Perfect Sampling of Hawkes Processes and Queues with Hawkes Arrivals

In this paper we develop to our best knowledge the first perfect sampling algorithm for queues with Hawkes input (i.e., single-server queues with Hawkes arrivals and independent and identically distributed 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 processes with improved computational efficiency compared with the existing algorithm. Theoretical analysis and numerical tests on the algorithms’ correctness and efficiency are also included.