@inproceedings{ef898c4e8ffb438c88dcc5bece9d11dc,
title = "On departure process in a production model with cyclic working and repair periods",
abstract = "A finite-buffer queueing system of the M/M/1/N type is used for modeling the operation of a single-machine production line with cyclic failure-free and repair periods. The arriving jobs enter randomly according to a Poisson process and are being processed individually with service times having the common exponential distribution. After an exponentially distributed working period a breakdown of the machine occurs, starting an exponentially distributed repair time during which the service process is stopped. At the completion epoch of the repair time a new working period begins and so on. A system of integral equations for conditional probability distributions of the number of jobs completely processed before the fixed time t (departure process) is built, using the concept of embedded Markov chain and the total probability law. Applying linear-algebraic approach the compact-form solution of the corresponding system written for double transforms of departure process is found.",
keywords = "Departure process, Finite-buffer queue, Machine breakdown, Total probability law, Transient state",
author = "Kempa, \{Wojciech M.\} and Iwona Paprocka and Krzysztof Kalinowski and Cezary Grabowik",
note = "Publisher Copyright: {\textcopyright} (2014) Trans Tech Publications, Switzerland.",
year = "2014",
doi = "10.4028/www.scientific.net/AMR.1036.846",
language = "English",
series = "Advanced Materials Research",
publisher = "Trans Tech Publications Ltd.",
pages = "846--851",
editor = "Alexander Mikhaylov and Dumitru Nedelcu and Alexei Toca and Andrzej Wrobel and Constantin Carausu and Emil Oanta",
booktitle = "Modern Technologies in Industrial Engineering II",
address = "Switzerland",
}