Workload distributions in ASIP queueing networks

Onno Boxma (), Offer Kella () and Uri Yechiali ()
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Onno Boxma: Eindhoven University of Technology
Offer Kella: The Hebrew University of Jerusalem
Uri Yechiali: Tel Aviv University

Queueing Systems: Theory and Applications, 2021, vol. 97, issue 1, No 4, 100 pages

Abstract: 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 ( $$k\le n$$ 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.

Keywords: ASIP queueing networks; Lévy networks; ASIP with leakage; ASIP queues in series; Workload; Primary: 60K20; 60K25; 60K30; Secondary: 60G51 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11134-020-09678-4

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