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Discrete-Time Queues with Disasters

(2018)
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Abstract
We study the behavior of a discrete-time queueing system in the presence of disasters. Upon occurrence of such a disaster, all the customers in the system are removed at once, so the system becomes empty instantaneously. The concept of a disaster can be used for instance to model a virus infection or a server reset in a computer or communication system, destroying all the jobs or information present in the system. Disasters are also referred to as catastrophes, queue flushing, stochastic clearing or mass exodus in the literature. In our work, we extend the literature on discrete-time queues with disasters to the case of a queueing model with both general independent arrivals and general independent service times. More specifically, the numbers of customer arrivals in the system during different slots have a general distribution and are independent from slot to slot. The customer service times have a general distribution and are independent from customer to customer. Disasters are assumed to occur independently from slot to slot according to a Bernoulli arrival process. In our analysis, we make use of the supplementary random variable technique and introduce a suitable two-dimensional Markovian state description. As results, expressions are obtained for the probability generating functions of both the system content at the beginning of a slot and the sojourn time of an arbitrary customer in steady state, as well as for the mean values and variances of these quantities. By means of numerical examples we illustrate the impact of several model parameters, such as the disaster probability or the customer arrival characteristics, on the queueing behavior.
Keywords
queueing theory, discrete-time queue, disaster, system content, sojourn time

Citation

Please use this url to cite or link to this publication:

MLA
Demircioglu, Mustafa, Herwig Bruneel, and Sabine Wittevrongel. “Discrete-Time Queues with Disasters.” 2018. Print.
APA
Demircioglu, M., Bruneel, H., & Wittevrongel, S. (2018). Discrete-Time Queues with Disasters. Presented at the 7th EWG STOCHMOD.
Chicago author-date
Demircioglu, Mustafa, Herwig Bruneel, and Sabine Wittevrongel. 2018. “Discrete-Time Queues with Disasters.” In .
Chicago author-date (all authors)
Demircioglu, Mustafa, Herwig Bruneel, and Sabine Wittevrongel. 2018. “Discrete-Time Queues with Disasters.” In .
Vancouver
1.
Demircioglu M, Bruneel H, Wittevrongel S. Discrete-Time Queues with Disasters. 2018.
IEEE
[1]
M. Demircioglu, H. Bruneel, and S. Wittevrongel, “Discrete-Time Queues with Disasters,” presented at the 7th EWG STOCHMOD, Lancaster, 2018.
@inproceedings{8567474,
  abstract     = {We study the behavior of a discrete-time queueing system in the presence of disasters. Upon occurrence of such a disaster, all the customers in the system are removed at once, so the system becomes empty instantaneously. The concept of a disaster can be used for instance to model a virus infection or a server reset in a computer or communication system, destroying all the jobs or information present in the system. Disasters are also referred to as catastrophes, queue flushing, stochastic clearing or mass exodus in the literature. In our work, we extend the literature on discrete-time queues with disasters to the case of a queueing model with both general independent arrivals and general independent service times. More specifically, the numbers of customer arrivals in the system during different slots have a general distribution and are independent from slot to slot. The customer service times have a general distribution and are independent from customer to customer. Disasters are assumed to occur independently from slot to slot according to a Bernoulli arrival process. In our analysis, we make use of the supplementary random variable technique and introduce a suitable two-dimensional Markovian state description. As results, expressions are obtained for the probability generating functions of both the system content at the beginning of a slot and the sojourn time of an arbitrary customer in steady state, as well as for the mean values and variances of these quantities. By means of numerical examples we illustrate the impact of several model parameters, such as the disaster probability or the customer arrival characteristics, on the queueing behavior. },
  author       = {Demircioglu, Mustafa and Bruneel, Herwig and Wittevrongel, Sabine},
  keywords     = {queueing theory,discrete-time queue,disaster,system content,sojourn time},
  location     = {Lancaster},
  title        = {Discrete-Time Queues with Disasters},
  year         = {2018},
}