A Probabilistic Approach to Growth Networks

Abstract

Single-class closed queueing networks, consisting of infinite-server and single-server queues with exponential service times and probabilistic routing, admit product-from solutions. Such solutions, although seemingly tractable, are difficult to characterize explicitly for practically relevant problems due to the exponential combinatorial complexity of its normalization constant (partition function). In “A Probabilistic Approach to Growth Networks,” Jelenković, Kondev, Mohapatra, and Momčilović 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. From a methodological perspective, a fundamental feature of the proposed approach is that it provides exact results for order-one probabilities, even though the analysis involves large-deviations rate functions, which characterize only vanishing probabilities on a logarithmic scale.