# Queueing Theory

Last Updated: Feb 15, 2024

**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**

**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.