Analysis of Jackson networks with infinite supply and unreliable nodes

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 steadystate 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 queuelength 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.

Robustness analysis of generalized Jackson network

“…We present a brief review of the theory of JN's with breakdowns and repairs. For details we refer to Sommer et al (2017). The network consists of J exponential single server nodes with service discipline "First-Come-First-Served" (FCFS), the node set is denoted byJ = {1, .…”

“…These constraints ensure that solution η i , i ∈J , from (3) is also the solution of the traffic equations for unreliable Jackson networks under any breakdown scenario. For more details see Sommer et al (2017). Under these assumptions, we provide an overview on the studied performance characteristics in the following.…”

“…Under these assumptions, we provide an overview on the studied performance characteristics in the following. For an overview of other performance characteristics see Sommer et al (2017). Under stalling the stationary throughput at nodes i ∈ W (no infinite supply) is…”

“…Like for classical JN's, one can obtain for these extended JN's the steady-state distribution of the queue-length vector at stable nodes in product-from for different type of failure-regimes (a precise definition of "stable node" will be provided later in the text), see Sommer et al (2017). In addition, closed-form solutions for the long-run throughput of subnetworks and of the complete network are provided.…”

“…Elaborating on the product-form results in Sommer et al (2017), we will in this paper investigate the impact of the distribution of the time between breakdowns of the individual servers on the throughput of the network. More specifically, we will model the breakdown behavior through a parameterized distribution, and provide a robustness analysis of the system throughput with respect to the uncertainty parameters.…”