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 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.

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 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 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%.

Optimal control of service rates in networks of queues

1987 ◽  
Vol 19 (1) ◽  
pp. 202-218 ◽  
Author(s):  
Richard R. Weber ◽  
Shaler Stidham
Keyword(s):  
Rate Control ◽  
Queueing Networks ◽  
Arrival Rate ◽  
Service Rate ◽  
Discounted Cost ◽  
Holding Costs ◽  
Optimal Service ◽  
Monotonicity Result ◽  
Service Rates ◽  
Number Of Customers

We prove a monotonicity result for the problem of optimal service rate control in certain queueing networks. Consider, as an illustrative example, a number of ·/M/1 queues which are arranged in a cycle with some number of customers moving around the cycle. A holding cost hi(xi) is charged for each unit of time that queue i contains xi customers, with hi being convex. As a function of the queue lengths the service rate at each queue i is to be chosen in the interval , where cost ci(μ) is charged for each unit of time that the service rate μis in effect at queue i. It is shown that the policy which minimizes the expected total discounted cost has a monotone structure: namely, that by moving one customer from queue i to the following queue, the optimal service rate in queue i is not increased and the optimal service rates elsewhere are not decreased. We prove a similar result for problems of optimal arrival rate and service rate control in general queueing networks. The results are extended to an average-cost measure, and an example is included to show that in general the assumption of convex holding costs may not be relaxed. A further example shows that the optimal policy may not be monotone unless the choice of possible service rates at each queue includes 0.

scholarly journals Service Rate Optimization of Finite Population Queueing Model with State Dependent Arrival and Service Rates

2018 ◽  
Vol 13 (1) ◽  
pp. 60-68
Author(s):  
Sushil Ghimire ◽  
Gyan Bahadur Thapa ◽  
Ram Prasad Ghimire
Keyword(s):  
Finite Population ◽  
Arrival Rate ◽  
Service Rate ◽  
Queueing Model ◽  
State Dependent ◽  
Service Rates ◽  
Rate Optimization

 Providing service immediately after the arrival is rarely been used in practice. But there are some situations for which servers are more than the arrivals and no one has to wait to get served. In this model, arrival rate is

Optimization of Queuing Theory Based on Vague Environment

2016 ◽  
Vol 5 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Verónica Andrea González-López ◽  
Ramin Gholizadeh ◽  
Aliakbar M. Shirazi
Keyword(s):  
Everyday Life ◽  
Real World ◽  
Queuing Theory ◽  
Arrival Rate ◽  
Service Rate ◽  
New Approach ◽  
The Real ◽  
Processing Times ◽  
Queuing Models ◽  
Service Rates

Waiting lines or queues are commonly occurred both in everyday life and in a variety of business and industrial situations. The various arrival rates, service rates and processing times of jobs/tasks usually assumed are exact. However, the real world is complex and the complexity is due to the uncertainty. The queuing theory by using vague environment is described in this paper. To illustrate, the approach analytical results for M/M/1/8 and M/M/s/8 systems are presented. It optimizes queuing models such that the arrival rate and service rate are vague numbers. This paper results a new approach for queuing models in the vague environment that it can be more effective than deterministic queuing models. A numerical example is illustrated to check the validity of the proposed method.

ANALYSIS OF A BULK QUEUE WITH FAST AND SLOW SERVICE RATES AND MULTIPLE VACATIONS

2005 ◽  
Vol 22 (02) ◽  
pp. 239-260 ◽  
Author(s):  
R. ARUMUGANATHAN ◽  
K. S. RAMASWAMI
Keyword(s):  
Performance Measures ◽  
Queue Length ◽  
Queueing System ◽  
Cost Model ◽  
Probability Generating Function ◽  
Service Rate ◽  
Multiple Vacations ◽  
Bulk Queue ◽  
Service Rates ◽  
Number Of Customers

We analyze a Mx/G(a,b)/1 queueing system with fast and slow service rates and multiple vacations. The server does the service with a faster rate or a slower rate based on the queue length. At a service completion epoch (or) at a vacation completion epoch if the number of customers waiting in the queue is greater than or equal to N (N > b), then the service is rendered at a faster rate, otherwise with a slower service rate. After finishing a service, if the queue length is less than 'a' the server leaves for a vacation of random length. When he returns from the vacation, if the queue length is still less than 'a' he leaves for another vacation and so on until he finally finds atleast 'a' customers waiting for service. After a service (or) a vacation, if the server finds atleast 'a' customers waiting for service say ξ, then he serves a batch of min (ξ, b) customers, where b ≥ a. We derive the probability generating function of the queue size at an arbitrary time. Various performance measures are obtained. A cost model is discussed with a numerical solution.

Rare events in series of queues

1992 ◽  
Vol 29 (1) ◽  
pp. 168-175 ◽  
Author(s):  
Pantelis Tsoucas
Keyword(s):  
Queueing Networks ◽  
Total Population ◽  
Large Deviation ◽  
Rare Event ◽  
Arrival Rate ◽  
Service Rate ◽  
Action Functional ◽  
In Series ◽  
Service Rates ◽  
Queues In Series

In an ergodic network of K M/M/1 queues in series we consider the rare event that, as N increases, the total population in the network exceeds N during a busy period. By utilizing the contraction principle of large deviation theory, an action functional is obtained for this exit problem. The ensuing minimization is carried out for K = 2 and an indication is given for arbitrary K. It is shown that, asymptotically and for unequal service rates, the ‘most likely' path for this rare event is one where the arrival rate has been interchanged with the smallest service rate. The problem has been posed in Parekh and Walrand [7] in connection with importance sampling simulation methods for queueing networks. Its solution has previously been obtained only heuristically.

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.

Sign in / Sign up

Export Citation Format

Share Document