Scalable Stochastic Modelling for Resilience Jeremy T. Bradley 1 , Lucia Cloth 2 , Richard Hayden 1 , Le¨ ıla Kloul 3 Philipp Reinecke 4 , Markus Siegle 5 , Nigel Thomas 6 , and Katinka Wolter 4 1 Department of Computing, Imperial College London, UK 2 Department of Applied Information Technology, GU Tech, Oman 3 Laboratoire PRiSM, Universit´ e de Versailles, France 4 Institute of Computer Science, Freie Universit¨ at Berlin, Germany 5 Department of Computer Science, Universit¨ at der Bundeswehr M¨ unchen, Germany 6 School of Computing Science, Newcastle University Abstract. This chapter summarises techniques that are suitable for performance and resilience modelling and analysis of massive stochas- tic systems. We will introduce scalable techniques that can be applied to models constructed using DTMCs and CTMCs as well as compositional formalisms such as stochastic automata networks, stochastic process al- gebras and queueing networks. We will briefly show how techniques such as mean value analysis, mean-field analysis, symbolic data structures and fluid analysis can be used to analyse massive models specifically for resilience in networks, communication and computer architectures. 1 Introduction The techniques presented in this chapter represent the state of the art in per- formance and resilience analysis when it comes to coping with massive state- space models. Many existing analysis techniques rely on generating underlying stochastic models, such as continuous-time Markov chains. Where there is too close a correspondence between the state space of the model and that of the underlying stochastic process, the state-space explosion in the former can lead to intractability in the latter. The presented techniques in this chapter were cho- sen as they represent instances of the main approaches to state-space reduction in stochastic systems: aggregation, decomposition, symbolic representation and continuum approximation. We realise that accurate resilience analysis relies on a detailed and complex model. This kind of model generates huge state spaces and computation time if handled na¨ ıvely. In this chapter, we are specifically interested in analysis tech- niques that side-step the state space explosion problem by making use of effi- cient representation mechanisms. This is necessary if we are to make headway in directly analysing problems in mobile networks (Chapter 29), critical infras- tructures (Chapter 7 and 30) and Cloud systems (Chapter 13 and 28).