Probability Seminar

Andrew DawCornell University
Self-Exciting Processes in Queues

Monday, February 11, 2019 - 4:00pm
Malott 406

A point process is called "self-exciting" if the occurrence of an arrival increases the likelihood that additional arrivals occur soon after. These dynamics lead to temporal clustering of the arrivals and over-dispersion of the counting process. Often referred to as Hawkes processes, these processes have been the subject of recent study in a wide variety of applications, including finance, social media, seismology, and neurology. In this talk we explore the use of Hawkes processes in queueing theory and the impact of self-excitement on these models. Furthermore, we also investigate a model in which the self-exciting process responds to the queue, meaning that the arrival rate increases an entity arrives and then also decreases when the entity departs. In doing so, we both gain insight into the Hawkes process itself and connect self-exciting processes to other well known probability models.