A mixed service for two queue gated vacation with Bernoulli schedule policy

2012 ◽  
Author(s):  
Dibyajyoti Guha ◽  
S.S. Pathak
Keyword(s):  
Schedule Policy ◽  
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.

Performance Analysis of an M/G/1 Feedback Retrial Queue with Two Types of Service and Bernoulli Vacation

2016 ◽  
pp. 38-54
Author(s):  
Arivudainambi D ◽  
Gowsalya Mahalingam
Keyword(s):  
Retrial Queue ◽  
Single Server ◽  
Supplementary Variable ◽  
Number Of Customers ◽  
Bernoulli Schedule ◽  
Schedule Mechanism ◽  
Fcfs Discipline ◽  
Bernoulli Vacation

This chapter is concerned with the analysis of a single server retrial queue with two types of service, Bernoulli vacation and feedback. The server provides two types of service i.e., type 1 service with probability??1 and type 2 service with probability ??2. We assume that the arriving customer who finds the server busy upon arrival leaves the service area and are queued in the orbit in accordance with an FCFS discipline and repeats its request for service after some random time. After completion of type 1 or type 2 service the unsatisfied customer can feedback and joins the tail of the retrial queue with probability f or else may depart from the system with probability 1–f. Further the server takes vacation under Bernoulli schedule mechanism, i.e., after each service completion the server takes a vacation with probability q or with probability p waits to serve the next customer. For this queueing model, the steady state distributions of the server state and the number of customers in the orbit are obtained using supplementary variable technique. Finally the average number of customers in the system and average number of customers in the orbit are also obtained.

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.

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