Response time distributions and network perturbation into product-form

Peter G. Harrison, Maria G. Vigliotti
2009 Proceedings of the 4th International ICST Conference on Performance Evaluation Methodologies and Tools  
Two new methodological results are obtained: first, a way to perturb a network into one with a product-form solution for its equilibrium state probabilities, and secondly, a new compositional approach to deriving corresponding response time distributions. The Reversed Compound Agent Theorem (RCAT) is used to construct suitable perturbations in near-product-form networks that render them separable by satisfying the conditions of this theorem. Response time calculations in stochastic networks are
more » ... usually developed in terms of sample path analyses beginning in an equilibrium state. We consider the joint probability distribution of the sojourn times of a tagged task at each node of a path in a network and observe that this is the same in both the forward and reversed processes. Therefore if the reversed process is known, each node-sojourn time can be taken from either process. In particular, the reversed process can be used for the first node in a path and the forward process for the other nodes in a recursive analysis. This approach derives, quickly and systematically, existing results for response time probability densities in tandem, open and closed tree-like, and overtake-free Markovian networks of queues. An example shows that the technique is far more widely applicable, constructing a perturbed network with productform, a new result in its own right, and then finding a very simple expression for its response time probability density function.
doi:10.4108/icst.valuetools2009.7776 dblp:conf/valuetools/HarrisonV09 fatcat:575utorwxzbqzbpndcmstl3ypq