scholarly journals M/M/c multiple synchronous vacation model with gated discipline

2012 ◽  
Vol 8 (4) ◽  
pp. 939-968 ◽  
Author(s):  
Zsolt Saffer ◽  
◽  
Wuyi Yue ◽  
Keyword(s):  
Vacation Model ◽  
Gated Discipline

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.

The backlog and depletion-time process for M/G/1 vacation models with exhaustive service discipline

1988 ◽  
Vol 25 (2) ◽  
pp. 404-412 ◽  
Author(s):  
Julian Keilson ◽  
Ravi Ramaswamy
Keyword(s):  
Steady State ◽  
Queueing System ◽  
Time Dependent ◽  
Service Discipline ◽  
Time Process ◽  
State Space Methods ◽  
Ergodic Distribution ◽  
Vacation Model ◽  
Primary Service ◽  
Decomposition Theorems

The vacation model studied is an M/G/1 queueing system in which the server attends iteratively to ‘secondary' or ‘vacation' tasks at ‘primary' service completion epochs, when the primary queue is exhausted. The time-dependent and steady-state distributions of the backlog process [6] are obtained via their Laplace transforms. With this as a stepping stone, the ergodic distribution of the depletion time [5] is obtained. Two decomposition theorems that are somewhat different in character from those available in the literature [2] are demonstrated. State space methods and simple renewal-theoretic tools are employed.

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.

scholarly journals Exhaustive fluid vacation model with positive fluid rate during service

2015 ◽  
Vol 91 ◽  
pp. 286-302 ◽  
Author(s):  
Gábor Horváth ◽  
Miklós Telek
Keyword(s):  
Vacation Model

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.

$$M/D^{[y]}/1$$ M / D [ y ] / 1 Periodically gated vacation model and its application to IEEE 802.16 network

2014 ◽  
Vol 239 (2) ◽  
pp. 497-520 ◽  
Author(s):  
Zsolt Saffer ◽  
Sergey Andreev ◽  
Yevgeni Koucheryavy
Keyword(s):  
Ieee 802.16 ◽  
Vacation Model

scholarly journals Note sur un modele de file GI/G/1 a service autonome (avec vacances du serveur)

1987 ◽  
Vol 19 (1) ◽  
pp. 289-291 ◽  
Author(s):  
Christine Fricker
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Time Distribution ◽  
Conditional Distribution ◽  
Stochastic Decomposition ◽  
Analytic Method ◽  
Service Time Distribution ◽  
Waiting Time Distribution ◽  
Vacation Model ◽  
The Law

Keilson and Servi introduced in [5] a variation of a GI/G/1 queue with vacation, in which at the end of a service time, either the server is not idle, and he starts serving the first customer in the queue with probability p, or goes on vacation with probability 1 – p, or he is idle, and he takes a vacation. At the end of a vacation, either customers are present, and the server starts serving the first customer, or he is idle, and he takes a vacation. The case p = 1, called the GI/G/1/V queue, was studied analytically by Gelenbe and Iasnogorodski [3] (see also [4]) and then by Doshi [1] and Fricker [2] who obtained stochastic decomposition results on the waiting-time of the nth customer extending the law decomposition result of [3]. Keilson and Servi [5] give a more complete analytic method of treating both the GI/G/1/V model and the Bernoulli vacation model: instead of the waiting time, they use a bivariate process at the service and vacation initiation epochs and the waiting-time distribution is computed as a conditional distribution of the above. In this note the law decomposition result is obtained from a reduction to the GI/G/1/V model with a modified service-time distribution just using the waiting time, with simple path arguments so that by [1] and [2] stochastic decomposition results are valid, which extend the result of [5].

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