Exact simulation of the queue-hawkes process

The Queue-Hawkes process is a generalization of the self-exciting Hawkes process in which the counting process is coupled with an infinite server queue. That is, when a service is completed the process intensity jumps downwards. Thus, the influence an arrival brings to the intensity is ephemeral, as it expires upon the entity's departure. In this poster we provide an exact simulation procedure for this new process via an update of methodology from the traditional Hawkes process literature and discuss the model in general.