@inproceedings{4c9c1ae49af0447a9d60cb0e8b141b5d,
title = "Queueing Delay in a Finite-Buffer Model with Failures and Bernoulli Feedback",
abstract = "In the paper a finite-capacity queueing model with server breakdowns is considered. Jobs arrive according to a Poisson process and are being served during exponentially distributed processing time under the FIFO service discipline. During the operation of the system successive exponential failure-free times are followed by generally distributed repair periods. After the processing a job may rejoin the queue (feedback) with probability q or leave the system with probability 1 − q. Applying the analytical approach based on the idea of Markov chain and the formula of total probability, a system of integral equations for the transient queueing delay distribution is built, conditioned by the initial buffer state. Algebraic method based on the idea of Korolyuk{\textquoteright}s potential is used to obtain the solution of the corresponding system written for Laplace transforms in a closed form. Numerical example is attached as well.",
keywords = "Bernoulli feedback, Finite-Buffer queue, Integral equations, Queueing delay, Transient state",
author = "Kempa, \{Wojciech M.\}",
note = "Publisher Copyright: {\textcopyright} 2018, Springer International Publishing AG.; 38th International Conference on Information Systems Architecture and Technology, ISAT 2017 ; Conference date: 17-09-2017 Through 19-09-2017",
year = "2018",
doi = "10.1007/978-3-319-67229-8\_21",
language = "English",
isbn = "9783319672281",
series = "Advances in Intelligent Systems and Computing",
publisher = "Springer Verlag",
pages = "229--238",
editor = "Leszek Borzemski and Jerzy Swiatek and Zofia Wilimowska",
booktitle = "Information Systems Architecture and Technology",
address = "Germany",
}