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.
Classical Jackson networks are a well established tool for the analysis of complex systems. In this paper we analyze Jackson networks with the additional features that (i) nodes may have an infinite supply of low priority work and (ii) nodes may be unstable in the sense that the queue length at these nodes grows beyond any bound. We provide the limiting distribution of the queue length distribution at stable nodes, which turns out to be of product-form. A key step in establishing this result is the development of a new algorithm based on adjusted traffic equations for detecting instable nodes. Our results complement the results known in the literature for the sub-cases of Jackson networks with either infinite supply nodes or unstable nodes by providing an analysis of the significantly more challenging case of networks with both types of nonstandard nodes present. Building on our product-form results, we provide closed-form solutions for common customer and system oriented performance measures.
Queuing networks are a well-established approach to modeling and analysis of complex systems. This paper develops an approach to risk-analysis of queuing network models, where "risk" is understood as the possible impact of ignoring parameter insecurity. Our approach allows to compute the value at risk of performance characteristics of queuing networks under parameter insecurity. Keywords Robustness analysis • Queuing network • Parameter insecurity 1 Introduction Jackson networks (henceforth JN), to be formally introduced later on, are a well established class of models in, e.g., production, telecommunication, computer systems; for surveys see Kelly (1979) and Chen and Yao (2001). JN's have the desirable property that the distribution of the stationary queue length vector is of product-form, which allows for quick numerical evaluation of performance measures, such as the the mean B Bernd Heidergott
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