Queueing metaphors

• Infinite-server queues with Hawkes arrival processes. Biology: an infinite server queue fed by a branching process.
• Shot-noise queueing models. The more work one has, the harder one works.
• Gordon-Newell networks. No one ever enters, and no one ever leaves, an eternal cycle of queues, samsara.

BRAVO effect

• Glynn & Wang, A heavy-traffic perspective on departure process variability

First passage times

• de la Iglesia 2022 – Spectral analysis of bilateral birth–death processes: some new explicit examples
• Giorno & Nobile 2019, First-passage times and related moments for continuous-time birth–death chains
• Jouini & Dallery 2006, Moments of first passage times in general birth–death processes
• Fiorini 2021, Analyzing the busy period of the M/M/1 queue via order statistics and record values
• Harrison & Knottenbelt 2002, Passage time distributions in large Markov chains
• Dautenhahn & Saloff-Coste 2023, Hitting probabilities and uniformly S-transient subgraphs
• Glynn, Nakayama, Tuffin 2020, Comparing regenerative-simulation-based estimateors of the distribution of the hitting time to a rarely visited set

Extreme values

• Fork-join queues
• Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit

Estimation

• Asanjarani, Nazarathy, Taylor 2021 – A survey of parameter and state estimation in queues.

Book / etc.

• Robert Cooper’s lectures

History and Future

• J.F.C. Kingman 2009 – The first Erlang century – and the next.
• Glynn 2022 – Queueing theory: past, present, and future.