Industrial and Systems Engineering Seminar Series: “A Probabilistic Approach to Growth Networks”
About the seminar
Closed product-form networks, consisting of single-server and infinite-server queues, have emerged as relevant models for several applications. Although such models admit a seemingly tractable product-form solution, explicit analytical characterization of its partition function is difficult in the case of large-scale networks. To this end, we develop a novel methodology, based on a probabilistic representation of product-form solutions and large-deviations concentration inequalities, which identifies distinct operating regimes and yields explicit expressions for the marginal distributions of queue lengths. The parameters of the derived distributions can be computed from equations involving large-deviations rate functions, often admitting closed-form algebraic expressions. From a methodological perspective, a fundamental feature of our approach is that it provides exact results for order-one probabilities, even though our analysis involves large-deviations rate functions, which characterize only vanishing probabilities on a logarithmic scale.