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.

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.

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 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.

ANALYSIS OF FUZZY QUEUES BY USING PENTAGONAL FUZZY NUMBER

2021 ◽  
Vol 23 (04) ◽  
pp. 211-224
Author(s):  
Gurcharan Singh ◽  
◽  
Baljodh Singh ◽  
Neelam Kumari ◽  
◽  
...  
Keyword(s):  
Probability Theory ◽  
Fuzzy Set ◽  
Fuzzy Number ◽  
Queuing Theory ◽  
Fuzzy Numbers ◽  
Real Life ◽  
Linguistic Terms

This paper deals with the fact thatpentagonal fuzzy numbers are pre-owned and systematic outcomes are discussed in real-life situations. The fuzzy set supposition is combined with well-established classical queuing theory but the classical queuing theory is far away from real-life situations. In this approach, we can use both fuzzy and probability theory to make this work more realistic with the help of the α-cut technique. Symmetric pentagonal fuzzy numbers are used to elaborate on the situation of the queue in linguistic terms.

PRICING STOCK OPTIONS USING BLACK-SCHOLES AND FUZZY SETS

2008 ◽  
Vol 04 (02) ◽  
pp. 165-176 ◽  
Author(s):  
JAMES J. BUCKLEY ◽  
ESFANDIAR ESLAMI
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Fuzzy Number ◽  
Stock Options ◽  
Fuzzy Numbers ◽  
Black Scholes

We use the basic Black-Scholes equation for pricing European stock options but we allow some of the parameters in the model to be uncertain and we model this uncertainty using fuzzy numbers. We compute the fuzzy number for the call value of option with and without uncertain dividends. This fuzzy set displays the uncertainty in the option's value due to the uncertainty in the input values to the model. We also correct an error in a recent paper which also fuzzified the Black-Scholes equation.

scholarly journals PENERAPAN METODE ANTRIAN DALAM MENENTUKAN FASILITAS YANG OPTIMAL PADA SPBU MAWADDAH

2018 ◽  
Vol 3 (5) ◽  
Author(s):  
Diana Khairani Sofyan ◽  
Sri Meutia
Keyword(s):  
Diesel Fuel ◽  
Arrival Rate ◽  
Service Level ◽  
Service Rate ◽  
Queuing Model ◽  
Fuel Pump ◽  
Gas Stations ◽  
Scenario Design ◽  
Service Rates ◽  
Number Of Customers

Gas stations Mawaddah Is one of the gas stations located in the Village Batuphat East Lhokseumawe. The gas station has 5 oil pumps consisting of premium with two pumps, diesel consists of two pumps, and pertamax consists of one pump. Preliminary data have been made regarding the arrival rate of vehicles in each pump, which is a two-wheeled premium filling pump of 195 vehicles, four or more 166 wheels or four wheels filling pumps, four or more diesel fuel pumps of 156 and a feeding pump of 138 vehicles. High vehicle arrival rate resulted in queue. To calculate the level of service has never been done so it is not known the maximum time for service on each pump. The research method used is queuing model related to arrival rate and service level, with result of research which obtained is vehicle arrival rate at each pump that is 2 wheel of premium gasoline pump is 2.59 minutes. The premium 4 wheels charging pump is 6.98. The 4 wheelers diesel fuel pump is 5.97 minutes and the first charging pump is 6.65 minutes with the facility number 1. Vehicle service rates of premium 2 and 4 wheelers are 15.52 minutes and 14.11 minutes, 4 wheel diesel fuel pump is 14.21 minutes and the first feed pump is 13.55 minutes with scenario design on each pump is Scenario 1 with 2 pumps, Probability of medium system empty 0.87500, Number of subscribers in the system and number of customers waiting in the queue of each 1 customer, the average customer time in the system 0.06696 minutes and waiting time as long as the customer in the queue 0.00030 minutes.Keywords: Queue, facility, arrival rate, service rate.

scholarly journals A Study of Service in Restaurant by Using Queuing Model

2013 ◽  
Vol 5 ◽  
pp. 14-18
Author(s):  
G.D. Mishra ◽  
Vijiya Singh Chauhan ◽  
Nikita Chandra
Keyword(s):  
Numerical Model ◽  
Waiting Time ◽  
Queuing Theory ◽  
Arrival Rate ◽  
Utilization Rate ◽  
Service Rate ◽  
Case Scenario ◽  
Queuing Model ◽  
Restaurant Management ◽  
Potential Customers

The restaurants want to avoid losing their customers due to a long wait on the line. This shows a need of a numerical model for the restaurant management to understand the situation better. This paper aims to show that queuing theory satisfies the model when tested with a real-case scenario. We obtained the data from a restaurant. We then derive the arrival rate, service rate, utilization rate, waiting time in queue and the probability of potential customers to balk based on the data using Little’s Theorem and M/M/1 queuing model. We conclude the paper by discussing the benefits of performing queuing analysis to a busy restaurant.

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.

Arithmetic Behaviors of P-Norm Generalized Trapezoidal Intuitionistic Fuzzy Numbers with Application to Circuit Analysis

2017 ◽  
Vol 6 (3) ◽  
pp. 6-58
Author(s):  
Sanhita Banerjee ◽  
Tapan Kumar Roy
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Circuit Analysis ◽  
Extension Principle ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
The Given ◽  
Trapezoidal Intuitionistic Fuzzy Number ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

P-norm Generalized Trapezoidal Intuitionistic Fuzzy Number is the most generalized form of Fuzzy as well as Intuitionistic Fuzzy Number. It has a huge application while solving various problems in imprecise environment. In this paper the authors have discussed some basic arithmetic operations of p-norm Generalized Trapezoidal Intuitionistic Fuzzy Numbers using two different methods (extension principle method and vertex method) and have solved a problem of circuit analysis taking the given data as p-norm Generalized Trapezoidal Intuitionistic Fuzzy Numbers.

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.

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