Discrete state-space stochastic networks with product form – discovery or invention?

Probability models have long been used in computer science and engineering to study the performance of systems, software, networks and algorithms, and to analyze their reliability. Their closed form analytical solutions are used in industry to compute performance metrics such as response times, throughput and resource bottlenecks. However, the search for mathematical solutions of significant classes of models, such as queueing networks that are the key mathematical models for Internet nodes and traffic, is an active but difficult are of research. This talk will focus on probability models, including “G-networks”, auctions systems, and neural networks models, that have analytical or quasi-analytical solutions in “product form” – i.e., they are provably “separable” in steady-state, despite the fact that the models are tightly coupled, leading to computatinal algorithms which are polynomial in the number of state variables, whereas purely numerical solutions would have to enumerate all possible combinations of states. Applications will be described from network routing, energy management, video compression, systems of interacting resources, web auctions, neural networks, theoretical chemistry and gene regulatory networks.