Analysis of an N-policy M/Ek/1 Queueing system with Unreliable server, Multiple Vacations and Balking

2015 ◽  
Vol 21 (2) ◽  
pp. 77-82
Author(s):  
P Jayachitra ◽  
◽  
A.James Albert
Keyword(s):  
Queueing System ◽  
Multiple Vacations ◽  
Unreliable Server

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.

Transient Analysis of a Two-Heterogeneous Severs Queue with Impatient Behaviour and Multiple Vacations

2018 ◽  
Vol 6 (1) ◽  
pp. 69-84
Author(s):  
Jia Xu ◽  
Liwei Liu ◽  
Taozeng Zhu
Keyword(s):  
Generating Functions ◽  
Transient Analysis ◽  
Bessel Functions ◽  
Queueing System ◽  
System Size ◽  
Heterogeneous Servers ◽  
Modified Bessel Functions ◽  
Multiple Vacations ◽  
Special Cases ◽  
Mean And Variance

AbstractWe consider anM/M/2 queueing system with two-heterogeneous servers and multiple vacations. Customers arrive according to a Poisson process. However, customers become impatient when the system is on vacation. We obtain explicit expressions for the time dependent probabilities, mean and variance of the system size at timetby employing probability generating functions, continued fractions and properties of the modified Bessel functions. Finally, two special cases are provided.

scholarly journals Analysis and Comparison of Queue with N-Policy and Unreliable Server

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Qing Ma ◽  
Xuelu Zhang
Keyword(s):  
Social Welfare ◽  
Poisson Process ◽  
Queueing System ◽  
Management Decision ◽  
Dormant State ◽  
Unreliable Server ◽  
The Social ◽  
Number Of Customers ◽  
Potential Customers ◽  
Strong Ability

This work considers a queueing system with N-policy and unreliable server, where potential customers arrive at the system according to Poisson process. If there is no customer waiting in the system, instead of shutting down, the server turns into dormant state and does not afford service until the number of customers is accumulated to a certain threshold. And in the working state, the server is apt to breakdown and affords service again only after it is repaired. According to whether the server state is observable or not, the numerical optimal arrival rates are computed to maximize the social welfare and throughput of the system. The results illustrate their tendency in two cases so that the manager has a strong ability to decide which is more crucial in making management decision.

Sign in / Sign up

Export Citation Format

Share Document