scholarly journals Families of birth-death processes with similar time-dependent behaviour

2000 ◽  
Vol 37 (3) ◽  
pp. 835-849 ◽  
Author(s):  
R. B. Lenin ◽  
P. R. Parthasarathy ◽  
W. R. W. Scheinhardt ◽  
E. A. van Doorn
Keyword(s):  
Death Rate ◽  
General Setting ◽  
Time Dependent ◽  
Death Process ◽  
Similar Time ◽  
Death Rates ◽  
Transition Functions ◽  
Time Dependent Behaviour ◽  
Dependent Behaviour ◽  
Birth Death

We consider birth-death processes taking values in but allow the death rate in state 0 to be positive, so that escape from is possible. Two such processes with transition functions are said to be similar if, for all there are constants cij such that for all t ≥ 0. We determine conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes, and we identify the members of such a family. These issues are also resolved in the more general setting in which the two processes are called similar if there are constants cij and ν such that for all t ≥ 0.

scholarly journals Families of birth-death processes with similar time-dependent behaviour

2000 ◽  
Vol 37 (03) ◽  
pp. 835-849 ◽  
Author(s):  
R. B. Lenin ◽  
P. R. Parthasarathy ◽  
W. R. W. Scheinhardt ◽  
E. A. van Doorn
Keyword(s):  
Death Rate ◽  
General Setting ◽  
Time Dependent ◽  
Death Process ◽  
Similar Time ◽  
Death Rates ◽  
Transition Functions ◽  
Time Dependent Behaviour ◽  
Dependent Behaviour ◽  
Birth Death

We consider birth-death processes taking values in but allow the death rate in state 0 to be positive, so that escape from is possible. Two such processes with transition functions are said to be similar if, for all there are constants c ij such that for all t ≥ 0. We determine conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes, and we identify the members of such a family. These issues are also resolved in the more general setting in which the two processes are called similar if there are constants c ij and ν such that for all t ≥ 0.

A birth, death and migration process

1969 ◽  
Vol 6 (03) ◽  
pp. 687-691 ◽  
Author(s):  
S. R. Adke
Keyword(s):  
Time Dependent ◽  
Death Process ◽  
Migration Process ◽  
Death Rates ◽  
And Migration ◽  
Birth Death

A model proposed by Bailey (1968) for migratory individuals which reproduce according to a simple birth-death process is generalized to include time dependent birth and death rates.

A TIME-DEPENDENT STUDY OF THE KNOCKOUT QUEUE

2013 ◽  
Vol 27 (3) ◽  
pp. 309-317
Author(s):  
Brian Fralix
Keyword(s):  
Queue Length ◽  
Queueing Systems ◽  
Time Dependent ◽  
Death Process ◽  
Birth Rates ◽  
Death Rates ◽  
Current State ◽  
Dependent Behavior ◽  
Number Of Customers ◽  
Birth Death

We examine the time-dependent behavior of a birth–death process, whose birth rates and death rates are decreasing and increasing, respectively, with respect to the current state. Such models can be used to describe Markovian queueing systems with exponential reneging, where potential arrivals balk with a certain probability that depends on the number of customers observed upon arrival. Our results are derived by interpreting the birth–death process as the queue-length process of what we refer to as the “knockout queue.”

A birth, death and migration process

1969 ◽  
Vol 6 (3) ◽  
pp. 687-691 ◽  
Author(s):  
S. R. Adke
Keyword(s):  
Time Dependent ◽  
Death Process ◽  
Migration Process ◽  
Death Rates ◽  
And Migration ◽  
Birth Death

A model proposed by Bailey (1968) for migratory individuals which reproduce according to a simple birth-death process is generalized to include time dependent birth and death rates.

Application of shotcrete constitutive model to the time dependent behavior of TBM tunnel lining

2018 ◽  
Vol 7 (3) ◽  
pp. 1826
Author(s):  
Heyam H. Shaalan ◽  
Mohd Ashraf Mohamad Ismail ◽  
Romziah Azit
Keyword(s):  
Constitutive Model ◽  
Steel Fibre ◽  
Tunnel Lining ◽  
Time Dependent ◽  
Elastic Behaviour ◽  
Elastic Analysis ◽  
Time Dependent Behaviour ◽  
Shotcrete Lining ◽  
Creep And Shrinkage ◽  
Dependent Behaviour

Shotcrete is ordinary concrete applied to the surface under high pressure. It demonstrates a highly time-dependent behaviour after few hours of application. Traditional approaches assume a simple linear elastic behaviour using a hypothetical young modulus to investigate the time-dependency and creep effects. In this paper, a new constitutive model of shotcrete is applied to evaluate the time-dependent behaviour of a TBM tunnel lining and investigate the parameters that can influence this behaviour. The Shotcrete model is based on the framework of Elasto-plasticity and designed to model shotcrete linings more realistically. The basic data of Pahang-Selangor Raw Water Transfer Project is used for the analysis study. An attempt is made to investigate the influence of some input parameters of the shotcrete model on the time-dependent behaviour of the shotcrete lining. These parameters include the time-dependent stiffness/strength parameters, creep and shrinkage parameters and steel fibre parameters. The variation in shotcrete strength classes causes a noticeable influence on the development of shotcrete compressive strength with time, particularly during the first days of application. The creep and shrinkage strain cause a considerable reduction in the development of the shotcrete stress with time. The impact of steel fibre content is determined, and the result indicated that the development of plain shotcrete stresses with time is lower than that of the reinforced shotcrete. In addition, a comparison study is performed to analyse the tunnel lining behaviour using both shotcrete model and an elastic analysis. Significant differences in shotcrete lining stresses are achieved when using the elastic analysis while the shotcrete model results in a reasonable result that can be used for the design requirements. 

scholarly journals Application of micro-computer tomography and inverse finite element analysis for characterizing the visco-hyperelastic response of bulk liver tissue using indentation

2021 ◽  
Vol 3 (5) ◽  
Author(s):  
Rajeswara R. Resapu ◽  
Roger D. Bradshaw
Keyword(s):  
Finite Element ◽  
Liver Tissue ◽  
Loading Rate ◽  
Time Dependent ◽  
Nonlinear Material ◽  
Computational Time ◽  
List Type ◽  
Prony Series ◽  
Time Dependent Behaviour ◽  
Dependent Behaviour

Abstract In-vitro mechanical indentation experimentation is performed on bulk liver tissue of lamb to characterize its nonlinear material behaviour. The material response is characterized by a visco-hyperelastic material model by the use of 2-dimensional inverse finite element (FE) analysis. The time-dependent behaviour is characterized by the viscoelastic model represented by a 4-parameter Prony series, whereas the large deformations are modelled using the hyperelastic Neo-Hookean model. The shear response described by the initial and final shear moduli and the corresponding Prony series parameters are optimized using ANSYS with the Root Mean Square (RMS) error being the objective function. Optimized material properties are validated using experimental results obtained under different loading histories. To study the efficacy of a 2D model, a three dimensional (3D) model of the specimen is developed using Micro-CT of the specimen. The initial elastic modulus of the lamb liver obtained was found to 13.5 kPa for 5% indentation depth at a loading rate of 1 mm/sec for 1-cycle. These properties are able to predict the response at 8.33% depth and a loading rate of 5 mm/sec at multiple cycles with reasonable accuracy. Article highlights The visco-hyperelastic model accurately models the large displacement as well as the time-dependent behaviour of the bulk liver tissue. Mapped meshing of the 3D FE model saves computational time and captures localized displacement in an accurate manner. The 2D axisymmetric model while predicting the force response of the bulk tissue, cannot predict the localized deformations.

scholarly journals A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process

2021 ◽  
Author(s):  
Michel Mandjes ◽  
Birgit Sollie
Keyword(s):  
Continuous Time ◽  
Real Life ◽  
Numerical Approach ◽  
Time Dependent ◽  
Death Process ◽  
Continuous Time Markov Chain ◽  
Likelihood Estimator ◽  
Real Life Data ◽  
The Matrix ◽  
Birth Death

AbstractThis paper considers a continuous-time quasi birth-death (qbd) process, which informally can be seen as a birth-death process of which the parameters are modulated by an external continuous-time Markov chain. The aim is to numerically approximate the time-dependent distribution of the resulting bivariate Markov process in an accurate and efficient way. An approach based on the Erlangization principle is proposed and formally justified. Its performance is investigated and compared with two existing approaches: one based on numerical evaluation of the matrix exponential underlying the qbd process, and one based on the uniformization technique. It is shown that in many settings the approach based on Erlangization is faster than the other approaches, while still being highly accurate. In the last part of the paper, we demonstrate the use of the developed technique in the context of the evaluation of the likelihood pertaining to a time series, which can then be optimized over its parameters to obtain the maximum likelihood estimator. More specifically, through a series of examples with simulated and real-life data, we show how it can be deployed in model selection problems that involve the choice between a qbd and its non-modulated counterpart.

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