Analysis of Jackson networks with infinite supply and unreliable nodes

Jennifer Sommer (), Joost Berkhout (), Hans Daduna () and Bernd Heidergott ()
Additional contact information
Jennifer Sommer: HPC Hamburg Port Consulting GmbH
Joost Berkhout: Centrum Wiskunde & Informatica (CWI)
Hans Daduna: University of Hamburg
Bernd Heidergott: Vrije Universiteit

Queueing Systems: Theory and Applications, 2017, vol. 87, issue 1, No 9, 207 pages

Abstract: Abstract Jackson networks are versatile models for analyzing complex networks. In this paper we study generalized Jackson networks with single-server stations, where nodes may have an infinite supply of work. We allow simultaneous breakdown of servers and consider group repair strategies. We establish the existence of a steady-state distribution of the queue-length vector at stable nodes for different types of failure regimes. In steady state the distribution of the failure/repair regime and of the queue-length vector at stable nodes decouples in a product-form way. We provide closed-form solutions for the classical performance measures such as throughput or mean sojourn time at a station.

Keywords: Jackson networks; Group breakdowns; Group repairs; Infinite supply; 68M20 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11134-017-9542-1

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