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2 Tanguy Christian

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Influence of transients on end-to-end availability for a meshed network

Tanguy Christian

Safety and Reliability of Systems and Processes

2023

Summer Safety and Reliability Seminar 2023

207--226

The disruption of services must be kept at a minimum in telecommunications networks so that the consequences are not too severe and their durations are as short as possible. Maintenance policies often rely on the steady-state availabilities of each element of the system, and focus on the system’s weak links. The end-to-end (or two-terminal) availability – a standard performance index – of a meshed network has long been studied, but mainly for small systems, and assuming constant values for the availability of each element. When taken into account, the time-dependent contributions of links and nodes to the system unavailability were computed using exponential failure and repair distributions. In this work we revisit the meshed network first proposed by Walter, Esch, and Limbourg (ESREL 2008), and compute the end-to-end availability between two nodes, where the individual contributions of links and nodes are kept. This allows the ranking of links and nodes, using well-known performance indices (Birnbaum, Risk Reduction Worth, etc.). We can thus determine the elements that should receive due attention in maintenance and resilience studies. However, as the steady-state availability may not always be a lower bound to the transient availability in the case of non-exponential failure and repair distributions, we have studied the influence of such configurations on the time-dependent behaviours of all the aforementioned quantities. We then discuss the influence of uncertainty in the availability values, and compare the results obtained for the all-terminal reliability, another often-used performance criterion of networks.

Transient behaviour of instantaneous and average availabilities in non-Markovian configuration

Tanguy Christian

Safety and Reliability of Systems and Processes

2022

Summer Safety and Reliability Seminar 2022

185--194

In this work, we calculate the exact instantaneous and average availabilities for a system in which the failure distribution is a gamma distribution with a rational shape parameter α, and the repair time distribution is exponential. Various regimes exist, for which the availabilities may or may not attain values below the asymptotic limit. This is an example of configurations where using the steady-state value may lead to an overoptimistic assessment of the availability of an equipment or system during its mission time.