TY - JOUR
T1 - Workload distributions in ASIP queueing networks
AU - Boxma, Onno
AU - Kella, Offer
AU - Yechiali, Uri
PY - 2021/2
Y1 - 2021/2
N2 - 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 Lévy 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.
AB - 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 Lévy 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.
KW - ASIP queueing networks
KW - ASIP queues in series
KW - ASIP with leakage
KW - Lévy networks
KW - Workload
UR - http://www.scopus.com/inward/record.url?scp=85098725505&partnerID=8YFLogxK
U2 - 10.1007/s11134-020-09678-4
DO - 10.1007/s11134-020-09678-4
M3 - Article
AN - SCOPUS:85098725505
SN - 0257-0130
VL - 97
SP - 81
EP - 100
JO - Queueing Systems: Theory and Applications
JF - Queueing Systems: Theory and Applications
IS - 1-2
ER -