On fluctuation problems in the theory of queues

1976 ◽  
Vol 8 (03) ◽  
pp. 548-583 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Generating Functions ◽  
Finite Differences ◽  
Historical Development ◽  
Banach Algebras ◽  
Point Of View ◽  
Mathematical Methods ◽  
Operator Calculus ◽  
Complex Functions

This paper gives a survey of the historical development of the solutions of various fluctuation problems in the theory of queues from the point of view of the mathematical methods used. These methods include Markov chains, Markov processes, integral equations, complex functions, generating functions, Laplace transforms, factorization of functions, operator calculus, Banach algebras and some particular methods, such as calculus of finite differences and combinatorics. In addition, the paper contains several recent results of the author for semi-Markov queuing processes.

On fluctuation problems in the theory of queues

1976 ◽  
Vol 8 (3) ◽  
pp. 548-583 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Generating Functions ◽  
Finite Differences ◽  
Historical Development ◽  
Banach Algebras ◽  
Point Of View ◽  
Mathematical Methods ◽  
Operator Calculus ◽  
Complex Functions

This paper gives a survey of the historical development of the solutions of various fluctuation problems in the theory of queues from the point of view of the mathematical methods used. These methods include Markov chains, Markov processes, integral equations, complex functions, generating functions, Laplace transforms, factorization of functions, operator calculus, Banach algebras and some particular methods, such as calculus of finite differences and combinatorics. In addition, the paper contains several recent results of the author for semi-Markov queuing processes.

Importance of Promoting Metacognitive Awareness at University

2018 ◽  
Vol 29 (1) ◽  
pp. 3-18
Author(s):  
Masoodi Marjan
Keyword(s):  
Task Performance ◽  
Positive Feedback ◽  
Historical Development ◽  
Metacognitive Strategies ◽  
Point Of View ◽  
Metacognitive Awareness ◽  
Self Confidence ◽  
Self Knowledge ◽  
Knowledge Of Learners ◽  
Theoretical Overview

Abstract The aim of this study is to furnish a reliable theoretical overview on metacognitive awareness. This research is carried out to (1) familiarize the researchers with the definition, components and sub-components of metacognitive awareness (2) discuss a brief outline of metacognitive awareness along with its origin and essence from the point of view of its historical development (3) link metacognitive awareness to a number of other constructs, including motivation (4) illustrate the features of self-regulated students and their recruited metacognitive strategies and (5) briefly examine the major challenges in the implementation of metacognitive awareness. In conclusion, this research reveals that the analysis of metacognitive awareness and its components gives rise to a new notion of auto-noetic (self) knowledge of learners through planning, monitoring and reflectively evaluating task performance, and creates higher levels of self-efficacy which provides students with different educational contexts in which they are able to have more self-confidence, get more positive feedback both from an instructor and classmates and cultivate in learners more self-regulatory characteristics that enable them to learn autonomously, be completely equipped with motivation and be welcoming to challenges. The study provides benefits to both learners and educators. Learners can receive guidance on how to foster metacognitive awareness for being more competent learners. Furthermore, it provides meaningful insights for curriculum developers to provide metacognitive awareness-based curricula.

scholarly journals The Metano Modeling Toolbox MMTB: An Intuitive, Web-Based Toolbox Introduced by Two Use Cases

Metabolites ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 113
Author(s):  
Julia Koblitz ◽  
Sabine Will ◽  
S. Riemer ◽  
Thomas Ulas ◽  
Meina Neumann-Schaal ◽  
...  
Keyword(s):  
Metabolic Networks ◽  
Point Of View ◽  
Use Cases ◽  
Mathematical Methods ◽  
State Behavior ◽  
Web Based ◽  
Research Fields ◽  
Balance Analysis ◽  
Metabolic Models ◽  
User Friendly

Genome-scale metabolic models are of high interest in a number of different research fields. Flux balance analysis (FBA) and other mathematical methods allow the prediction of the steady-state behavior of metabolic networks under different environmental conditions. However, many existing applications for flux optimizations do not provide a metabolite-centric view on fluxes. Metano is a standalone, open-source toolbox for the analysis and refinement of metabolic models. While flux distributions in metabolic networks are predominantly analyzed from a reaction-centric point of view, the Metano methods of split-ratio analysis and metabolite flux minimization also allow a metabolite-centric view on flux distributions. In addition, we present MMTB (Metano Modeling Toolbox), a web-based toolbox for metabolic modeling including a user-friendly interface to Metano methods. MMTB assists during bottom-up construction of metabolic models by integrating reaction and enzymatic annotation data from different databases. Furthermore, MMTB is especially designed for non-experienced users by providing an intuitive interface to the most commonly used modeling methods and offering novel visualizations. Additionally, MMTB allows users to upload their models, which can in turn be explored and analyzed by the community. We introduce MMTB by two use cases, involving a published model of Corynebacterium glutamicum and a newly created model of Phaeobacter inhibens.

Spectral analysis of M/G/1 and G/M/1 type Markov chains

1996 ◽  
Vol 28 (01) ◽  
pp. 114-165 ◽  
Author(s):  
H. R. Gail ◽  
S. L. Hantler ◽  
B. A. Taylor
Keyword(s):  
Markov Chains ◽  
Generating Functions ◽  
Complex Analysis ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Equilibrium Analysis ◽  
Transform Method ◽  
Technical Problems ◽  
The Matrix ◽  
Transient Case

When analyzing the equilibrium behavior of M/G/1 type Markov chains by transform methods, restrictive hypotheses are often made to avoid technical problems that arise in applying results from complex analysis and linear algebra. It is shown that such restrictive assumptions are unnecessary, and an analysis of these chains using generating functions is given under only the natural hypotheses that first moments (or second moments in the null recurrent case) exist. The key to the analysis is the identification of an important subspace of the space of bounded solutions of the system of homogeneous vector-valued Wiener–Hopf equations associated with the chain. In particular, the linear equations in the boundary probabilities obtained from the transform method are shown to correspond to a spectral basis of the shift operator on this subspace. Necessary and sufficient conditions under which the chain is ergodic, null recurrent or transient are derived in terms of properties of the matrix-valued generating functions determined by transitions of the Markov chain. In the transient case, the Martin exit boundary is identified and shown to be associated with certain eigenvalues and vectors of one of these generating functions. An equilibrium analysis of the class of G/M/1 type Markov chains by similar methods is also presented.

scholarly journals Probability Models for Assessing Effectiveness of Advertising Channels in the Internet Environment

2018 ◽  
pp. 209-215
Keyword(s):  
Graph Theory ◽  
Markov Chains ◽  
Markov Processes ◽  
The Internet ◽  
Probability Models ◽  
Method Of Calculation ◽  
Internet Environment ◽  
The Impact ◽  
Theory Of Graphs ◽  
Selection Of

Nowadays, marketing specialists simultaneously use several channels to attract visitors to websites. There is a difficulty in assessing not only the efficiency and conversion of each channel separately, but also in their interconnection. The problem occurs when users visit a website from several sources and only after that do the key action. To assess the effectiveness and selection of the most optimal channels, different models of attribution are used. The models are reviewed in the article. However, we propose to use multi-channel attribution, which provides an aggregate assessment of multi-channel sequences, taking into account that they are interdependent. The purpose of the paper is to create an attribution model that comprehensively evaluates multi-channel sequences and shows the effect of each channel on the conversion. The presented model of attribution can be based on the theory of graphs or Markov chains. The first method of calculation is more visual, the second (based on Markov chains) allows for work with a large amount of data. As a result, a model of multi-channel attribution was presented, which is based on Markov processes or graph theory. It allows for maximum comprehensive assessing of the impact of each channel on the conversion. On the basis of the two methods, calculations were carried out, confirming the adequacy of the model used for the tasks assigned.

scholarly journals First Passage and Collective Marks

2019 ◽  
Vol 8 (6) ◽  
pp. 47
Author(s):  
Yiping Zhang ◽  
Myron Hlynka ◽  
Percy H. Brill
Keyword(s):  
Markov Chains ◽  
Generating Functions ◽  
First Passage Times ◽  
System Of Equations ◽  
First Passage ◽  
Probability Generating Functions ◽  
Collective Marks ◽  
Passage Times

Probability generating functions for first passage times of Markov chains are found using the method of collective marks. A system of equations is found which can be used to obtain moments of the first passage times. Second passage probabilities are discussed.

scholarly journals The Position of Heterodox Economics in Economic Science

2021 ◽  
Vol 66 (2) ◽  
pp. 275-290
Author(s):  
Eleonóra Matoušková
Keyword(s):  
Point Of View ◽  
Austrian School ◽  
Economic Science ◽  
Left Wing ◽  
Mathematical Methods ◽  
Heterodox Economics ◽  
Homo Economicus ◽  
Common Features ◽  
Economic Problems ◽  
Theoretical Approaches

In economic science dominate orthodox economics (mainstream economics respectively neoclassical economics). Despite its numerous intellectual failures, orthodox economics continue to prevail in teaching at universities. A certain alternative to orthodox economics is heterodox economics, which consists of three groups of theoretical approaches, represented by the Left-wing heterodoxy and Neo-Austrian school (we include them together in the Old heterodoxy) and the New heterodoxy. The objective of this article is to define the differences between orthodox economics and heterodox economics, to find common features of individual heterodox approaches and identify substantial differences between them and also highlight the relevance of these heterodox approaches from the point of view of the challenges we are facing today. A common characteristic of heterodoxy is the rejection of orthodoxy, especially its research methods. Heterodox economists reject the axiom that individuals are always rational, the concept of ‘homo economicus’, the application of a formal-deductive approach, the use of mathematical methods in cases that are not appropriate for this, and access from a closed system position. Heterodoxy is a very diverse theoretical tradition, and there are differences not only between the Left-wing heterodoxy, Neo-Austrian school and New heterodoxy, but also within these heterodox groups. They differ on specific topics they deal with and proposed solutions to socio-economic problems.

scholarly journals Financial control between Rashidun Caliphs and the late 11th century

Khatulistiwa ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 43
Author(s):  
Bassem Mohammad Ismail
Keyword(s):  
Control System ◽  
Historical Development ◽  
Point Of View ◽  
Self Control ◽  
Financial Control ◽  
Islamic State ◽  
Historical Evidence ◽  
Efficiency And Effectiveness ◽  
The Subject ◽  
Descriptive Approach

Many modern concepts of financial control and its types that are now adopted have already existed in the Islamic state from Prophet Muhammad message through the Rashidun Caliphs and then the Umayyad and Abbasid through establishing Baitul Mal. This article try to investigate the concept of financial control and types in Islam and the historical development of financial control in Islam. Also clarify the principles of financial control in Islam. The research based on the descriptive approach through the use of scientific studies which dealt with the subject of research, in addition to the historical approach through the use of historical evidence in the way enhancing the opinions presented by the research in the rooting of its themes from the Islamic point of view. This paper give an attention to the behavioral principle and self-control of individuals when working in different areas of life in general and financial in particular, as they have direct causes of increased efficiency and effectiveness financial control system.

Sign in / Sign up

Export Citation Format

Share Document