We present an essentially philosophical account of a mathematical approach to systems and services modelling for the purpose for understanding the functionality, performance, reliability, and security - in short, the integrity - of ICT systems. We describe the economic background to the need for effective modelling technologies, and explain the principal strengths of a key existing technology, the experience of which we build upon. Building squarely on this industrially validated practical experience, we then describe a rather general but directly applicable mathematical framework, and discuss how to model central issues in access control, such as roles and impersonation, data integrity, and most interestingly, stewardship. Our mathematical framework combines combinatorial, logical, algebraic, topological, and, critically, stochastic methods. We emphasize that we are not overly concerned with the formal specification of the detailed behaviour of systems and services. Rather, our interest is focused upon a framework for building particular mathematical models of specific aspects of enterprise-scale systems and services at appropriate levels of abstraction. This framework is constructed to help explore questions concerning, for instance, combinations of services availability and systems accessibility properties. In particular, we aim to use models that capture performance to address also systems security questions such as whether a given system model is capable of complying with a security policy requirement, as expressed by a service-level agreement. Further, we aim to quantify the operational impact and cost of both failure to comply and of transition to compliance. 26 Pages
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