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

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.