Analysis of customer's impatience on bulk service queueing system with unreliable server, setup time and two types of multiple vacations

2021 ◽  
Vol 38 (2) ◽  
pp. 198
Author(s):  
G. Ayyappan ◽  
M. Nirmala
Keyword(s):  
Queueing System ◽  
Setup Time ◽  
Multiple Vacations ◽  
Unreliable Server ◽  
Bulk Service

Analysis of the M x/G/1 queue by N-policy and multiple vacations

1994 ◽  
Vol 31 (02) ◽  
pp. 476-496
Author(s):  
Ho Woo Lee ◽  
Soon Seok Lee ◽  
Jeong Ok Park ◽  
K. C. Chae
Keyword(s):  
Performance Measures ◽  
Queue Length ◽  
Time Distribution ◽  
Queueing System ◽  
Random Variables ◽  
System Size ◽  
The Other ◽  
Waiting Time Distribution ◽  
Multiple Vacations ◽  
Linear Cost

We consider an Mx /G/1 queueing system with N-policy and multiple vacations. As soon as the system empties, the server leaves for a vacation of random length V. When he returns, if the queue length is greater than or equal to a predetermined value N(threshold), the server immediately begins to serve the customers. If he finds less than N customers, he leaves for another vacation and so on until he finally finds at least N customers. We obtain the system size distribution and show that the system size decomposes into three random variables one of which is the system size of ordinary Mx /G/1 queue. The interpretation of the other random variables will be provided. We also derive the queue waiting time distribution and other performance measures. Finally we derive a condition under which the optimal stationary operating policy is achieved under a linear cost structure.

scholarly journals M/G/1 vacation model with limited service discipline and hybrid switching-on policy

1997 ◽  
Vol 3 (3) ◽  
pp. 243-253
Author(s):  
Alexander V. Babitsky
Keyword(s):  
Generating Function ◽  
Busy Period ◽  
Optimization Problem ◽  
Queueing System ◽  
Service Discipline ◽  
Multiple Vacations ◽  
Queueing Process ◽  
Vacation Model ◽  
Hybrid Switching ◽  
Limited Service

The author studies an M/G/1 queueing system with multiple vacations. The server is turned off in accordance with the K-limited discipline, and is turned on in accordance with the T-N-hybrid policy. This is to say that the server will begin a vacation from the system if either the queue is empty orKcustomers were served during a busy period. The server idles until it finds at leastNwaiting units upon return from a vacation.Formulas for the distribution generating function and some characteristics of the queueing process are derived. An optimization problem is discussed.

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