@article{8707e5fc8c244cda870a628d4eced769,
title = "Workload distributions in ASIP queueing networks",
abstract = "The workload of a generalized n-site asymmetric simple inclusion process (ASIP) is investigated. Three models are analyzed. The first model is a serial network for which the steady-state Laplace–Stieltjes transform (LST) of the total workload in the first k sites (k≤ n) just after gate openings and at arbitrary epochs is derived. In a special case, the former (just after gate openings) turns out to be an LST of the sum of k independent random variables. The second model is a 2-site ASIP with leakage from the first queue. Gate openings occur at exponentially distributed intervals, and the external input processes to the stations are two independent subordinator L{\'e}vy processes. The steady-state joint workload distribution right after gate openings, right before gate openings and at arbitrary epochs is derived. The third model is a shot-noise counterpart of the second model where the workload at the first queue behaves like a shot-noise process. The steady-state total amount of work just before a gate opening turns out to be a sum of two independent random variables.",
keywords = "ASIP queueing networks, ASIP queues in series, ASIP with leakage, L{\'e}vy networks, Workload",
author = "Onno Boxma and Offer Kella and Uri Yechiali",
note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.",
year = "2021",
month = feb,
doi = "10.1007/s11134-020-09678-4",
language = "אנגלית",
volume = "97",
pages = "81--100",
journal = "Queueing Systems",
issn = "0257-0130",
publisher = "Springer Netherlands",
number = "1-2",
}