scholarly journals Optimal Control Policy for a Two-Phase M/M/1 Unreliable Gated Queue under N-Policy with a Fuzzy Environment

2021 ◽  
Vol 26 (4) ◽  
pp. 357-364
Author(s):  
Hanumantha Rao Sama ◽  
Vasanta Kumar Vemuri ◽  
Venkata Siva Nageswara Hari Prasad Boppana
Keyword(s):  
Nonlinear Programming ◽  
Performance Measures ◽  
Fuzzy Numbers ◽  
Upper And Lower Bounds ◽  
Service Rate ◽  
Extension Principle ◽  
Single Server ◽  
Two Phase ◽  
Expected Cost ◽  
Fuzzy Environment

The two-phase service models analyzed by several authors considered only the probabilistic nature of the queue parameters with fixed cost elements. But the queue parameters and cost elements will be in general are of both possibilistic and probabilistic in nature. Analyzing the performance of the queueing systems with fuzzy environment facilitates to investigate for the possibilistic interval estimates to the performance measures of a queueing system rather than point estimates. In this work, it is proposed to construct membership function of the fuzzy cost function to obtain confidence estimates for some performance measures of a controllable two-phase service single server Markovian gated queue with server startups and breakdowns under N-policy in which the queue parameters viz. arrival rate, startup rate, batch service rate, individual service rate, repair rate and cost elements are all defined as fuzzy numbers. Based on Zadeh’s extension principle and the α-cuts, a set of parametric nonlinear programming problems are developed to find the upper and lower bounds of the minimum total expected cost per unit time at the possibility level α. As the analytical solutions of the nonlinear programming problems developed for the proposed model are tedious, considering the system parameters and cost elements as trapezoidal fuzzy numbers, numerical results for the lower and upper bounds of the optimal threshold N* and the minimum total expected cost per unit time are computed using the nonlinear programming solver available in MATLAB.

scholarly journals A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Ekaterina Evdokimova ◽  
Sabine Wittevrongel ◽  
Dieter Fiems
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Poisson Processes ◽  
Series Expansions ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
State Space Explosion ◽  
Finite Queues ◽  
Service Rates

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

Fuzzy Reliability of an Imprecise Failure to Start of an Automobile Using Pseudo-Parabolic Fuzzy Numbers

2018 ◽  
Vol 14 (03) ◽  
pp. 323-341 ◽  
Author(s):  
F. Abbasi
Keyword(s):  
Fuzzy Systems ◽  
Fuzzy Numbers ◽  
Extension Principle ◽  
Fuzzy Arithmetic ◽  
Fuzzy Reliability ◽  
Fuzzy Environment ◽  
Distributed Components ◽  
Proposed Model ◽  
New Type ◽  
The Membership Function

In this paper, we propose the notion of pseudo-parabolic fuzzy numbers and the component failure probabilities are considered as a new type of fuzzy number as pseudo-parabolic to incorporate the uncertainties in the parameter, due to a more realistic estimate of them. Then, we analyze the reliability of fuzzy system (particularly, series and parallel system) with independent and non-identically distributed components, and using the new operations of TA [F. Abbasi et al., Journal of Intelligent and Fuzzy Systems 29 (2015) 851–861], due to the smaller results support, easier calculations and special properties than fuzzy arithmetic operations based on the extension principle (in the domain of the membership function) and the interval arithmetic (in the domain of the [Formula: see text]-cuts). We provide a more realistic fuzzy reliability analysis. Finally, an imprecise failure to start of an automobile is considered in fuzzy environment. The reliability of components of the proposed model is considered as pseudo-parabolic fuzzy numbers.

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 Performance Measures of State Dependent MMPP/M/1 Queue

2018 ◽  
Vol 7 (4.10) ◽  
pp. 942 ◽  
Author(s):  
R. Sakthi ◽  
V. Vidhya ◽  
K. Mahaboob Hassain Sherieff ◽  
. .
Keyword(s):  
Performance Measures ◽  
Research Work ◽  
Arrival Process ◽  
Service Rate ◽  
Single Server ◽  
State Dependent ◽  
Markov Modulated ◽  
Service State ◽  
Modulated Process ◽  
Stationary Probability Vector

In this research work we are concerned with single unit server queue  queue with Markov Modulated process in Poisson fashion and the service time follow exponential distribution. The system is framed as a state dependent with the arrival process as Markov Modulated input and service is rendered by a single server with variation in service rate based on the intensity of service state of the system. The rate matrix that is essential to compute the stationary probability vector is obtained and various performance measures are computed using matrix method.

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.

Estimation of Failure Using Fault Tree Analysis Based on New Operations on LR-Type Flat Fuzzy Numbers

2020 ◽  
pp. 1-22
Author(s):  
F. Abbasi ◽  
T. Allahviranloo
Keyword(s):  
Fuzzy Systems ◽  
Fuzzy Numbers ◽  
Fault Tree Analysis ◽  
Extension Principle ◽  
Fuzzy Arithmetic ◽  
General Shape ◽  
Fuzzy Environment ◽  
Distributed Components ◽  
Proposed Model ◽  
Arithmetic Operator

In this paper, we analyze the reliability of fuzzy system (particularly, series and parallel system) with independent and non-identically distributed components using the new operations of TA [F. Abbasi, T. Allahviranloo and S. Abbasbandy, A new attitude coupled with fuzzy thinking to fuzzy rings and fields, Journal of Intelligent and Fuzzy Systems 29 (2015) 851–861.] due to the smaller results support, easier calculations and special properties than operations based on the extension principle (in the domain of the membership function) and the interval arithmetic (in the domain of the [Formula: see text]-cuts). we propose the new fuzzy arithmetic operations based on transmission average(TA) on LR type flat fuzzy numbers. In the proposed formulae, LR type flat fuzzy numbers are not restricted to have the same [Formula: see text] and [Formula: see text] shape functions. This allows arithmetic operator for arithmetic involving LR type flat fuzzy numbers of different and general shape. Finally, an imprecise failure to start of an automobile is considered in fuzzy environment. The reliability of components of the proposed model is considered as LR type flat fuzzy numbers.

Performance Analysis of in-Out System of Railway Container Terminal Based on Fuzzy Queuing Model

2012 ◽  
Vol 542-543 ◽  
pp. 324-327 ◽  
Author(s):  
Bing Kun Lin ◽  
Wen Ming Cheng
Keyword(s):  
Container Terminal ◽  
Arrival Rate ◽  
Parametric Programming ◽  
Upper And Lower Bounds ◽  
Service Rate ◽  
Extension Principle ◽  
Queuing Model ◽  
System Service ◽  
Theoretical Support ◽  
Definition Of

The in-out system of railway container terminal is a fuzzy queue system when the container truck arrival rate and in-out system service rate are fuzzy. To construct the membership functions of the performance measures, two rates were both represented as trapezoidal fuzzy numbers and the definition of α-cut and Zadeh’s extension principle were applied to transform fuzzy queues into traditional queues. The upper and lower bounds of the system eigenvalues were obtained with a parametric programming method. The membership function of the system eigenvalue was solved with a numerical computation of various α levels. The more information and theoretical support was provided for analysis and optimization of the in-out system of railway container terminal.

scholarly journals Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1272
Author(s):  
Bogdana Stanojević ◽  
Milan Stanojević ◽  
Sorin Nădăban
Keyword(s):  
Mathematical Programming ◽  
Fuzzy Numbers ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Extension Principle ◽  
Fuzzy Arithmetic ◽  
Advantages And Disadvantages ◽  
Fuzzy Environment ◽  
Basic Ideas ◽  
Mathematical Programming Problems

Optimization problems in the fuzzy environment are widely studied in the literature. We restrict our attention to mathematical programming problems with coefficients and/or decision variables expressed by fuzzy numbers. Since the review of the recent literature on mathematical programming in the fuzzy environment shows that the extension principle is widely present through the fuzzy arithmetic but much less involved in the foundations of the solution concepts, we believe that efforts to rehabilitate the idea of following the extension principle when deriving relevant fuzzy descriptions to optimal solutions are highly needed. This paper identifies the current position and role of the extension principle in solving mathematical programming problems that involve fuzzy numbers in their models, highlighting the indispensability of the extension principle in approaching this class of problems. After presenting the basic ideas in fuzzy optimization, underlying the advantages and disadvantages of different solution approaches, we review the main methodologies yielding solutions that elude the extension principle, and then compare them to those that follow it. We also suggest research directions focusing on using the extension principle in all stages of the optimization process.

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.

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