Workload distributions in ASIP queueing networks

Onno Boxma, Offer Kella (Corresponding author), Uri Yechiali

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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 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.

Original languageEnglish
Pages (from-to)81-100
Number of pages20
JournalQueueing Systems
Volume97
Issue number1-2
DOIs
Publication statusPublished - Feb 2021

Keywords

  • ASIP queueing networks
  • ASIP queues in series
  • ASIP with leakage
  • Lévy networks
  • Workload

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