Policy-centric integration and dynamic composition of autonomic computing techniques

This paper presents innovative work in the development of policy-based autonomic computing. The core of the work is a powerful and flexible policy-expression language AGILE, which facilitates run-time adaptable policy configuration of autonomic systems. AGILE also serves as an integrating platform for other self-management technologies including signal processing, automated trend analysis and utility functions. Each of these technologies has specific advantages and applicability to different types of dynamic adaptation. The AGILE platform enables seamless interoperability of the different technologies to each perform various aspects of self-management within a single application. The various technologies are implemented as object components. Self-management behaviour is specified using the policy language semantics to bind the various components together as required. Since the policy semantics support run-time re-configuration, the self-management architecture is dynamically composable. Additional benefits include the standardisation of the application programmer interface, terminology and semantics, and only a single point of embedding is required.

A versatile policy toolkit supporting run-time policy reconfiguration

This paper describes an autonomics development tool which serves as both a powerful and flexible policy-expression language and a policy-based framework that supports the integration and dynamic composition of several autonomic computing techniques including signal processing, automated trend analysis and utility functions. Each of these technologies has specific advantages and applicability to different types of dynamic adaptation. The AGILE platform enables seamless interoperability of the different technologies to each perform various aspects of self-management within a single application. Self-management behaviour is specified using the policy language semantics to bind the various technologies together as required. Since the policy semantics support run-time re-configuration, the self-management architecture is dynamically composable. The policy language and implementation library have integrated support for self-stabilising behaviour, enabling oscillation and other forms of instability to be handled at the policy level with very little effort on the part of the application developer. Example applications are presented to illustrate the integration of different autonomics techniques, and the achievement of dynamic composition.

Stochastic comparability and dual q-functions

In this paper we discuss the relationship and characterization of stochastic comparability, duality, and Feller–Reuter–Riley transition functions which are closely linked with each other for continuous time Markov chains. A necessary and sufficient condition for two Feller minimal transition functions to be stochastically comparable is given in terms of their density q-matrices only. Moreover, a necessary and sufficient condition under which a transition function is a dual for some stochastically monotone q-function is given in terms of, again, its density q-matrix. Finally, for a class of q-matrices, the necessary and sufficient condition for a transition function to be a Feller–Reuter–Riley transition function is also given.

Applications of Feller-Reuter-Riley transition functions

A Feller–Reuter–Riley function is a Markov transition function whose corresponding semigroup maps the set of the real-valued continuous functions vanishing at infinity into itself. The aim of this paper is to investigate applications of such functions in the dual problem, Markov branching processes, and the Williams-matrix. The remarkable property of a Feller–Reuter–Riley function is that it is a Feller minimal transition function with a stable q-matrix. By using this property we are able to prove that, in the theory of branching processes, the branching property is equivalent to the requirement that the corresponding transition function satisfies the Kolmogorov forward equations associated with a stable q-matrix. It follows that the probabilistic definition and the analytic definition for Markov branching processes are actually equivalent. Also, by using this property, together with the Resolvent Decomposition Theorem, a simple analytical proof of the Williams' existence theorem with respect to the Williams-matrix is obtained. The close link between the dual problem and the Feller–Reuter–Riley transition functions is revealed. It enables us to prove that a dual transition function must satisfy the Kolmogorov forward equations. A necessary and sufficient condition for a dual transition function satisfying the Kolmogorov backward equations is also provided.