Impatient customer queue with Bernoulli schedule vacation interruption

2015 ◽  
Vol 56 ◽  
pp. 1-7 ◽  
Author(s):  
P. Vijaya Laxmi ◽  
K. Jyothsna
Keyword(s):  
Impatient Customer ◽  
Vacation Interruption ◽  
Bernoulli Schedule

scholarly journals Fluid Queue Driven by anM/M/1Queue Subject to Bernoulli-Schedule-Controlled Vacation and Vacation Interruption

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Kolinjivadi Viswanathan Vijayashree ◽  
Atlimuthu Anjuka
Keyword(s):  
Death Process ◽  
Queueing Model ◽  
Fluid Queue ◽  
Stationary Analysis ◽  
Governing System ◽  
Matrix Geometric Method ◽  
Vacation Interruption ◽  
Model Subject ◽  
Steady State Probabilities ◽  
Bernoulli Schedule

This paper deals with the stationary analysis of a fluid queue driven by anM/M/1queueing model subject to Bernoulli-Schedule-Controlled Vacation and Vacation Interruption. The model under consideration can be viewed as a quasi-birth and death process. The governing system of differential difference equations is solved using matrix-geometric method in the Laplacian domain. The resulting solutions are then inverted to obtain an explicit expression for the joint steady state probabilities of the content of the buffer and the state of the background queueing model. Numerical illustrations are added to depict the convergence of the stationary buffer content distribution to one subject to suitable stability conditions.

scholarly journals An M/M/1 Queue with Working Vacation and Vacation Interruption Under Bernoulli Schedule

2018 ◽  
Vol 7 (4.10) ◽  
pp. 448
Author(s):  
P. Manoharan ◽  
A. Ashok
Keyword(s):  
Geometric Approach ◽  
Stochastic Decomposition ◽  
Working Vacation ◽  
System Parameters ◽  
Mean Waiting Time ◽  
The Mean ◽  
Vacation Interruption ◽  
Mean Queue Length ◽  
Vacation Period ◽  
Bernoulli Schedule

This work deals with M/M/1 queue with Vacation and Vacation Interruption Under Bernoulli schedule. When there are no customers in the system, the server takes a classical vacation with probability p or a working vacation with probability 1-p, where . At the instants of service completion during the working vacation, either the server is supposed to interrupt the vacation and returns back to the non-vacation period with probability 1-q or the sever will carry on with the vacation with probability q. When the system is non empty after the end of vacation period, a new non vacation period begins. A matrix geometric approach is employed to obtain the stationary distribution for the mean queue length and the mean waiting time and their stochastic decomposition structures. Numerous graphical demonstrations are presented to show the effects of the system parameters on the performance measures.  

scholarly journals Finite Buffer GI/M(n)/1 Queue with Bernoulli-Schedule Vacation Interruption under N-Policy

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
P. Vijaya Laxmi ◽  
V. Suchitra
Keyword(s):  
Performance Measures ◽  
Finite Buffer ◽  
Supplementary Variable ◽  
Working Vacation ◽  
Variable Technique ◽  
Special Cases ◽  
Vacation Interruption ◽  
System Length ◽  
Vacation Period ◽  
Bernoulli Schedule

We study a finite buffer N-policy GI/M(n)/1 queue with Bernoulli-schedule vacation interruption. The server works with a slower rate during vacation period. At a service completion epoch during working vacation, if there are at least N customers present in the queue, the server interrupts vacation and otherwise continues the vacation. Using the supplementary variable technique and recursive method, we obtain the steady state system length distributions at prearrival and arbitrary epochs. Some special cases of the model, various performance measures, and cost analysis are discussed. Finally, parameter effect on the performance measures of the model is presented through numerical computations.

scholarly journals Analysis of Impatient Customers in Queues with Bernoulli Schedule Working Vacations and Vacation Interruption

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Veena Goswami
Keyword(s):  
Performance Measures ◽  
System Size ◽  
Stochastic Decomposition ◽  
Model Parameters ◽  
The Mean ◽  
Working Vacations ◽  
Vacation Interruption ◽  
The Impact ◽  
Vacation Period ◽  
Bernoulli Schedule

This paper analyzes customers’ impatience in Markovian queueing system with multiple working vacations and Bernoulli schedule vacation interruption, where customers’ impatience is due to the servers’ vacation. During the working vacation period, if there are customers in the queue, the vacation can be interrupted at a service completion instant and the server begins a regular busy period with probability 1-q or continues the vacation with probability q. We obtain the probability generating functions of the stationary state probabilities and deduce the explicit expressions of the system sizes when the server is in a normal service period and in a Bernoulli schedule vacation interruption, respectively. Various performance measures such as the mean system size, the proportion of customers served, the rate of abandonment due to impatience, and the mean sojourn time of a customer served are derived. We obtain the stochastic decomposition structures of the queue length and waiting time. Finally, some numerical results to show the impact of model parameters on performance measures of the system are presented.

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