Queuing Systems with a Time Lag

2021 ◽  
Vol 27 (6) ◽  
pp. 291-298
Author(s):  
V. N. Tarasov ◽  
Keyword(s):  
Integral Equation ◽  
Waiting Time ◽  
Zero Point ◽  
Queuing Systems ◽  
Average Waiting Time ◽  
Average Value ◽  
Special Cases ◽  
Wide Range ◽  
Distribution Laws ◽  
The Right

The article discusses various queuing systems (QS) formed by four laws of probability distributions: exponential, hyperexponential, Erlang and hyper-Erlang of the second order. These four laws form sixteen different QS. In contrast to the classical theory, this article considers QS with distribution laws shifted to the right from the zero point. Such QS are of type G/G/1 with arbitrary laws of the distribution of intervals between the requirements of the input flow and the service time. As you know, for such systems it is impossible to obtain solutions for the main characteristic of QS the average waiting time in the general case. Therefore, studies of such systems are important for special cases of distribution laws. The article provides an overview of the author's results for the average waiting time in a queue in a closed form for systems with input distributions shifted to the right from the zero point. To solve this problem, the spectral decomposition method for solving the Lindley integral equation was used. In the course of solving the problem, spectral decompositions of the solution of the Lindley integral equation for eight systems were obtained and with their help calculation formulas were derived for the average waiting time in the queue. It is shown that in systems with delay, the average waiting time is shorter than in conventional systems. The obtained calculation formulas for the average waiting time expand and complement the well-known incomplete formula of the queuing theory for the average waiting time for G/G/1 systems. The proposed approach allows us to calculate the average value and moments of higher orders of waiting time for these systems in mathematical packages for a wide range of changes in traffic parameters. Given the fact that the variation in packet delay (jitter) in the telecommunications standard is defined as the spread of waiting time around its average value, the jitter can be determined through the variance of the waiting time.

scholarly journals COMPARISON OF TWO FORMS OF ERLANGIAN DISTRIBUTION LAW IN QUEUING THEORY

2021 ◽  
pp. 48-56
Author(s):  
V. N. Tarasov
Keyword(s):  
Integral Equation ◽  
Closed Form ◽  
Waiting Time ◽  
Service Time ◽  
Queuing Theory ◽  
Time Shift ◽  
Queuing Systems ◽  
Average Waiting Time ◽  
Coefficients Of Variation ◽  
Erlang Distributions

Context. For modeling various data transmission systems, queuing systems G/G/1 are in demand, this is especially important because there is no final solution for them in the general case. The problem of the derivation in closed form of the solution for the average waiting time in the queue for ordinary system with erlangian input distributions of the second order and for the same system with shifted to the right distributions is considered. Objective. Obtaining a solution for the main system characteristic – the average waiting time for queue requirements for three types of queuing systems of type G/G/1 with usual and shifted erlangian input distributions. Method. To solve this problem, we used the classical method of spectral decomposition of the solution of Lindley integral equation, which allows one to obtain a solution for average the waiting time for systems under consideration in a closed form. For the practical application of the results obtained, the well-known method of moments of the theory of probability was used. Results. For the first time, spectral expansions of the solution of the Lindley integral equation for systems with ordinary and shifted Erlang distributions are obtained, with the help of which the calculation formulas for the average waiting time in the queue for the above systems in closed form are derived. Conclusions. The difference between the usual and normalized distribution is that the normalized distribution has a mathematical expectation independent of the order of the distribution k, therefore, the normalized and normal Erlang distributions differ in numerical characteristics. The introduction of the time shift parameter in the laws of input flow distribution and service time for the systems under consideration turns them into systems with a delay with a shorter waiting time. This is because the time shift operation reduces the coefficient of variation in the intervals between the receipts of the requirements and their service time, and as is known from queuing theory, the average wait time of requirements is related to these coefficients of variation by a quadratic dependence. The system with usual erlangian input distributions of the second order is applicable only at a certain point value of the coefficients of variation of the intervals between the receipts of the requirements and their service time. The same system with shifted distributions allows us to operate with interval values of coefficients of variations, which expands the scope of these systems. This approach allows us to calculate the average delay for these systems in mathematical packages for a wide range of traffic parameters.

scholarly journals DELAY MODELS BASED ON SYSTEMS WITH USUAL AND SHIFTED HYPEREXPONENTIAL AND HYPERERLANGIAN INPUT DISTRIBUTIONS

2021 ◽  
pp. 56-64
Author(s):  
V. N. Tarasov ◽  
N. F. Bakhareva
Keyword(s):  
Integral Equation ◽  
Closed Form ◽  
Waiting Time ◽  
Service Time ◽  
Spectral Decomposition ◽  
Flow Distribution ◽  
Input Flow ◽  
Average Delay ◽  
Spectral Expansions ◽  
Wide Range

Context. In the queueing theory, the study of systems with arbitrary laws of the input flow distribution and service time is relevant because it is impossible to obtain solutions for the waiting time in the final form for the general case. Therefore, the study of such systems for particular cases of input distributions is important. Objective. Getting a solution for the average delay in the queue in a closed form for queuing systems with ordinary and with shifted to the right from the zero point hyperexponential and hypererlangian distributions in stationary mode. Method. To solve this problem, we used the classical method of spectral decomposition of the solution of the Lindley integral equation. This method allows to obtaining a solution for the average delay for two systems under consideration in a closed form. The method of spectral decomposition of the solution of the Lindley integral equation plays an important role in the theory of systems G/G/1. For the practical application of the results obtained, the well-known method of moments of probability theory is used. Results. For the first time, a spectral decomposition of the solution of the Lindley integral equation for systems with ordinary and with shifted hyperexponential and hyperelangian distributions is obtained, which is used to derive a formula for the average delay in a queue in closed form. Conclusions. It is proved that the spectral expansions of the solution of the Lindley integral equation for the systems under consideration coincide; therefore, the formulas for the mean delay will also coincide. It is shown that in systems with a delay, the average delay is less than in conventional systems. The obtained expression for the waiting time expands and complements the wellknown incomplete formula of queuing theory for the average delay for systems with arbitrary laws of the input flow distribution and service time. This approach allows us to calculate the average delay for these systems in mathematical packages for a wide range of traffic parameters. In addition to the average waiting time, such an approach makes it possible to determine also moments of higher orders of waiting time. Given the fact that the packet delay variation (jitter) in telecommunications is defined as the spread of the waiting time from its average value, the jitter can be determined through the variance of the waiting time.

scholarly journals The Timeliness of the Reserved Service in the Cluster with the Regulation of the Time of Destruction of Overdue Requests in the Node Queues

2021 ◽  
Author(s):  
Vladimir Bogatyrev ◽  
Stanislav Bogatyrev ◽  
Anatoly Bogatyrev
Keyword(s):  
Distributed Computing ◽  
Real Time ◽  
Distributed Control ◽  
Waiting Time ◽  
Significant Influence ◽  
Queuing Systems ◽  
Time Limits ◽  
Average Waiting Time ◽  
Insufficient Time ◽  
Maximum Allowable Time

With the increasing complexity of distributed control tasks based on their intellectualization, there are problems of insufficient time and computing resources for functioning in real time. In this regard, there is a need to develop methods for organizing distributed real-time computer systems, based on the consolidation of distributed computing resources with their integration into clusters. The possibilities of increasing the probability of timely servicing of waiting- critical requests in the cluster as a result of query replication and controlling the time of destruction of potentially expired replicas in node queues are investigated. The cluster is represented as a group of queuing systems with infinite queues with a limited average waiting time. The effectiveness of the reserved service of a real-time request is determined by the probability of executing at least one of the generated copies of the request in the maximum allowable time without losing it due to errors and waiting time limits in the queues of cluster nodes. It is shown that there is an optimal multiplicity of query replication with a significant influence of the choice of restrictions on the waiting time for requests in queues before they are destroyed.

scholarly journals The Solution Method for Lindley Integral Equation

Telecom IT ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 1-11
Author(s):  
I. Kartashevskiy
Keyword(s):  
Integral Equation ◽  
Waiting Time ◽  
General Type ◽  
Solution Method ◽  
Queueing System ◽  
Statistical Characteristics ◽  
Practical Relevance ◽  
Research Subject ◽  
Average Waiting Time ◽  
System Method

Research subject. This article considers the problem of solving the Lindley integral equation for esti-mating the average waiting time of a request in a queue in the general type queueing system. Method. Here we obtain a solution of the Lindley integral equation using selective functions. Core results. The proposed solution is based on the “degeneration” of the kernel of the Lindley integral equation where the kernel is factorized by its variables. Practical relevance. The considered procedure allows to obtain a solution of the integral equation for any statistical characteristics of the served traffic.

scholarly journals Comparison of Approximation Methods for the Estimation of Distributions in the Analysis of the G/G/1 Queue

2019 ◽  
Vol 4 (4) ◽  
pp. 1040-1050 ◽  
Author(s):  
O. Karaulova ◽  
N. Kireeva ◽  
L. Chupakhina ◽  
A. Gazizulina
Keyword(s):  
Integral Equation ◽  
Data Analysis ◽  
Waiting Time ◽  
Statistical Data ◽  
Distribution Functions ◽  
Statistical Data Analysis ◽  
Average Waiting Time ◽  
Spectral Solution ◽  
Protocol Analyzer

The analysis of Weibull and Pareto distribution functions in the approximation of the density of a sum of damping functions, PMRQ approximation and approximation of service distribution in the peak mode of the flow. There was found one of the characteristics of the network, the average waiting time of packets in the queue after application of spectral method of the Lindley’s integral equation. Finally, PMRQ approximation of the average waiting time in TES+/G/1, MMPR, was compared with the analytic values of the same value in the spectral solution of the Lindley’s integral equation obtained by simulation with real traffic. Traffic is captured using the Wireshark protocol analyzer program. The time distributions were obtained in the EasyFit data analysis program, designed for quick statistical data analysis and decision making. Methods of approximation of network traffic allows us to estimate the average packet latency using statistical data analysis, which will improve the quality of service and predict the behavior of traffic.

Evaluation of 99mTc-Label led Vitamin K4 as an Agent for Testicular Imaging

1991 ◽  
Vol 30 (01) ◽  
pp. 35-39 ◽  
Author(s):  
H. S. Durak ◽  
M. Kitapgi ◽  
B. E. Caner ◽  
R. Senekowitsch ◽  
M. T. Ercan
Keyword(s):  
Soft Tissue ◽  
Room Temperature ◽  
Normal Subjects ◽  
Left Testis ◽  
Wide Range ◽  
Activity Ratios ◽  
The Right ◽  
Radioactivity Levels

Vitamin K4 was labelled with 99mTc with an efficiency higher than 97%. The compound was stable up to 24 h at room temperature, and its biodistribution in NMRI mice indicated its in vivo stability. Blood radioactivity levels were high over a wide range. 10% of the injected activity remained in blood after 24 h. Excretion was mostly via kidneys. Only the liver and kidneys concentrated appreciable amounts of radioactivity. Testis/soft tissue ratios were 1.4 and 1.57 at 6 and 24 h, respectively. Testis/blood ratios were lower than 1. In vitro studies with mouse blood indicated that 33.9 ±9.6% of the radioactivity was associated with RBCs; it was washed out almost completely with saline. Protein binding was 28.7 ±6.3% as determined by TCA precipitation. Blood clearance of 99mTc-l<4 in normal subjects showed a slow decrease of radioactivity, reaching a plateau after 16 h at 20% of the injected activity. In scintigraphic images in men the testes could be well visualized. The right/left testis ratio was 1.08 ±0.13. Testis/soft tissue and testis/blood activity ratios were highest at 3 h. These ratios were higher than those obtained with pertechnetate at 20 min post injection.99mTc-l<4 appears to be a promising radiopharmaceutical for the scintigraphic visualization of testes.

It is better an approximate answer to the right question than the exact answer to the wrong question : the case of the psychometric analysis of the ASQ:SE

2020 ◽  
Author(s):  
Luis Anunciacao ◽  
janet squires ◽  
J. Landeira-Fernandez
Keyword(s):  
Internal Structure ◽  
Statistical Methods ◽  
Principal Component ◽  
Psychological Theory ◽  
Published Data ◽  
Multivariate Statistical ◽  
Exact Answer ◽  
Wide Range ◽  
Ages And Stages Questionnaire ◽  
The Right

One of the main activities in psychometrics is to analyze the internal structure of a test. Multivariate statistical methods, including Exploratory Factor analysis (EFA) and Principal Component Analysis (PCA) are frequently used to do this, but the growth of Network Analysis (NA) places this method as a promising candidate. The results obtained by these methods are of valuable interest, as they not only produce evidence to explore if the test is measuring its intended construct, but also to deal with the substantive theory that motivated the test development. However, these different statistical methods come up with different answers, providing the basis for different analytical and theoretical strategies when one needs to choose a solution. In this study, we took advantage of a large volume of published data (n = 22,331) obtained by the Ages and Stages Questionnaire Social-Emotional (ASQ:SE), and formed a subset of 500 children to present and discuss alternative psychometric solutions to its internal structure, and also to its subjacent theory. The analyses were based on a polychoric matrix, the number of factors to retain followed several well-known rules of thumb, and a wide range of exploratory methods was fitted to the data, including EFA, PCA, and NA. The statistical outcomes were divergent, varying from 1 to 6 domains, allowing a flexible interpretation of the results. We argue that the use of statistical methods in the absence of a well-grounded psychological theory has limited applications, despite its appeal. All data and codes are available at https://osf.io/z6gwv/.

THE VALUE OF LOVE IN THE SYSTEM OF FORMATION OF THE PROFESSIONAL MATURITY OF THE EDUCATOR

2020 ◽  
Vol 1 (10(79)) ◽  
pp. 12-18
Author(s):  
G. Bubyreva
Keyword(s):  
Russian Federation ◽  
The State ◽  
Educational Process ◽  
Wide Range ◽  
The Family ◽  
The Russian Federation ◽  
The Government ◽  
The Individual ◽  
The Right

The existing legislation determines the education as "an integral and focused process of teaching and upbringing, which represents a socially important value and shall be implemented so as to meet the interests of the individual, the family, the society and the state". However, even in this part, the meaning of the notion ‘socially significant benefit is not specified and allows for a wide range of interpretation [2]. Yet the more inconcrete is the answer to the question – "who and how should determine the interests of the individual, the family and even the state?" The national doctrine of education in the Russian Federation, which determined the goals of teaching and upbringing, the ways to attain them by means of the state policy regulating the field of education, the target achievements of the development of the educational system for the period up to 2025, approved by the Decree of the Government of the Russian Federation of October 4, 2000 #751, was abrogated by the Decree of the Government of the Russian Federation of March 29, 2014 #245 [7]. The new doctrine has not been developed so far. The RAE Academician A.B. Khutorsky believes that the absence of the national doctrine of education presents a threat to national security and a violation of the right of citizens to quality education. Accordingly, the teacher has to solve the problem of achieving the harmony of interests of the individual, the family, the society and the government on their own, which, however, judging by the officially published results, is the task that exceeds the abilities of the participants of the educational process.  The particular concern about the results of the patriotic upbringing served as a basis for the legislative initiative of the RF President V. V. Putin, who introduced the project of an amendment to the Law of RF "About Education of the Russian Federation" to the State Duma in 2020, regarding the quality of patriotic upbringing [3]. Patriotism, considered by the President of RF V. V. Putin as the only possible idea to unite the nation is "THE FEELING OF LOVE OF THE MOTHERLAND" and the readiness for every sacrifice and heroic deed for the sake of the interests of your Motherland. However, the practicing educators experience shortfalls in efficient methodologies of patriotic upbringing, which should let them bring up citizens, loving their Motherland more than themselves. The article is dedicated to solution to this problem based on the Value-sense paradigm of upbringing educational dynasty of the Kurbatovs [15].

The Right to Bodily Integrity

2018 ◽  
Author(s):  
Alison Brysk
Keyword(s):  
Sexual Assault ◽  
Sexual Violence ◽  
Public Space ◽  
Transitional Justice ◽  
The United States ◽  
Bodily Integrity ◽  
Global Pattern ◽  
Popular Resistance ◽  
Wide Range ◽  
The Right

In Chapter 7, we profile the global pattern of sexual violence. We will consider conflict rape and transitional justice response in Peru and Colombia, along with the plight of women displaced by conflict from Syria and Central America, and limited international policy response. State-sponsored sexual violence and popular resistance to reclaim public space will be chronicled in Egypt as well as Mexico. We will track intensifying public sexual assault amid social crisis in Turkey, South Africa, and India, which has been met by a wide range of public protest, legal reform, and policy change. For a contrasting experience of the privatization of sexual assault in developed democracies, we will trace campus, workplace, and military rape in the United States.

Lying in Early Modern English Culture

2017 ◽  
Author(s):  
Andrew Hadfield
Keyword(s):  
Early Modern ◽  
Cultural History ◽  
Identity Politics ◽  
Social Life ◽  
Thomas More ◽  
Early Modern English ◽  
Wide Range ◽  
Constant Feature ◽  
The Right ◽  
English Culture

Lying in Early Modern English Culture is a major study of ideas of truth and falsehood from the advent of the Reformation to the aftermath of the Gunpowder Plot. The period is characterized by panic and chaos when few had any idea how religious, cultural, and social life would develop after the traumatic division of Christendom. Many saw the need for a secular power to define the truth; others declared that their allegiances belonged elsewhere. Accordingly there was a constant battle between competing authorities for the right to declare what was the truth and so label opponents as liars. Issues of truth and lying were, therefore, a constant feature of everyday life, determining ideas of identity, politics, speech, sex, marriage, and social behaviour, as well as philosophy and religion. This book is a cultural history of truth and lying from the 1530s to the 1610s, showing how lying needs to be understood in practice and theory, concentrating on a series of particular events, which are read in terms of academic debates and more popular notions of lying. The book covers a wide range of material such as the trials of Anne Boleyn and Thomas More, the divorce of Frances Howard, and the murder of Anthony James by Annis and George Dell; works of literature such as Othello, The Faerie Queene, A Mirror for Magistrates, and The Unfortunate Traveller; works of popular culture such as the herring pamphlet of 1597; and major writings by Castiglione, Montaigne, Erasmus, Luther, and Tyndale.

Sign in / Sign up

Export Citation Format

Share Document