Connecting internally balanced quasi-reversible Markov processes

1992 ◽  
Vol 24 (4) ◽  
pp. 934-959 ◽  
Author(s):  
W. Henderson ◽  
C. E. M. Pearce ◽  
P. K. Pollett ◽  
P. G. Taylor
Keyword(s):  
Invariant Measure ◽  
Markov Processes ◽  
General Framework ◽  
Feedback Mechanism ◽  
Product Form ◽  
Reversible Markov Processes ◽  
The Individual ◽  
Internal Balance ◽  
Feedback Queues ◽  
Individual Nodes

We provide a general framework for interconnecting a collection of quasi-reversible nodes in such a way that the resulting process exhibits a product-form invariant measure. The individual nodes can be quite general, although some degree of internal balance will be assumed. Any of the nodes may possess a feedback mechanism. Indeed, we pay particular attention to a class of feedback queues, characterized by the fact that their state description allows one to maintain a record of the order in which events occur. We also examine in some detail the problem of determining for which values of the arrival rates a node does exhibit quasi-reversibility.

Connecting internally balanced quasi-reversible Markov processes

1992 ◽  
Vol 24 (04) ◽  
pp. 934-959 ◽  
Author(s):  
W. Henderson ◽  
C. E. M. Pearce ◽  
P. K. Pollett ◽  
P. G. Taylor
Keyword(s):  
Invariant Measure ◽  
Markov Processes ◽  
General Framework ◽  
Feedback Mechanism ◽  
Product Form ◽  
Reversible Markov Processes ◽  
The Individual ◽  
Internal Balance ◽  
Feedback Queues ◽  
Individual Nodes

We provide a general framework for interconnecting a collection of quasi-reversible nodes in such a way that the resulting process exhibits a product-form invariant measure. The individual nodes can be quite general, although some degree of internal balance will be assumed. Any of the nodes may possess a feedback mechanism. Indeed, we pay particular attention to a class of feedback queues, characterized by the fact that their state description allows one to maintain a record of the order in which events occur. We also examine in some detail the problem of determining for which values of the arrival rates a node does exhibit quasi-reversibility.

Connecting reversible Markov processes

1986 ◽  
Vol 18 (4) ◽  
pp. 880-900 ◽  
Author(s):  
P. K. Pollett
Keyword(s):  
Invariant Measure ◽  
Random Walks ◽  
Markov Processes ◽  
Product Form ◽  
Migration Process ◽  
Reversible Markov Processes

We provide a framework for interconnecting a collection of reversible Markov processes in such a way that the resulting process has a product-form invariant measure with respect to which the process is reversible. A number of examples are discussed including Kingman&s reversible migration process, interconnected random walks and stratified clustering processes.

Connecting reversible Markov processes

1986 ◽  
Vol 18 (04) ◽  
pp. 880-900 ◽  
Author(s):  
P. K. Pollett
Keyword(s):  
Invariant Measure ◽  
Random Walks ◽  
Markov Processes ◽  
Product Form ◽  
Migration Process ◽  
Reversible Markov Processes

We provide a framework for interconnecting a collection of reversible Markov processes in such a way that the resulting process has a product-form invariant measure with respect to which the process is reversible. A number of examples are discussed including Kingman&s reversible migration process, interconnected random walks and stratified clustering processes.

Development and destruction of the liberal prison system in Spain: a general framework for studying the topic

2019 ◽  
Vol 5 (10) ◽  
pp. 424
Author(s):  
Luis Gargallo Vaamonde
Keyword(s):  
Civil War ◽  
20Th Century ◽  
General Framework ◽  
Belief System ◽  
Prison System ◽  
Early Years ◽  
Second Republic ◽  
Social Harmony ◽  
The Government ◽  
The Individual

During the Restoration and the Second Republic, up until the outbreak of the Civil War, the prison system that was developed in Spain had a markedly liberal character. This system had begun to acquire robustness and institutional credibility from the first dec- ade of the 20th Century onwards, reaching a peak in the early years of the government of the Second Republic. This process resulted in the establishment of a penitentiary sys- tem based on the widespread and predominant values of liberalism. That liberal belief system espoused the defence of social harmony, property and the individual, and penal practices were constructed on the basis of those principles. Subsequently, the Civil War and the accompanying militarist culture altered the prison system, transforming it into an instrument at the service of the conflict, thereby wiping out the liberal agenda that had been nurtured since the mid-19th Century.

Teacher’s Corner: Toward a Coherent View of Reliability in Test Theory

1997 ◽  
Vol 22 (4) ◽  
pp. 478-484
Author(s):  
Heng Li ◽  
Howard Wainer
Keyword(s):  
Internal Consistency ◽  
Test Scores ◽  
General Framework ◽  
Test Theory ◽  
Mathematical Framework ◽  
Individual Character ◽  
The Individual ◽  
Reliability Coefficients

Reliability of test scores, as estimated through measures of internal consistency, has been characterized mathematically in many ways that appear, on the surface at least, to be very dissimilar to one another. In this essay we provide a general mathematical framework that specializes to four different reliability coefficients. Through consideration of this general framework it becomes easier to convey to students both the individual character of the different formulations of reliability and the extent of their underlying similarity. In addition to providing a coherent view of reliability, the unified formula is also found to be a convenient vehicle for introducing more specialized topics, such as the Kaiser-Guttman rule.

Toward an Agenda for Error Research

1992 ◽  
Vol 36 (9) ◽  
pp. 640-643 ◽  
Author(s):  
Neville Moray
Keyword(s):  
Cognitive Psychology ◽  
General Framework ◽  
Human Error ◽  
Social Impact ◽  
Great Increase ◽  
Restricted Area ◽  
Psychological Mechanisms ◽  
The Individual ◽  
And Control

There has been a great increase in interest in human error and its impact on the individual and society in recent years. The present symposium is but one example of this in a restricted area. Several general accounts of human error and the psychological mechanisms which underlie it have appeared in recent years, but for the most part these have concentrated on accounts of error based on research on the cognitive psychology of the individual. In this paper I discuss a more general framework for the stidy of error, not for the purpose of understanding it alone, but rather for putting into place a program for muitigating its effect in the larger arena of social impact. Only by integrating research at a variety of levels and using a variety of techniques can we hope to understand and control the effects of error.

scholarly journals Limit Theorems for Reversible Markov Processes

1973 ◽  
Vol 1 (6) ◽  
pp. 1014-1025
Author(s):  
Michael L. Levitan ◽  
Lawrence H. Smolowitz
Keyword(s):  
Markov Processes ◽  
Limit Theorems ◽  
Reversible Markov Processes

2-D AUTOMATIC COMPOSITION OF NODAL VALUES FROM NUMERICAL MODEL USING SCRIPT PROGRAMMING

2013 ◽  
Vol 62 (1) ◽  
Author(s):  
Rudi Heriansyah
Keyword(s):  
Finite Element ◽  
Numerical Modeling ◽  
Numerical Model ◽  
Finite Difference ◽  
Two Dimensional ◽  
Commercial Software ◽  
One Dimensional ◽  
Automatic Composition ◽  
The Individual ◽  
Individual Nodes

There are many commercial software to perform numerical modeling based on finite element (FEM) and finite difference (FDM) methods. It is often a requirement to the designer, that the values of the individual nodes in the numerical model are known. Usually, these softwares provide two methods to achieve this; firstly, by clicking directly onto the nodes of interest and secondly, by saving or exporting the whole nodal values to an external file. The former way is appropriate for models with small number of nodes, but as the number of nodes increases, it is no longer an efficient or effective way. Through the latter method, all nodal values are obtained, however the values are one-dimensional, and in some cases, only certain nodal values are required for presentation. In this paper, an algorithm for automatic composition of nodal values obtained from the second method mentioned above. The composed nodal values will be in two-dimensional form as this is the format used for uniform shaped model (square or rectangular). Since numerical softwares usually have facilities to save the data in a spreadsheet format, the proposed algorithm is implemented in this environment by using spreadsheet script programming.

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