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.

Group breakdowns, Group repairs, Infinite supply, Jackson networks
HPC Hamburg Port Consulting GmbH, Hamburg, Germany
Queueing Systems
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Sommer, J, Berkhout, J, Daduna, H, & Heidergott, B.F. (2017). Analysis of Jackson networks with infinite supply and unreliable nodes. Queueing Systems, 87(1-2), 181–207. doi:10.1007/s11134-017-9542-1