scholarly journals Mathematical model of delay based on a system with gamma distribution

2021 ◽  
Vol 24 (2) ◽  
pp. 62-67
Author(s):  
Veniamin N. Tarasov
Keyword(s):  
Gamma Distribution ◽  
Spectral Decomposition ◽  
Queuing Theory ◽  
Queuing System ◽  
Arbitrary Distribution ◽  
Distribution Law ◽  
Average Delay ◽  
Switched Networks ◽  
Packet Delays ◽  
Distribution Laws

This article is devoted to the analysis of a queuing system formed by two flows with density functions of the gamma distribution law in order to derive a solution for the average delay of requests in the queue, which is the main characteristic for any queuing system. According to this characteristic, for example, packet delays in packet-switched networks are estimated when they are modeled using the queuing system. In queuing theory, studies of G/G/1 systems are especially relevant because there is no solution in the final form for the general case. Therefore, in the study of such systems, various particular distribution laws are used as an arbitrary distribution law for G. In the study of G/G/1 systems, an important role is played by the method of spectral decomposition of the solution of the Lindley integral equation, and most of the results in the theory of queuing were obtained using this method. The article presents the derivation of the calculation formula for the average delay of requests in the queue in the system under consideration, also based on the spectral decomposition method.

Mathematical Model of the Delay in Communication Networks Based on QS with a Time Lag

2021 ◽  
Vol 27 (12) ◽  
pp. 634-641
Author(s):  
V. N. Tarasov ◽  
◽  
N. F. Bakhareva ◽  
Keyword(s):  
Mathematical Model ◽  
Communication Networks ◽  
Spectral Decomposition ◽  
Queuing Theory ◽  
Time Lag ◽  
Telecommunication Networks ◽  
Arbitrary Distribution ◽  
Unknown Parameters ◽  
Average Delay ◽  
Distribution Laws

In the mathematical modeling of modern computer networks, telecommunication networks, traffic flows, logistics and many others, the methods of queuing theory are widely used. In turn, in studies of queuing systems (QS) G/G/1 with arbitrary distribution laws of intervals between adjacent requirements of the incoming flow and their service time, the spectral decomposition method (MSD) of solving the Lindley integral equation is often used. This method is based on the search for zeros and poles of the constructed spectral decomposition in the form of some fractional-rational function using numerical methods to determine the roots of polynomials. In this case, the coefficients of the polynomial in the numerator of the expansion are expressed through the unknown parameters of the distribution laws used to describe the QS. In the case of teletraffic research, usually these unknown parameters of the distribution laws can be determined through the numerical characteristics of the intervals between traffic packets by the method of moments. The purpose of this article is to present a fundamentally new mathematical model of a system formed by two flows with distribution laws shifted to the right. This is possible only for those probability distribution laws whose density functions are Laplace transformable. The main advantages of such systems, let us call them time lag systems, are that they provide less queue latency compared to conventional systems, and that they extend the range of traffic parameters. The article presents the results obtained on the average delay of requests in the queue for a system with exponential and hyper-Erlang distributions, an algorithm for calculating the average delay and the results of computational experiments in the Mathcad package.

scholarly journals MODELING DATA TRANSMISSION SYSTEMS USING MODERN INFORMATION TECHNOLOGIES

T-Comm ◽  
2021 ◽  
Vol 15 (8) ◽  
pp. 52-57
Author(s):  
Eleonora G. Akhmetshina ◽  
Keyword(s):  
Data Transmission ◽  
Simulation Modeling ◽  
Queuing Theory ◽  
Analytical Modeling ◽  
Telecommunication Networks ◽  
Erlang Distribution ◽  
Transmission Systems ◽  
Average Delay ◽  
Distribution Laws ◽  
Modeling Data

When modeling data transmission systems for various purposes, including computer and telecommunication networks, both components of mathematical modeling are widely used. These are simulation modeling and analytical modeling based on queuing theory. At the same time, researchers can always compare the results obtained by means of simulation and analytical modeling. From modern technologies of simulation modeling, one can single out the IT GURU Academic Edition technologies, represented by the Opnet Modeler and Riverbed Modeler software products with powerful graphical editors. Graphic editors allow you to create simulation models of data transmission systems of any complexity, and launch and run their models to obtain statistics of the main performance indicators of these systems. Comparison of the simulation results with the results of queuing systems (QS) of the G/G/1 type makes it possible to assess the adequacy of those and other mathematical models. This article summarizes the results of the author’s publications on G/G/1 systems based on time-shifted distribution laws such as exponential, hyperexponential, and Erlang distribution. Thus, these distribution laws for the random variables used provide the coefficients of variation less than, equal or greater than one. This fact is important from the point of view of the queuing theory, because the average delay of claims in the system directly depends on the coefficients of variations in the time intervals for the arrival and servicing of claims.

scholarly journals MATHEMATICAL DELAY MODEL BASED ON SYSTEMS WITH HYPERERLANGIAN AND ERLANGIAN DISTRIBUTIONS

2021 ◽  
Vol 1 (1) ◽  
pp. 87-96
Author(s):  
V. N. Tarasov
Keyword(s):  
Integral Equation ◽  
Closed Form ◽  
Service Time ◽  
Spectral Decomposition ◽  
Queuing Theory ◽  
Input Flow ◽  
Average Delay ◽  
Spectral Expansions ◽  
Wide Range ◽  
Two Systems

Context. Studies of G/G/1 systems in queuing theory are relevant because such systems are of interest for analyzing the delay of data transmission systems. At the same time, it is impossible to obtain solutions for the delay in the final form in the general case for arbitrary laws of distribution of the input flow and service time. Therefore, it is important to study such systems for particular cases of input distributions. We consider the problem of deriving a solution for the average queue delay in a closed form for two systems with ordinary and shifted hypererlangian and erlangian input distributions. Objective. Obtaining a solution for the main characteristic of the system – the average delay of requests in the queue for two queuing systems of the G/G/1 type with ordinary and with shifted hypererlangian and erlangian input distributions. 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 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, spectral expansions of the solution of the integral Lindley equation for two systems are obtained, with the help of which calculation formulas for the average delay in a queue in a closed form are derived. Thus, mathematical models of queuing delay for these systems have been built. Conclusions. These formulas expand and supplement the known queuing theory formulas for the average delay G/G/1 systems with arbitrary laws distributions of input flow 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 delay, 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 delay from its average value, the jitter can be determined through the variance of the delay.

scholarly journals Performance Modelling of Health-care Service Delivery in Adekunle Ajasin University, Akungba-Akoko, Nigeria Using Queuing Theory

2020 ◽  
pp. 119-127
Author(s):  
Orimoloye Segun Michael
Keyword(s):  
Health Care ◽  
Service Delivery ◽  
Queuing Theory ◽  
Health Care Service ◽  
Health Centre ◽  
Arrival Rate ◽  
Queuing System ◽  
Service Rate ◽  
Suitable Model ◽  
The Mean

The queuing theory is the mathematical approach to the analysis of waiting lines in any setting where arrivals rate of the subject is faster than the system can handle. It is applicable to the health care setting where the systems have excess capacity to accommodate random variation. Therefore, the purpose of this study was to determine the waiting, arrival and service times of patients at AAUA Health- setting and to model a suitable queuing system by using simulation technique to validate the model. This study was conducted at AAUA Health- Centre Akungba Akoko. It employed analytical and simulation methods to develop a suitable model. The collection of waiting time for this study was based on the arrival rate and service rate of patients at the Outpatient Centre. The data was calculated and analyzed using Microsoft Excel. Based on the analyzed data, the queuing system of the patient current situation was modelled and simulated using the PYTHON software. The result obtained from the simulation model showed that the mean arrival rate of patients on Friday week1 was lesser than the mean service rate of patients (i.e. 5.33> 5.625 (λ > µ). What this means is that the waiting line would be formed which would increase indefinitely; the service facility would always be busy. The analysis of the entire system of the AAUA health centre showed that queue length increases when the system is very busy. This work therefore evaluated and predicted the system performance of AAUA Health-Centre in terms of service delivery and propose solutions on needed resources to improve the quality of service offered to the patients visiting this health centre.

Antnet Routing Algorithm with Link Evaporation and Multiple Ant Colonies to Overcome Stagnation Problem

2013 ◽  
pp. 255-274
Author(s):  
Firat Tekiner ◽  
Zabih Ghassemlooy
Keyword(s):  
Routing Algorithm ◽  
Packet Delay ◽  
Average Delay ◽  
Ant Colonies ◽  
Feedback Information ◽  
Switched Networks ◽  
Agent Based ◽  
Data Packets ◽  
Reinforcement Parameter ◽  
Distance Vector

Antnet is a software agent-based routing algorithm that is influenced by the unsophisticated and individual ant’s emergent behaviour. The aim of this chapter is twofold, firstly to introduce improvements to the antnet routing algorithm and then to critically review the work that is done around antnet and reinforcement learning in routing applications. In this chapter a modified antnet algorithm for packet-based networks has been proposed, which offers improvement in the throughput and the average delay by detecting and dropping packets routed through the non-optimal routes. The effect of traffic fluctuations has been limited by applying boundaries to the reinforcement parameter. The round trip feedback information supplied by the software agents is reinforced by updated probability entries in the distance vector table. In addition, link usage information is also used to prevent stagnation problems. Also discussed is antnet with multiple ant colonies applied to packet switched networks. Simulation results show that the average delay experienced by data packets is reduced for evaporation for all cases when non-uniform traffic model traffic is used. However, there is no performance gain on the uniform traffic models. In addition, multiple ant colonies are applied to the packet switched networks, and results are compared with the other approaches. Results show that the throughput could be increased when compared to other schemes, but with no gain in the average packet delay time.

The Application of Computer Simulation Technology in the Queuing System Optimization

2014 ◽  
Vol 556-562 ◽  
pp. 3849-3851
Author(s):  
Rong Hua Tan
Keyword(s):  
Computer Simulation ◽  
Queuing Theory ◽  
Optimization Problem ◽  
Classical Model ◽  
Discrete Event ◽  
System Optimization ◽  
Discrete Event System ◽  
Queuing System ◽  
Event System ◽  
Definition Of

The optimization Problem of queuing system is an important research subject in the queuing system.There are two ways to solve this problem:one is the traditional theoretical analysis, the other is the application of computer simulation. This thesis introduces the queuing theory and the simulation technique of discrete event system, including fundamental conceptions, methods, performance index and classical model of queuing system, as well as the definition of simulation and the procedure of the simulation of discrete event system. And procedure and parameters set of general modeling methods are analyzed.

scholarly journals Invite Your Friend and You’ll Move Up in Line: Optimal Design of Referral Priority Programs

2020 ◽  
Author(s):  
Luyi Yang
Keyword(s):  
Optimal Design ◽  
Queuing Theory ◽  
Problem Definition ◽  
Waiting List ◽  
System Throughput ◽  
Market Size ◽  
Customer Acquisition ◽  
Average Delay ◽  
Managerial Implications ◽  
First In First Out

Problem definition: This paper studies the optimal design of referral priority programs, in which customers on a waiting list can jump the line by inviting their friends to also join the waiting list. Academic/practical relevance: Recent years have witnessed a growing presence of referral priority programs as a novel customer-acquisition strategy for firms that maintain a waiting list. Different variations of this scheme are seen in practice, raising the question of what should be the optimal referral priority mechanism. Methodology: I build an analytical model that integrates queuing theory into a mechanism design framework in which the objective of the firm is to maximize the system throughput, that is, accelerate customer acquisition as much as possible. Results: My analysis shows that the optimal mechanism has one of the following structures: full priority; partial priority; first in, first out (FIFO); and strategic delay. A full-priority (partial-priority) scheme enables referring customers to get ahead of all (only some) nonreferring ones. A FIFO scheme does not provide any priority-based referral incentive. A strategic-delay scheme grants full priority to referring customers but artificially inflates the delay of nonreferring ones. I show that FIFO is optimal if either the base-market size or the referral cost is large. Otherwise, partial priority is optimal if the base-market size is above a certain threshold; full priority is optimal at the threshold base-market size; strategic delay is optimal if the base-market size is below the threshold. I also find that referrals motivate the firm to maintain a larger capacity and therefore can surprisingly shorten the average delay, even though more customers sign up and strategic delay is sometimes inserted. Managerial implications: My paper provides prescriptive guidance for launching an optimal referral priority program and rationalizes common referral schemes seen in practice.

Residual Oil Distribution Law and Controlling Factors of Chang 6 Reservoir in Liutai Area

2014 ◽  
Vol 1010-1012 ◽  
pp. 1735-1739
Author(s):  
Feng Run Zhang ◽  
Ai Hua Guo ◽  
Huai En Cai
Keyword(s):  
Sedimentary Facies ◽  
Geological Structure ◽  
Controlling Factors ◽  
Water Flooding ◽  
Residual Oil ◽  
Distribution Law ◽  
Total Recovery ◽  
Main Layer ◽  
Oil Distribution ◽  
Distribution Laws

Because of the high heterogeneity, late water flooding and irregular well network, the distribution law of residual oil reserve in Chang 6 reservoir becomes much complicated. Combining the geology with dynamics of the reservoir, volumetric and formation coefficient methods are adapted to calculated the residual reserves, and then the distribution laws and controlling factors are analyzed. The results indicate that: there are still large amounts of residual reserve in main layer Chang 622; the residual reserve can be classified into three kinds, Class I and class II are distributed concentrative in main layer; the controlling factors include property, sedimentary facies, heterogeneity, well network controlling and geological structure and so on. Finally, according to the distribution laws and controlling factors, targeted measures are proposed. The studying results provide well foundations for improving recovery of residual oil reserves and the total recovery of the reservoir.

scholarly journals Effective school cooperative-mart queuing system

2017 ◽  
Vol 13 (4-1) ◽  
pp. 412-415
Author(s):  
Ahmad Ridhuan Hamdan ◽  
Ruzana Ishak ◽  
Mohd Fais Usop
Keyword(s):  
Queuing Theory ◽  
Service Level ◽  
Queuing System ◽  
Queuing Model ◽  
Effective School ◽  
Service Centre ◽  
Large Numbers ◽  
Female Data ◽  
Waiting Line ◽  
Number Of Customers

Queuing Theory is a branch of knowledge in operation research that concerning the analysis of queues when a customer arrives at a service centre and shall queue in a line to get some service. The theory pays attention to how organizations can serve a large number of customers who demand a quality services and a queue of customers waiting to be served. Eventually, the store owners have to attend to large numbers of customers at a time have attempted to measure and manage queues to reduce the customer procession time. Besides, to increase sales and profit, productivity and operation efficiency, satisfaction levels and customer loyalty in using the service provided. In line to the situation, this study is to determine the effectiveness of the waiting line using Queuing Theory at cooperative-mart. Until today, no research conducted about school cooperatives-mart to observe and solve the massive inflow of customers at lines at a given time especially during lunch hour. The purposes of this study are to determine the customer congestion at the payment counter and to propose the effective queuing system at Cooperative-mart. Waiting and services times of customers at cooperative-mart is studied in three times period that to be considered as peak hours in two types of counter which are for male and female.  Data collection was observed by using queuing theory and the M/M/1/∞/∞ queuing model has been implemented.  The results show that for optimum service level, the counter must be changed from one to two counters each side.  The summary and finding of the study shall be used as guideline for the management of cooperative-mart in deciding improvement of its operation. 

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