# Ergodic theorems for queuing systems with dependent inter-arrival times

arXiv: https://arxiv.org/abs/2004.01475 · HTML: https://mlsanity.com/paper/2004.01475/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2020.

## Built on by (most cited first, 1 of 1)

- [Transition of α-mixing in Random Iterations with Applications in Queuing Theory](https://mlsanity.com/paper/2410.05056/) (2024)

## Abstract (arXiv)

We study a G/GI/1 single-server queuing model with i.i.d. service times that are independent of a stationary process of inter-arrival times. We show that the distribution of the waiting time converges to a stationary law as time tends to infinity provided that inter-arrival times satisfy a G"artner-Ellis type condition. A convergence rate is given and a law of large numbers established. These results provide tools for the statistical analysis of such systems, transcending the standard case with independent inter-arrival times.