An Improved Analytical Approach for Modeling the Effect of Rotor Wake Curvature Using Finite-State Induced Flow Models

In many communication and computer systems, information arrives to a multiplexer, switch or information processor at a rate which fluctuates randomly, often with a high degree of correlation in time. The information is buffered for service (the server typically being a communication channel or processing unit) and the service rate may also vary randomly. Accurate capture of the statistical properties of these fluctuations is facilitated by modeling the arrival and service rates as superpositions of a number of independent finite state reversible Markov processes. We call such models separable Markov-modulated rate processes (MMRP). In this work a general mathematical model for separable MMRPs is presented, focusing on Markov-modulated continuous flow models. An efficient procedure for analyzing their performance is derived. It is shown that the ‘state explosion' problem typical of systems composed of a large number of subsystems, can be circumvented because of the separability property, which permits a decomposition of the equations for the equilibrium probabilities of these systems. The decomposition technique (generalizing a method proposed by Kosten) leads to a solution of the equilibrium equations expressed as a sum of terms in Kronecker product form. A key consequence of decomposition is that the computational complexity of the problem is vastly reduced for large systems. Examples are presented to illustrate the power of the solution technique.

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Analytical Approach to the Induced Flow of a Helicopter Rotor in Vertical Descent

Journal of the American Helicopter Society ◽

10.4050/jahs.35.92 ◽

1990 ◽

Vol 35 (1) ◽

pp. 92-98 ◽

Cited By ~ 8

Author(s):

Wang Shi‐cun

Keyword(s):

Analytical Approach ◽

Helicopter Rotor ◽

Vertical Descent ◽

Induced Flow

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Analysis of separable Markov-modulated rate models for information-handling systems

Advances in Applied Probability ◽

10.2307/1427514 ◽

1991 ◽

Vol 23 (1) ◽

pp. 105-139 ◽

Cited By ~ 144

Author(s):

Thomas E. Stern ◽

Anwar I. Elwalid

Keyword(s):

Solution Technique ◽

Service Rate ◽

Processing Unit ◽

Equilibrium Equations ◽

Flow Models ◽

Separability Property ◽

Finite State ◽

Service Rates ◽

Rate Processes ◽

Markov Modulated

In many communication and computer systems, information arrives to a multiplexer, switch or information processor at a rate which fluctuates randomly, often with a high degree of correlation in time. The information is buffered for service (the server typically being a communication channel or processing unit) and the service rate may also vary randomly. Accurate capture of the statistical properties of these fluctuations is facilitated by modeling the arrival and service rates as superpositions of a number of independent finite state reversible Markov processes. We call such models separable Markov-modulated rate processes (MMRP).In this work a general mathematical model for separable MMRPs is presented, focusing on Markov-modulated continuous flow models. An efficient procedure for analyzing their performance is derived. It is shown that the ‘state explosion' problem typical of systems composed of a large number of subsystems, can be circumvented because of the separability property, which permits a decomposition of the equations for the equilibrium probabilities of these systems. The decomposition technique (generalizing a method proposed by Kosten) leads to a solution of the equilibrium equations expressed as a sum of terms in Kronecker product form. A key consequence of decomposition is that the computational complexity of the problem is vastly reduced for large systems. Examples are presented to illustrate the power of the solution technique.

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Effects of acoustic-streaming-induced flow in evaporating nanofluid droplets

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.505 ◽

2011 ◽

Vol 692 ◽

pp. 207-219 ◽

Cited By ~ 20

Author(s):

Abhishek Saha ◽

Saptarshi Basu ◽

Ranganathan Kumar

Keyword(s):

Particle Size ◽

Analytical Approach ◽

Particle Concentration ◽

Morphological Evolution ◽

Acoustic Streaming ◽

Density Stratification ◽

Fluid Viscosity ◽

Initial Particle ◽

Levitated Droplet ◽

Induced Flow

AbstractWe study the effect of acoustic streaming on nanoparticle motion and morphological evolution inside an acoustically levitated droplet using an analytical approach coupled with experiments. Nanoparticle migration due to internal recirculation forms a density stratification, the location of which depends on initial particle concentration. The time scale of density stratification is similar to that of perikinetic-driven agglomeration of particle flocculation. The density stratification ultimately leads to force imbalance leading to a unique bowl-shaped structure. Our analysis shows the mechanism of bowl formation and how it is affected by particle size, concentration, internal recirculation and fluid viscosity.

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On fractional flow models and equivalent finite state processes

Journal of Mathematical Analysis and Applications ◽

10.1016/0022-247x(88)90410-6 ◽

1988 ◽

Vol 133 (2) ◽

pp. 395-403

Author(s):

James Flynn ◽

Jacob Wijngaard

Keyword(s):

Fractional Flow ◽

Flow Models ◽

Finite State

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Accuracy of Semi-Analytical and Numerical Approaches in the Evaluation of Serial Bernoulli Production Lines

Mathematics ◽

10.3390/math9131461 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1461

Author(s):

Viktor Ložar ◽

Neven Hadžić ◽

Tihomir Opetuk ◽

Vedran Slapničar

Keyword(s):

Performance Measures ◽

Analytical Approach ◽

Manufacturing Industry ◽

Production Systems ◽

Numerical Approach ◽

Production Lines ◽

State Behavior ◽

Finite State ◽

State Method ◽

Numerical Approaches

The manufacturing industry has a great impact on the economic growth of countries. It is, therefore, crucial to master the skills of the production system by mathematical tools that enable the evaluation of the production systems’ performance measures. Four mathematical approaches toward the modeling of steady-state behavior of serial Bernoulli production lines were considered in this study, namely, the analytical approach, the finite state method, the aggregation procedure, and numerical modeling. The accuracy of the performance measures determined using the semi-analytical methods and the numerical approach was validated using numerous theoretical examples and the results obtained using the analytical model. All of the considered methods demonstrated relevant reliability, regardless of the different theoretical backgrounds.

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