Two-way communication retrial queue with unreliable server and multiple types of outgoing calls

2020 ◽  
Vol 28 (1) ◽  
pp. 49-61
Author(s):  
Anatoly A. Nazarov ◽  
Svetlana V. Paul ◽  
Olga D. Lizyura
Keyword(s):  
Probability Distribution ◽  
Call Center ◽  
Poisson Point Process ◽  
Retrial Queue ◽  
Idle Time ◽  
High Rate ◽  
Exponential Distributions ◽  
Limit Condition ◽  
Different Types ◽  
Incoming Call

Retrial queue under consideration is the model of call center operator switching between input and outgoing calls. Incoming calls form a Poisson point process. Upon arrival, an incoming call occupies the server for an exponentially distributed service time if the server is idle. If the server if busy, an incoming call joins the orbit to make a delay before the next attempt to take the server. The probability distribution of the length of delay is an exponential distribution. Otherwise, the server makes outgoing calls in its idle time. There are multiple types of outgoing calls in the system. Outgoing call rates are different for each type of outgoing call. Durations of different types of outgoing calls follow distinct exponential distributions. Unsteadiness is that the server crashes after an exponentially distributed time and needs recovery. The rates of breakdowns and restorations are different and depend on server state. Our contribution is to obtain the probability distribution of the number of calls in the orbit under high rate of making outgoing calls limit condition. Based on the obtained asymptotics, we have built the approximations of the probability distribution of the number of calls in the orbit.

scholarly journals Two-way communication retrial queue with unreliable server and multiple types of outgoing calls

2020 ◽  
Vol 28 (1) ◽  
pp. 49-61
Author(s):  
Anatoly A. Nazarov ◽  
Svetlana V. Paul ◽  
Olga D. Lizyura
Keyword(s):  
Probability Distribution ◽  
Call Center ◽  
Poisson Point Process ◽  
Retrial Queue ◽  
Idle Time ◽  
High Rate ◽  
Exponential Distributions ◽  
Limit Condition ◽  
Different Types ◽  
Incoming Call

Retrial queue under consideration is the model of call center operator switching between input and outgoing calls. Incoming calls form a Poisson point process. Upon arrival, an incoming call occupies the server for an exponentially distributed service time if the server is idle. If the server if busy, an incoming call joins the orbit to make a delay before the next attempt to take the server. The probability distribution of the length of delay is an exponential distribution. Otherwise, the server makes outgoing calls in its idle time. There are multiple types of outgoing calls in the system. Outgoing call rates are different for each type of outgoing call. Durations of different types of outgoing calls follow distinct exponential distributions. Unsteadiness is that the server crashes after an exponentially distributed time and needs recovery. The rates of breakdowns and restorations are different and depend on server state. Our contribution is to obtain the probability distribution of the number of calls in the orbit under high rate of making outgoing calls limit condition. Based on the obtained asymptotics, we have built the approximations of the probability distribution of the number of calls in the orbit.

Two-way communication retrial queue with unreliable server and multiple types of outgoing calls

2020 ◽  
Vol 28 (1) ◽  
pp. 49-61
Author(s):  
Anatoly A. Nazarov ◽  
Svetlana V. Paul ◽  
Olga D. Lizyura
Keyword(s):  
Probability Distribution ◽  
Call Center ◽  
Poisson Point Process ◽  
Retrial Queue ◽  
Idle Time ◽  
High Rate ◽  
Exponential Distributions ◽  
Limit Condition ◽  
Different Types ◽  
Incoming Call

Retrial queue under consideration is the model of call center operator switching between input and outgoing calls. Incoming calls form a Poisson point process. Upon arrival, an incoming call occupies the server for an exponentially distributed service time if the server is idle. If the server if busy, an incoming call joins the orbit to make a delay before the next attempt to take the server. The probability distribution of the length of delay is an exponential distribution. Otherwise, the server makes outgoing calls in its idle time. There are multiple types of outgoing calls in the system. Outgoing call rates are different for each type of outgoing call. Durations of different types of outgoing calls follow distinct exponential distributions. Unsteadiness is that the server crashes after an exponentially distributed time and needs recovery. The rates of breakdowns and restorations are different and depend on server state. Our contribution is to obtain the probability distribution of the number of calls in the orbit under high rate of making outgoing calls limit condition. Based on the obtained asymptotics, we have built the approximations of the probability distribution of the number of calls in the orbit.

scholarly journals Heavy outgoing call asymptotics for retrial queue with two way communication and multiple types of outgoing calls

2019 ◽  
Vol 27 (1) ◽  
pp. 5-20
Author(s):  
Anatoly A Nazarov ◽  
Svetlana V Paul ◽  
Olga D Lizyura
Keyword(s):  
Probability Distribution ◽  
Poisson Process ◽  
Service Time ◽  
Retrial Queue ◽  
Idle Time ◽  
Single Server ◽  
Queueing Model ◽  
Exponential Distributions ◽  
Incoming Call

In this paper, we consider a single server queueing model M |M |1|N with two types of calls: incoming calls and outgoing calls, where incoming calls arrive at the server according to a Poisson process. Upon arrival, an incoming call immediately occupies the server if it is idle or joins an orbit if the server is busy. From the orbit, an incoming call retries to occupy the server and behaves the same as a fresh incoming call. The server makes an outgoing calls after an exponentially distributed idle time. It can be interpreted as that outgoing calls arrive at the server according to a Poisson process. There are N types of outgoing calls whose durations follow N distinct exponential distributions. Our contribution is to derive the asymptotics of the number of incoming calls in retrial queue under the conditions of high rates of making outgoing calls and low rates of service time of each type of outgoing calls. Based on the obtained asymptotics, we have built the approximations of the probability distribution of the number of incoming calls in the system.

Modeling a multi-layered blockchain framework for digital services that governments can implement

2021 ◽  
pp. 1-13
Author(s):  
Fernando Rebollar ◽  
Rocío Aldeco-Perez ◽  
Marco A. Ramos
Keyword(s):  
Statistical Analysis ◽  
General Population ◽  
Information Security ◽  
High Rate ◽  
The Internet ◽  
Sufficient Information ◽  
Electronic Network ◽  
Digital Services ◽  
Different Types ◽  
Cryptographic Techniques

The general population increasingly uses digital services, meaning services which are delivered over the internet or an electronic network, and events such as pandemics have accelerated the need of using new digital services. Governments have also increased their number of digital services, however, these digital services still lack of sufficient information security, particularly integrity. Blockchain uses cryptographic techniques that allow decentralization and increase the integrity of the information it handles, but it still has disadvantages in terms of efficiency, making it incapable of implementing some digital services where a high rate of transactions are required. In order to increase its efficient, a multi-layer proposal based on blockchain is presented. It has four layers, where each layer specializes in a different type of information and uses properties of public blockchain and private blockchain. An statistical analysis is performed and the proposal is modeled showing that it maintains and even increases the integrity of the information while preserving the efficiency of transactions. Besides, the proposal can be flexible and adapt to different types of digital services. It also considers that voluntary nodes participate in the decentralization of information making it more secure, verifiable, transparent and reliable.

The Strength Evaluation and Reliability Analysis of Periodic Symmetric Struts Support

2011 ◽  
Vol 462-463 ◽  
pp. 1164-1169
Author(s):  
Jing Xiang Yang ◽  
Ya Xin Zhang ◽  
Mamtimin Gheni ◽  
Ping Ping Chang ◽  
Kai Yin Chen ◽  
...  
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Stress Distribution ◽  
Least Squares ◽  
Reliability Analysis ◽  
Least Squares Method ◽  
Nonlinear Least Squares ◽  
Distribution Model ◽  
Different Types ◽  
Nonlinear Least Squares Method

In this paper, strength evaluations and reliability analysis are conducted for different types of PSSS(Periodically Symmetric Struts Supports) based on the FEA(Finite Element Analysis). The numerical models are established at first, and the PMA(Prestressed Modal Analysis) is conducted. The nodal stress value of all of the gauss points in elements are extracted out and the stress distributions are evaluated for each type of PSSS. Then using nonlinear least squares method, curve fitting is carried out, and the stress probability distribution function is obtained. The results show that although using different number of struts, the stress distribution function obeys the exponential distribution. By using nonlinear least squares method again for the distribution parameters a and b of different exponential functions, the relationship between number of struts and distribution function is obtained, and the mathematical models of the stress probability distribution functions for different supports are established. Finally, the new stress distribution model is introduced by considering the DSSI(Damaged Stress-Strength Interference), and the reliability evaluation for different types of periodically symmetric struts supports is carried out.

scholarly journals Number of cases of type 1 and 2 diabetes diagnosed in Amapá between 2007 and 2012

2020 ◽  
pp. 18-26
Author(s):  
Kauê de Melo Souza ◽  
Lucas Facco ◽  
Amanda Alves Fecury ◽  
Maria Helena Mendonça de Araújo ◽  
Euzébio de Oliveira ◽  
...  
Keyword(s):  
Diabetes Mellitus ◽  
Type 2 Diabetes ◽  
Genetic Factors ◽  
Sedentary Lifestyle ◽  
High Rate ◽  
Main Risk Factor ◽  
Food Education ◽  
Different Types

Diabetes mellitus is a succession of different types of disorders in metabolism that are characterized by causing a high rate of blood sugar. Because it is a disease with genetic factors type 1 diabetes has as main risk factor heredity, while type 2 diabetes besides these factors, includes obesity, high blood pressure, poor food education and advancing age. This study aims to show the number of cases of type 1 and 2 diabetes diagnosed in Amapá with the variables gender, age group, sedentary lifestyle, overweight, smoking, between 2007 and 2012. The data for the research were taken from the computer department of SUS, DATASUS (http://datasus.saude.gov.br). Type 1 and 2 diabetes mellitus (DM1 and DM2) are diseases that are tied to disturbances in production or in the efficient use of insulin. Smoking, as well as sedentary lifestyle and overweight are important risk factors for the development of DM2. Type 2 diabetes mellitus provides the development of various organic nerve lesions. In addition, DM2, through its chronicity, enables the development of retinopathies, nephropathies and other conditions negative to the individual’s health.

New trends in chromosomal investigation in children with cardiovascular malformations

2004 ◽  
Vol 14 (6) ◽  
pp. 622-629 ◽  
Author(s):  
Ruth Schellberg ◽  
Gesa Schwanitz ◽  
Lutz Grävinghoff ◽  
Rolf Kallenberg ◽  
Detlef Trost ◽  
...  
Keyword(s):  
Chromosomal Aberrations ◽  
In Situ Hybridisation ◽  
High Rate ◽  
Diagnostic Approach ◽  
Fluorescence In Situ Hybridisation ◽  
Cardiovascular Malformations ◽  
Genetic Investigation ◽  
Different Types ◽  
Cardiovascular Defects

We investigated a group of 376 children, seen over a period of 7 years with different types of congenital cardiovascular defects, to assess the presence of chromosomal aberrations. The diagnostic approach, achieved in 3 consecutive steps, revealed conventional chromosomal aberrations in 30 of the patients (8%) excluding trisomies 13, 18, 21. Fluorescence in situ hybridisation for microdeletions showed 51 microdeletions (15%), with 43 patients having deletions of 22q11.2, 7 patients with deletion of 7q11.23, and 1 patient with deletion of 4p16.3. In 23 patients with additional clinical abnormalities, we carried out a subtelomeric screening. This revealed, in two cases (9%), different subtelomeric aberrations, namely deletions of 1p and of 1q. Thus, subtelomeric screening proved to be a very valuable as a new diagnostic approach. Our approach to genetic investigation in three phases makes it possible to detect a high rate of pathologic karyotypes in patients with congenital cardiovascular malformations, thus guaranteeing more effective genetic counselling of the families, and a more precise prognosis for the patient.

scholarly journals The Degree Analysis of an Inhomogeneous Growing Network with Two Types of Vertices

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Huilin Huang
Keyword(s):  
Probability Distribution ◽  
Law Of Large Numbers ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Degree Sequences ◽  
Strong Law ◽  
Large Numbers ◽  
Different Types ◽  
Azuma's Inequality ◽  
Growing Network

We consider an inhomogeneous growing network with two types of vertices. The degree sequences of two different types of vertices are investigated, respectively. We not only prove that the asymptotical degree distribution of typesfor this process is power law with exponent2+1+δqs+β1-qs/αqs, but also give the strong law of large numbers for degree sequences of two different types of vertices by using a different method instead of Azuma’s inequality. Then we determine asymptotically the joint probability distribution of degree for pairs of adjacent vertices with the same type and with different types, respectively.

Wie Incoming Call Center funktionieren

1998 ◽  
pp. 129-142
Author(s):  
Brad Cleveland ◽  
Julia Mayben ◽  
Günter Greff
Keyword(s):  
Call Center ◽  
Incoming Call

The Birth and Death of a Neuron

The Neuron ◽  
2015 ◽  
pp. 329-352
Author(s):  
Irwin B. Levitan ◽  
Leonard K. Kaczmarek
Keyword(s):  
Nervous System ◽  
Transcription Factors ◽  
Bone Morphogenetic Proteins ◽  
Mitochondrial Membrane ◽  
Brain Regions ◽  
High Rate ◽  
Outer Mitochondrial Membrane ◽  
Programmed Death ◽  
Different Types ◽  
Specific Neuron

The development of the nervous system requires the participation of a variety of factors that influence neuronal determination, proliferation, migration, and differentiation. The earliest steps in the formation of a neuron involve the actions of factors such as the bone morphogenetic proteins and neural inducers. Acting on cells that still have the potential to develop into many different types of cells, these factors control the synthesis of transcription factors and determine whether the complement of genes that becomes activated corresponds to those required for building a neuron. The birth of new neurons occurs at a high rate early in development, but in some brain regions persists in adults. The normal formation of the nervous system also requires the programmed death of many neurons. Decisions as to whether a specific neuron survives or perishes during development are made by factors that control the permeability of the outer mitochondrial membrane.

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