Product-forms beyond quasi-reversibility

Abstract

Assessing the performance and reliability of computer and telecommunication systems requires the development of stochastic models whose state space are very large. This problem is often known as "State Space Explosion". As a consequence, general purpose algorithms for their solution cannot be applied straightforwardly. This problem may be found both at continuous or discrete time. To tackle this problem we resorted to the theory of product-forms, including the latest theoretical developments in the field such as the Reversed Compound Agents Theorem (RCAT) and new forms of time-reversibility. The main contribution of our work consists in the identification of classes of product-form models that are not captured by previous results. More specifically, our contribution can be summarized as follows: - We identified a process algebraic specification of models including instantaneous propagation of signals at continuous time such as those required to describe the G-networks with negative customers and triggers. As an application of this result we introduced an original model which allows one to perform an exact analysis for a class of cache systems based on the policy Time-To-Live (TTL) with resets. - We characterized a class of models suitable for the quantitative analysis of reversible computations. We showed that our results can be useful for the performance evaluation of speculative distributed simulations. - Finally, we analysed product-form models also at discrete time and provided a product-form formulation for the Probabilistic Input/Output Automata (PIOA).