A Product-form Model for the Analysis of Systems with Aging Objects

In this paper we propose a new model for the analysis of systems with aging objects such as Time-To-Live cache. We consider a model with an underlying Continuous Time Markov Chain in which objects can be completely or partially rejuvenated. In the former case the object becomes fresh, while in the latter all the objects are simultaneously rejuvenated so that the youngest becomes fresh. We show that under the so-called Independent Reference Model assumption our model is numerically tractable and has a product-form equilibrium distribution. Furthermore, we consider the case in which the object aging stops after a certain threshold and hence the partial rejuvenation introduces a probabilistic behaviour. Also in this case, we can derive a product-form equilibrium distribution under some mild conditions. The models presented in this paper may be interpreted as a new class of G-networks with catastrophes and partial flushing.