A Probabilistic Approach to Growth Networks

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