@inproceedings{b9efb20ed18b46c59a6e283876756f86,
title = "Time to Start a Crowded Period in a Finite-Buffer Queue with Poisson Input Flow and General Processing Times",
abstract = "A finite-capacity queueing model with Poisson input flow and generally distributed processing times of jobs is considered. An idea of a crowded period is introduced, namely the time period in the system operation during which the number of jobs present in the system is continually greater than or equal the fixed level \$\$M>0\$\$. A system of integral equations for the tail cumulative distribution function of the time to start a crowded period is derived, conditioned by the number of jobs present in the accumulating buffer before the start moment. A solution of the equivalent system written for Laplace transforms is found using the linear algebraic approach.",
keywords = "Crowded period, Finite buffer, Poisson process, Single-server queue, Transient state",
author = "Kempa, \{Wojciech M.\}",
note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.; 7th International Conference on Finite Difference Methods, FDM 2018 ; Conference date: 11-06-2018 Through 16-06-2018",
year = "2019",
doi = "10.1007/978-3-030-11539-5\_37",
language = "English",
isbn = "9783030115388",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "329--336",
editor = "Istv{\'a}n Farag{\'o} and Ivan Dimov and Lubin Vulkov",
booktitle = "Finite Difference Methods. Theory and Applications - 7th International Conference, FDM 2018, Revised Selected Papers",
address = "Germany",
}