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.

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.

The GI/G/1 queue with uniformly limited virtual waiting times; the finite dam

1980 ◽  
Vol 12 (2) ◽  
pp. 501-516 ◽  
Author(s):  
Do Le Minh
Keyword(s):  
Water Supply ◽  
Analytical Method ◽  
Busy Period ◽  
Queueing System ◽  
Waiting Times ◽  
Fixed Interval ◽  
Finite Capacity ◽  
Queueing Process ◽  
Finite Dam

This paper studies the GI/G/1 queueing system in which no customer can stay longer than a fixed interval D. This is also a model for the dam with finite capacity, instantaneous water supply and constant release rule. Using analytical method together with the property that the queueing process ‘starts anew’ probabilistically whenever an arriving customer initiates a busy period, we obtain various transient and stationary results for the system.

The generalised state-dependent queue: the busy period Erlangian

1974 ◽  
Vol 11 (03) ◽  
pp. 618-623
Author(s):  
B. W. Conolly
Keyword(s):  
Laplace Transform ◽  
Generating Function ◽  
Busy Period ◽  
Continued Fraction ◽  
Queueing System ◽  
Joint Probability ◽  
Single Server ◽  
System State ◽  
State Dependent ◽  
The Laplace Transform

A continued fraction representation is presented of the Laplace transform of the generating function of the fundamental joint probability and density of busy period length measured in customers served and duration in time. The setting is the single server Erlang queueing system where the parameters of negative exponentially distributed arrival and service times have a general dependence on instantaneous system state.

scholarly journals A discrete-time queueing system with changes in the vacation times

2016 ◽  
Vol 26 (2) ◽  
pp. 379-390 ◽  
Author(s):  
Ivan Atencia
Keyword(s):  
Performance Measures ◽  
Discrete Time ◽  
Busy Period ◽  
Queueing System ◽  
Probability Generating Function ◽  
Service Discipline ◽  
Numerical Examples ◽  
Extensive Analysis ◽  
The One ◽  
Steady State Performance

Abstract This paper considers a discrete-time queueing system in which an arriving customer can decide to follow a last come first served (LCFS) service discipline or to become a negative customer that eliminates the one at service, if any. After service completion, the server can opt for a vacation time or it can remain on duty. Changes in the vacation times as well as their associated distribution are thoroughly studied. An extensive analysis of the system is carried out and, using a probability generating function approach, steady-state performance measures such as the first moments of the busy period of the queue content and of customers delay are obtained. Finally, some numerical examples to show the influence of the parameters on several performance characteristics are given.

Analysis of an SPP/G/1 system with multiple vacations and E-limited service discipline

1993 ◽  
Vol 14 (3-4) ◽  
pp. 349-367 ◽  
Author(s):  
Shoji Kasahara ◽  
Tetsuya Takine ◽  
Yutaka Takahashi ◽  
Toshiharu Hasegawa
Keyword(s):  
Service Discipline ◽  
Multiple Vacations ◽  
Limited Service

The GI/G/1 queue with uniformly limited virtual waiting times; the finite dam

1980 ◽  
Vol 12 (02) ◽  
pp. 501-516 ◽  
Author(s):  
Do Le Minh
Keyword(s):  
Water Supply ◽  
Analytical Method ◽  
Busy Period ◽  
Queueing System ◽  
Waiting Times ◽  
Fixed Interval ◽  
Finite Capacity ◽  
Queueing Process ◽  
Finite Dam

This paper studies the GI/G/1 queueing system in which no customer can stay longer than a fixed interval D. This is also a model for the dam with finite capacity, instantaneous water supply and constant release rule. Using analytical method together with the property that the queueing process ‘starts anew’ probabilistically whenever an arriving customer initiates a busy period, we obtain various transient and stationary results for the system.

scholarly journals Bulk input queues with quorum and multiple vacations

1996 ◽  
Vol 2 (2) ◽  
pp. 95-106 ◽  
Author(s):  
Jewgeni H. Dshalalow ◽  
Jay Yellen
Keyword(s):  
Poisson Process ◽  
Preliminary Analysis ◽  
Queueing System ◽  
Compound Poisson Process ◽  
Batch Service ◽  
Single Server ◽  
Compound Poisson ◽  
Multiple Vacations ◽  
Queueing Process ◽  
Multiple Vacation

The authors study a single-server queueing system with bulk arrivals and batch service in accordance to the general quorum discipline: a batch taken for service is not less thanrand not greater thanR(≥r). The server takes vacations each time the queue level falls belowr(≥1)in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process. The analysis of the system is based on the theory of first excess processes developed by the first author. A preliminary analysis of such processes enabled the authors to obtain all major characteristics for the queueing process in an analytically tractable form. Some examples and applications are given.

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

1988 ◽  
Vol 25 (02) ◽  
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.

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