A Discrete-Time Single-Server Queueing System Under Multiple Vacations and Setup-Closedown Times

2009 ◽  
Vol 27 (2) ◽  
pp. 221-239 ◽  
Author(s):  
Pilar Moreno
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Single Server ◽  
Multiple Vacations

scholarly journals Analysis of a Discrete-Time Queueing Model with Disasters

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3283
Author(s):  
Mustafa Demircioglu ◽  
Herwig Bruneel ◽  
Sabine Wittevrongel
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Time Slot ◽  
Probability Distributions ◽  
Single Server ◽  
Bernoulli Process ◽  
Tail Probabilities ◽  
Mean Values ◽  
The Mean ◽  
The Impact

Queueing models with disasters can be used to evaluate the impact of a breakdown or a system reset in a service facility. In this paper, we consider a discrete-time single-server queueing system with general independent arrivals and general independent service times and we study the effect of the occurrence of disasters on the queueing behavior. Disasters occur independently from time slot to time slot according to a Bernoulli process and result in the simultaneous removal of all customers from the queueing system. General probability distributions are allowed for both the number of customer arrivals during a slot and the length of the service time of a customer (expressed in slots). Using a two-dimensional Markovian state description of the system, we obtain expressions for the probability, generating functions, the mean values, variances and tail probabilities of both the system content and the sojourn time of an arbitrary customer under a first-come-first-served policy. The customer loss probability due to a disaster occurrence is derived as well. Some numerical illustrations are given.

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.

An Unreliable Quorum Queueing System with Single and Multiple Vacations

2017 ◽  
Vol 34 (06) ◽  
pp. 1750036
Author(s):  
Lotfi Tadj
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Queueing System ◽  
System Size ◽  
Embedded Markov Chain ◽  
Queueing Models ◽  
Single Server ◽  
Multiple Vacations ◽  
Service Completion

This paper contributes to the literature of single server queueing models with a vacationing server. We have incorporated many features for a better control over the system. The server implements the N-policy, takes both single and multiple vacations, and is subject to breakdowns. The embedded Markov chain technique is used to obtain the pgf of the system size at a service completion epoch in the steady-state. The semi-regenerative technique is used to obtain the pgf of the system size at an arbitrary instant of time in the steady-state.

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