Perfect Sampling of Hawkes Processes and Queues with Hawkes Arrivals
Probability
2020-03-03 v2
Abstract
In this paper we develop the first perfect sampling algorithm for queues with Hawkes input, i.e. single-server queues with Hawkes arrivals and i.i.d. service times of general distribution. In addition to the stability condition, we also assume the excitation function of the Hawkes process has a light tail and the service time has finite moment generating function in the neighborhood of the origin. In this procedure, we also propose a new perfect sampling algorithm for Hawkes process with improved computational efficiency compared to the existing algorithm. Theoretical analysis and numerical tests on the algorithms' correctness and efficiency are also included.
Keywords
Cite
@article{arxiv.2002.06369,
title = {Perfect Sampling of Hawkes Processes and Queues with Hawkes Arrivals},
author = {Xinyun Chen},
journal= {arXiv preprint arXiv:2002.06369},
year = {2020}
}