scholarly journals A study on M/G/1 feedback retrial queue with subject to server breakdown and repair under multiple working vacation policy

2018 ◽  
Vol 57 (2) ◽  
pp. 947-962 ◽  
Author(s):  
P. Rajadurai ◽  
M.C. Saravanarajan ◽  
V.M. Chandrasekaran
Keyword(s):  
Retrial Queue ◽  
Working Vacation ◽  
Server Breakdown

scholarly journals M/M/1 Retrial Queue with Working Vacation Interruption and Feedback under N-Policy

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Li Tao ◽  
Liyuan Zhang ◽  
Shan Gao
Keyword(s):  
Retrial Queue ◽  
Stochastic Decomposition ◽  
Service Rate ◽  
Working Vacation ◽  
Stationary Probability Distribution ◽  
The Matrix ◽  
Vacation Interruption ◽  
Necessary And Sufficient ◽  
Vacation Period ◽  
Conditional Stochastic Decomposition

We consider an M/M/1 retrial queue with working vacations, vacation interruption, Bernoulli feedback, and N-policy simultaneously. During the working vacation period, customers can be served at a lower rate. Using the matrix-analytic method, we get the necessary and sufficient condition for the system to be stable. Furthermore, the stationary probability distribution and some performance measures are also derived. Moreover, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, we present some numerical examples and use the parabolic method to search the optimum value of service rate in working vacation period.

An M/G/1 retrial queue with single working vacation under Bernoulli schedule

2020 ◽  
Vol 54 (2) ◽  
pp. 471-488
Author(s):  
Tao Li ◽  
Liyuan Zhang ◽  
Shan Gao
Keyword(s):  
Cost Optimization ◽  
Retrial Queue ◽  
Service Rate ◽  
Working Vacation ◽  
Optimization Analysis ◽  
Normal Period ◽  
Necessary And Sufficient ◽  
Number Of Customers ◽  
Vacation Period ◽  
Bernoulli Schedule

In this paper, an M/G/1 retrial queue with general retrial times and single working vacation is considered. We assume that the customers who find the server busy are queued in the orbit in accordance with a first-come-first-served (FCFS) discipline and only the customer at the head of the queue is allowed access to the server. During the normal period, if the orbit queue is not empty at a service completion instant, the server begins a working vacation with specified probability q (0 ≤ q ≤ 1), and with probability 1 − q, he waits for serving the next customer. During the working vacation period, customers can be served at a lower service rate. We first present the necessary and sufficient condition for the system to be stable. Using the supplementary variable method, we deal with the generating functions of the server state and the number of customers in the orbit. Various interesting performance measures are also derived. Finally, some numerical examples and cost optimization analysis are presented.

scholarly journals Performance of an M/M/1 Retrial Queue with Working Vacation Interruption and Classical Retrial Policy

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Tao Li ◽  
Liyuan Zhang ◽  
Shan Gao
Keyword(s):  
Generating Functions ◽  
System Performance ◽  
Cost Optimization ◽  
Retrial Queue ◽  
Stable Condition ◽  
Working Vacation ◽  
Optimization Analysis ◽  
Vacation Interruption ◽  
Number Of Customers ◽  
Vacation Period

An M/M/1 retrial queue with working vacation interruption is considered. Upon the arrival of a customer, if the server is busy, it would join the orbit of infinite size. The customers in the orbit will try for service one by one when the server is idle under the classical retrial policy with retrial ratenα, wherenis the size of the orbit. During a working vacation period, if there are customers in the system at a service completion instant, the vacation will be interrupted. Under the stable condition, the probability generating functions of the number of customers in the orbit are obtained. Various system performance measures are also developed. Finally, some numerical examples and cost optimization analysis are presented.

scholarly journals Classical Fuzzy Retrial Queue with Working Vacation using Hexagonal Fuzzy Numbers

2021 ◽  
Vol 2070 (1) ◽  
pp. 012018
Author(s):  
G. Kannadasan ◽  
V. Padmavathi
Keyword(s):  
Sojourn Time ◽  
Fuzzy Numbers ◽  
Retrial Queue ◽  
Numerical Results ◽  
Working Vacation ◽  
Fuzzy Environment ◽  
Fuzzy Techniques

Abstract Using fuzzy techniques “Classical Fuzzy Retrial Queue with Working Vacation(WV) using Hexagonal Fuzzy Numbers” is discussed in this paper. We acquire model in fuzzy environment as the average orbit length, Probability(Pr) that the server busy, and Pr(the server is in a WV period), the sojourn time of a customer in the queue. Finally numerical results are presented.

scholarly journals Performance Analysis of Retrial Queueing Model with Working Vacation, Interruption, Waiting Server, Breakdown and Repair

2021 ◽  
Vol 13 (3) ◽  
pp. 833-844
Author(s):  
P. Gupta ◽  
N. Kumar
Keyword(s):  
Cost Optimization ◽  
Probability Generating Function ◽  
Function Technique ◽  
Service Rate ◽  
Queueing Model ◽  
Working Vacation ◽  
Retrial Queueing ◽  
Server Breakdown ◽  
Vacation Interruption ◽  
Vacation Period

In this present paper, an M/M/1 retrial queueing model with a waiting server subject to breakdown and repair under working vacation, vacation interruption is considered. Customers are served at a slow rate during the working vacation period, and the server may undergo breakdowns from a normal busy state. The customer has to wait in orbit for the service until the server gets repaired. Steady-state solutions are obtained using the probability generating function technique. Probabilities of different server states and some other performance measures of the system are developed.  The variation in mean orbit size, availability of the server, and server state probabilities are plotted for different values of breakdown parameter and repair rate with the help of MATLAB software. Finally, cost optimization of the system is also discussed, and the optimal value of the slow service rate for the model is obtained.

A DISCRETE-TIME Geo/G/1 RETRIAL QUEUE WITH SERVER BREAKDOWNS

2006 ◽  
Vol 23 (02) ◽  
pp. 247-271 ◽  
Author(s):  
IVAN ATENCIA ◽  
PILAR MORENO
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Discrete Time ◽  
Continuous Time ◽  
Queueing System ◽  
Retrial Queue ◽  
System Size ◽  
Stochastic Decomposition ◽  
Recursive Procedure ◽  
Server Breakdown

This paper discusses a discrete-time Geo/G/1 retrial queue with the server subject to breakdowns and repairs. The customer just being served before server breakdown completes his remaining service when the server is fixed. The server lifetimes are assumed to be geometrical and the server repair times are arbitrarily distributed. We study the Markov chain underlying the considered queueing system and present its stability condition as well as some performance measures of the system in steady-state. Then, we derive a stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions of our system and the corresponding system without retrials. Also, we introduce the concept of generalized service time and develop a recursive procedure to obtain the steady-state distributions of the orbit and system size. Finally, we prove the convergence to the continuous-time counterpart and show some numerical results.

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