M/G/1 Multiple Vacation Model with Balking for a Class of Disciplines

2015 ◽  
Vol 12 (3) ◽  
pp. 383-407 ◽  
Author(s):  
Zsolt Saffer ◽  
Wuyi Yue
Keyword(s):  
Multiple Vacation ◽  
Vacation Model

Time-dependent process of M/G/1 vacation models with exhaustive service

1992 ◽  
Vol 29 (02) ◽  
pp. 418-429 ◽  
Author(s):  
Hideaki Takagi
Keyword(s):  
Steady State ◽  
Initial Conditions ◽  
Setup Time ◽  
Time Dependent ◽  
Time Model ◽  
Vacation Models ◽  
Single Vacation ◽  
Multiple Vacation ◽  
Virtual Waiting Time ◽  
Vacation Model

Generalized M/G/1 vacation systems with exhaustive service include multiple and single vacation models and a setup time model possibly combined with an N-policy. In these models with given initial conditions, the time-dependent joint distribution of the server's state, the queue size, and the remaining vacation or service time is known (Takagi (1990)). In this paper, capitalizing on the above results, we obtain the Laplace transforms (with respect to time) for the distributions of the virtual waiting time, the unfinished work (backlog), and the depletion time. The steady-state limits of those transforms are also derived. An erroneous expression for the steady-state distribution of the depletion time in a multiple vacation model given by Keilson and Ramaswamy (1988) is corrected.

Time-dependent process of M/G/1 vacation models with exhaustive service

1992 ◽  
Vol 29 (2) ◽  
pp. 418-429 ◽  
Author(s):  
Hideaki Takagi
Keyword(s):  
Steady State ◽  
Initial Conditions ◽  
Setup Time ◽  
Time Dependent ◽  
Time Model ◽  
Vacation Models ◽  
Single Vacation ◽  
Multiple Vacation ◽  
Virtual Waiting Time ◽  
Vacation Model

Generalized M/G/1 vacation systems with exhaustive service include multiple and single vacation models and a setup time model possibly combined with an N-policy. In these models with given initial conditions, the time-dependent joint distribution of the server's state, the queue size, and the remaining vacation or service time is known (Takagi (1990)). In this paper, capitalizing on the above results, we obtain the Laplace transforms (with respect to time) for the distributions of the virtual waiting time, the unfinished work (backlog), and the depletion time. The steady-state limits of those transforms are also derived. An erroneous expression for the steady-state distribution of the depletion time in a multiple vacation model given by Keilson and Ramaswamy (1988) is corrected.

Well-Posedness of the Gnedenko System with Multiple Vacations

2012 ◽  
Vol 522 ◽  
pp. 902-909
Author(s):  
Bilikiz Yunus ◽  
Abdukerim Haji
Keyword(s):  
Semigroup Theory ◽  
Linear Operators ◽  
Well Posedness ◽  
Multiple Vacations ◽  
Dynamic Solution ◽  
Multiple Vacation ◽  
Gnedenko System

We investigate the solution of the Gnedenko system with multiple vacation of a repairman. By using-semigroup theory of linear operators, we prove well-posedness and the existence of the unique positive dynamic solution of the system.

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.

Time-changing and truncating K-capacity queues from one K to another

1991 ◽  
Vol 28 (3) ◽  
pp. 647-655 ◽  
Author(s):  
Paul Glasserman ◽  
Wei-Bo Gong
Keyword(s):  
Queue Length ◽  
Sample Path ◽  
Time Change ◽  
Random Time ◽  
Random Time Change ◽  
Vacation Model

For , we obtain a K′- capacity queue from a K- capacity queue through a random time change and a truncation, provided arrivals are Poisson or service is exponential. In the case of an M/G/1/K queue, the time change erases service intervals that begin with more than K′ customers in the systems. This construction yields a straightforward sample path proof of Keilson's result on the proportionality of the ergodic queue length probabilities in M/G/1/K queues. The same approach proves a strengthened result for ‘detailed' state probabilities. It also reproduces a proportionality result for a vacation model, due to Keilson and Servi. A ‘dual' construction yields a different kind of proportionality for the G/M/1/K queue.

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