Hierarchical composition and aggregation of state-based availability and performability models

Abstract

Telecommunication systems are large and complex, consisting of multiple intelligent modules in shelves, multiple shelves in frames, and multiple frames to compose a single network element. In the availability and performability analysis of such a complex system, combinatorial models are computationally efficient but have limited expressive power. State-based models are expressive but computationally complex. Furthermore, this complexity grows exponentially with the size of the model. This state-space explosion problem must be solved in order to model complex-systems using state-based models.The solution, in this paper, is to partition complex models into a hierarchy of submodels, to transform lower-level -state, -transition Markov reward models and stochastic reward nets into equivalent (with respect to their steady-state behavior) 2-state, 2-transition models, and then to back-substitute the equivalent submodels into the higher-level models. This paper also proposes a canonical form for the equivalent submodels. This technique is defined for availability models, where the state of the system is either up or down, and for performability models, where the state of the system may be up, down, or partially-up/partially-down. This paper also shows how this technique can be used to obtain common availability measures for telecommunication systems, and when to apply it to availability models and when to use it in performability models.For future work, it would be interesting to more tightly integrate this technique with modeling tools, perhaps coupled with a graphic front-end to facilitate the navigation of the model hierarchy.Index Terms-Equivalent failure rate, equivalent repair rate, hierarchical composition, Markov reward model, outage measure, "Reliability and Quality Measurements for Telecommunication Systems" measure, telecommunication system.

Availability Importance Measures for Virtualized System with Live Migration

“…This paper introduced the state-of-art component importance analysis [13] and applied it to the CTMC-based live migration model to reveal the component importance in the context of live migration. More precisely, our method is based on the aggregation techniques of CTMC-based availability models [18] and the importance measures with respect to failure and repair rates [16]. Also, we proposed a method to estimate the sensitivities of system availability with respect to component availabilities.…”

“…This paper proposes a preprocessing based on the aggregation of CTMC-based availability model [18] before applying the availability importance measures.…”

“…Also, , [18]. In this paper, we call the equivalent failure and repair rates as the effective failure and repair rates.…”

Optimal redundancy allocation for high availability routers

“…The CTMC for an HA router with N + M redundancy can transit into a two-state and two-transition Markov chain [18], as shown in Figure 2. One state is the Up with the reward rate HA ; the other state is the Down with the reward rate HA [18].…”

Automated generation of a Petri net model: Application to an end of life manufacturing process

“…The analytical reliability modelling techniques include various approaches from which an analyst is able to choose the most suitable technique for their given problem. The techniques for failure analysis consist of combinatorial models, including Reliability Block Diagrams (RBDs), Fault Trees (FTs) and Binary Decision Diagrams (BDDs), statespace models, including the subcategory of Markov approaches, and hierarchical models generated by the combination of combinatorial and state-space models, which are able to simplify the model and ease further analysis (Lanus et al 2003). With the current development in engineering technologies, the complexity of these engineering systems/processes is ever increasing and proportionally so potentially do the risks and hazards.…”