the number of customers goes up. In this paper, we develop an M/M/1/k queuing system with reverse balking. The steady-state probabilities of the model are obtained and closed forms of expression of a number of performance measures are derived.

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Coriolis force influence on the AKA effect

10.5194/egusphere-egu21-13421 ◽

2021 ◽

Author(s):

Peter Rutkevich ◽

Georgy Golitsyn ◽

Anatoly Tur

Keyword(s):

Steady State ◽

Stokes Equation ◽

Nonlinear Equations ◽

Coriolis Force ◽

Large Scale ◽

Fluid Velocity ◽

Navier Stokes ◽

Basic Solution ◽

Navier Stokes Equation ◽

Alpha Effect

Large-scale instability in incompressible fluid driven by the so called Anisotropic Kinetic Alpha (AKA) effect satisfying the incompressible Navier-Stokes equation with Coriolis force is considered. The external force is periodic; this allows applying an unusual for turbulence calculations mathematical method developed by Frisch et al [1]. The method provides the orders for nonlinear equations and obtaining large scale equations from the corresponding secular relations that appear at different orders of expansions. This method allows obtaining not only corrections to the basic solutions of the linear problem but also provides the large-scale solution of the nonlinear equations with the amplitude exceeding that of the basic solution. The fluid velocity is obtained by numerical integration of the large-scale equations. The solution without the Coriolis force leads to constant velocities at the steady-state, which agrees with the full solution of the Navier-Stokes equation reported previously. The time-invariant solution contains three families of solutions, however, only one of these families contains stable solutions. The final values of the steady-state fluid velocity are determined by the initial conditions. After account of the Coriolis force the solutions become periodic in time and the family of solutions collapses to a unique solution. On the other hand, even with the Coriolis force the fluid motion remains two-dimensional in space and depends on a single spatial variable. The latter fact limits the scope of the AKA method to applications with pronounced 2D nature. In application to 3D models the method must be used with caution.[1] U. Frisch, Z.S. She and P. L. Sulem, &#8220;Large-Scale Flow Driven by the Anisotropic Kinetic Alpha Effect,&#8221; Physica D, Vol. 28, No. 3, 1987, pp. 382-392.

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Investigating Fast- and Slow-settling Phosphorus Fractions in Lakes using Steady-state Modeling

10.5194/egusphere-egu21-13910 ◽

2021 ◽

Author(s):

Hamed Khorasani ◽

Zhenduo Zhu

Keyword(s):

Steady State ◽

Mass Balance ◽

Large Scale ◽

Hydraulic Residence Time ◽

Simple Method ◽

Retention Models ◽

Mass Balance Models ◽

Limiting Nutrient ◽

Fast Settling ◽

P Retention

Phosphorus (P) is the key and limiting nutrient in the eutrophication of freshwater resources. Modeling P retention in lakes using steady-state mass balance models (i.e. Vollenweider-type models) provides insights into the lake P management and a simple method for large-scale assessments of P in lakes. One of the basic problems in the mass balance modeling of P in lakes is the removal of P from the lake water column by settling. A fraction of the incoming P into the lake from the watershed is associated with fast-settling particles (e.g. sediment particles) that result in the removal of that fraction of P quickly at the lake entrance. However, existing models considering a constant fraction of fast-settling TP for all lakes are shown to result in overestimation of the retention of P in lakes with short hydraulic residence time. In this study, we combine a hypothesis of the fast- and slow-settling P fractions into the steady-state mass balance models of P retention in lakes. We use a large database of lakes to calibrate the model and evaluate the hypothesis. The results of this work can be used for the improvement of the prediction power of P retention models in lakes and help to better understand the processes of P cycling in lakes.

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