scholarly journals A Nonlinear Programming Approach for a Fuzzy Queue with an Unreliable Server

2012 ◽  
Vol 2 ◽  
pp. 44-56
Author(s):  
V. Ashok Kumar
Keyword(s):  
Fuzzy Numbers ◽  
Arrival Rate ◽  
Programming Approach ◽  
Service Rate ◽  
Membership Functions ◽  
Repair Rate ◽  
Breakdown Rate ◽  
Unreliable Server ◽  
The Family ◽  
System Characteristics

The aim of this paper is to develop the membership functions of the system characteristic of a queuing g model with an unreliable server, in which the arrival rate, service rate, breakdown rate and repair rate are all fuzzy numbers. The α-cut approach is used to transform a fuzzy queue with an unreliable server into a family of conventional crisp queues with an unreliable server. By using membership functions, a set of parametric nonlinear programmes are developed to describe the family of crisp queues with an unreliable server. An efficient algorithm is developed to find the optimal solutions at or different possibility level α. Numerical examples are solved successfully. Since the system characteristics being expressed and governed by membership functions, more information is provided for the management.

scholarly journals ANALYSIS OF PRIORITY QUEUES WITH PENTAGON FUZZY NUMBER

2020 ◽  
Vol 5 (4) ◽  
pp. 90-100
Author(s):  
W. Ritha ◽  
S. Josephine Vinnarasi
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Number ◽  
System Performance ◽  
Fuzzy Numbers ◽  
Arrival Rate ◽  
Service Rate ◽  
Extension Principle ◽  
Queuing Model ◽  
Set Operations ◽  
Mathematical Programming Method

Fuzziness is a sort of recent incoherence. Fuzzy set theory is asserted to depict vagueness. This study explores the queuing model of priority classes adopting pentagon fuzzy number with the inclusions of fuzzy set operations. A mathematical programming method is designed to establish the membership function of the system performance, in which the arrival rate and service rate of the system performance of two priority classes are utilized as fuzzy numbers. Based on  -cut approach and Zadeh’s extension principle, the fuzzy queues are scaled down to a family of ordinary queues. The potency of the performance measures of the characteristics of the queuing model is ensured with an illustration and its graph.

A Method for Analyzing Queues in Fuzzy Environment

2016 ◽  
pp. 1-21
Author(s):  
Thillaigovindan Natesan
Keyword(s):  
Fuzzy Numbers ◽  
Numerical Study ◽  
Compound Poisson Process ◽  
Arrival Rate ◽  
New Method ◽  
Service Rate ◽  
Fuzzy Environment ◽  
Restriction Policy ◽  
Bulk Queue ◽  
Number Of Customers

In this chapter a new method for analyzing queues in fuzzy environment is presented. After explaining the new technique, it is applied to a fuzzy bulk queue with modified Bernoulli vacation and restricted admissible customers. Batches of customers arrive at the system according to a compound Poisson process. All arriving batches are not allowed to enter the system. The restriction policy depends on availability or otherwise of the server. This system is analyzed in fuzzy environment using the new method developed. Some special cases are discussed and a numerical study is also carried out. The new method can be applied to any queuing system in fuzzy environment. In this method the input parameters like arrival rate, service rate, vacation rate etc. are described by fuzzy numbers of specific type (triangular, trapezoidal, quadratic, Gaussian etc.) and the system performance measures like average queue size, average waiting time in the queue, average number of customers in the system are all obtained as fuzzy numbers of the same type, which include the crisp solution.

scholarly journals Analysis of Fuzzy Non-preemptive Priority Queuing Model with Unequal Service Rate

2021 ◽  
Vol 12 (5) ◽  
pp. 1457-1460
Author(s):  
K. Selvakumari, Et. al.
Keyword(s):  
Performance Measures ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Arrival Rate ◽  
Triangular Fuzzy Number ◽  
Priority Queues ◽  
Service Rate ◽  
Preemptive Priority ◽  
Queuing Model ◽  
Service Rates

This article provides an effective method to analyze the performance measures of non-preemptive fuzzy priority queues with unequal service rates. Here the arrival rate and the service rate are in fuzzy numbers. Using a new ranking method, the fuzzy values are reduced to the crisp values. For that cause, both the Triangular Fuzzy Number (TFN) and Trapezoidal Fuzzy Number (TpFN) are chosen to establish the proposal's effectiveness. An illustration is given to find the efficiency of the performance measures of the fuzzy queuing model.

A MATHEMATICAL PROGRAMMING APPROACH TO FUZZY TANDEM QUEUES

2005 ◽  
Vol 13 (04) ◽  
pp. 425-436 ◽  
Author(s):  
SHIH-PIN CHEN
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Programming Approach ◽  
Extension Principle ◽  
Queueing Models ◽  
Membership Functions ◽  
Tandem Queues ◽  
Mathematical Programs ◽  
Mathematical Programming Approach

Tandem queueing models play an important role in many real world systems such as computer systems, production lines, and service systems. This paper proposes a procedure to construct the membership functions of the performance measures in tandem queueing systems, in that the arrival rate and service rates are fuzzy numbers. The basic idea is to transform a fuzzy tandem queue to a family of crisp tandem queues by applying the α -cut approach. Then on the basis of α -cut representation and the extension principle, a pair of mathematical programs is formulated to describe this family of crisp tandem queues, via which the membership functions of the performance measures are derived. Two numerical examples are solved successfully to demonstrate the validity of the proposed approach. Since the performance measures are expressed by membership functions rather than by crisp values, the fuzziness of input information is completely conserved. Thus the proposed approach for fuzzy systems can represent the system more accurately, and more information is provided for designing queueing systems. The successful extension of tandem queues to fuzzy environments permits tandem queueing models to have wider applications.

scholarly journals An Interpretation of Non-Preemptive Priority Fuzzy Queuing Model with Asymmetrical Service Rates

2021 ◽  
pp. 791-797
Author(s):  
Usha Prameela Karupothu ◽  
Richard Wurmbrand ◽  
R P S Jayakar
Keyword(s):  
Performance Measures ◽  
Fuzzy Numbers ◽  
Arrival Rate ◽  
Service Rate ◽  
Preemptive Priority ◽  
Queuing Model ◽  
Numerical Examples ◽  
Cut Method ◽  
Service Rates ◽  
Ranking Technique

This  paper presents Non-Preemptive  priority fuzzy queuing model with asymmetrical service rates. Arrival rate and  service rate are taken to be hexagonal, heptagonal, and octagonal fuzzy numbers. Here an interpretation  is given to determine the performance measures by applying a new  ranking technique through which the fuzzy values are reduced to the crisp values. This ranking technique has the benefit of being precise and relevant compared to other methods such as alpha-cut method and LR method. The main intention is to evaluate the fuzziness before the performance measures are processed by utilizing the regular queueing hypothesis. Three numerical examples are exhibited to show the validity implementation of the methodology.

scholarly journals Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1299
Author(s):  
Shengli Lv
Keyword(s):  
Steady State ◽  
Transient State ◽  
Repairable System ◽  
Repair Rate ◽  
Numerical Illustration ◽  
Transform Method ◽  
Unreliable Server ◽  
Busy Time ◽  
The Mean ◽  
Mean Time

This paper analyzed the multi-machine repairable system with one unreliable server and one repairman. The machines may break at any time. One server oversees servicing the machine breakdown. The server may fail at any time with different failure rates in idle time and busy time. One repairman is responsible for repairing the server failure; the repair rate is variable to adapt to whether the machines are all functioning normally or not. All the time distributions are exponential. Using the quasi-birth-death(QBD) process theory, the steady-state availability of the machines, the steady-state availability of the server, and other steady-state indices of the system are given. The transient-state indices of the system, including the reliability of the machines and the reliability of the server, are obtained by solving the transient-state probabilistic differential equations. The Laplace–Stieltjes transform method is used to ascertain the mean time to the first breakdown of the system and the mean time to the first failure of the server. The case analysis and numerical illustration are presented to visualize the effects of the system parameters on various performance indices.

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.

scholarly journals Multi Objective Multi Mode Project Management Problem in Triangular Fuzzy Environment

2020 ◽  
Vol 9 (2) ◽  
pp. 1772-1781
Keyword(s):  
Project Management ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Decision Makers ◽  
Programming Approach ◽  
Management Problem ◽  
Linguistic Variables ◽  
Multi Objective ◽  
Fuzzy Environment ◽  
Multi Mode

Execution of any project with optimum duration, cost, quality and risk is very significant for project administrators in recent very competitive commercial situation. Sometimes it is not possible to have detailed earlier statistics about project criteria. In such situations, estimation of different Decision makers are considered in linguistic variables and altered into triangular fuzzy numbers as fuzzy numbers have ability to deal with vagueness. In this paper, we frame a new multi-mode multi objective critical path problem and suggest a possibilistic methodology to find critical path for a project where three decision makers’ views are considered as three modes of execution in terms of linguistic variables. We have formulated model of multiple mode in project network problem and find its solution with fuzzy programming approach with exponential membership and linear membership function. The proposed approach is useful to solve multi-mode project management problem which calculates optimal critical path according to four criteria- time, cost, risk and quality with three activities modes of execution in fuzzy environment.

scholarly journals Style features of recoding the personal life-story in autobiographical memory as a result of intra-familial transmission

2015 ◽  
Vol 10 (2) ◽  
pp. 1-15
Author(s):  
A.R. Alyusheva
Keyword(s):  
Autobiographical Memory ◽  
Deviant Behavior ◽  
Life Story ◽  
Social Orientation ◽  
The Social ◽  
The Family ◽  
Stable Family ◽  
System Characteristics ◽  
Individual Style

We studied the stylistic features of autobiographical memory structure which can be significant for the understanding the sources of intrapersonal propensity for deviant behavior among young people. From the standpoint of the Vygotsky's theory we studied 102 "parent-teenager" dyads in order to examine the mechanisms of cultural determination of autobiographical memory macrostructure in context of reproducing the life scenarios. We differentiate the social influences of various levels on the formation of system characteristics of autobiographical memory, which constitute individual style of fixation personal stories of the past. We have found а stable family-reproduced indicators of autobiographical memories belonging to the "family life" scenario, these include the emotional profile of the memories of lives, the level of scenario (fixation of socially approved events); representation of memories of other people (social orientation). The low values of these indicators can be the risk factors for asocial behavior.

scholarly journals Large Deviations for the Single-Server Queue and the Reneging Paradox

2021 ◽  
Author(s):  
Rami Atar ◽  
Amarjit Budhiraja ◽  
Paul Dupuis ◽  
Ruoyu Wu
Keyword(s):  
Large Deviations ◽  
Decay Rate ◽  
Sample Path ◽  
Arrival Rate ◽  
Rate Function ◽  
Service Rate ◽  
Single Server ◽  
Large Deviations Principle ◽  
Long Run ◽  
The Individual

For the M/M/1+M model at the law-of-large-numbers scale, the long-run reneging count per unit time does not depend on the individual (i.e., per customer) reneging rate. This paradoxical statement has a simple proof. Less obvious is a large deviations analogue of this fact, stated as follows: the decay rate of the probability that the long-run reneging count per unit time is atypically large or atypically small does not depend on the individual reneging rate. In this paper, the sample path large deviations principle for the model is proved and the rate function is computed. Next, large time asymptotics for the reneging rate are studied for the case when the arrival rate exceeds the service rate. The key ingredient is a calculus of variations analysis of the variational problem associated with atypical reneging. A characterization of the aforementioned decay rate, given explicitly in terms of the arrival and service rate parameters of the model, is provided yielding a precise mathematical description of this paradoxical behavior.

Sign in / Sign up

Export Citation Format

Share Document