A Probabilistic Approach to Growth Networks Academic Article uri icon

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, Jelenkovi, Kondev, Mohapatra, and Momilovi 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.

published proceedings

  • Operations Research

author list (cited authors)

  • Jelenkovi, P., Kondev, J., Mohapatra, L., & Momilovi, P

publication date

  • January 1, 2021 11:11 AM