A Bulk Arrival Retrial Queue with Feedback and Exponentially Distributed Multiple Working Vacation

2019 ◽  
Vol 10 (1) ◽  
pp. 81-91 ◽  
Author(s):  
S. Pazhani Bala Murugan ◽  
R. Vijaykrishnaraj
Keyword(s):  
Retrial Queue ◽  
Working Vacation ◽  
Bulk Arrival

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.

Bulk arrival multi-stage retrial queue with vacation

2015 ◽  
Vol 9 ◽  
pp. 2691-2706
Author(s):  
J. Ebenesar Anna Bagyam ◽  
K. Udaya Chandrika ◽  
A. Viswanathan
Keyword(s):  
Retrial Queue ◽  
Multi Stage ◽  
Bulk Arrival

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.

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