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Infinite-server System with Hawkes Arrivals and Hawkes Services
Dharmaraja Selvamuthu, Paola Tardelli · 2022-08-06 · via math.PR updates on arXiv.org

This paper is devoted to the study of the number of customers in infinite-server systems driven by Hawkes processes. In these systems, the self-exciting arrival process is assumed to be represented by a Hawkes process and the self-exciting service process by a state-dependent Hawkes process (sdHawkes process). Under some suitable conditions, for the Hawkes/sdHawkes/infty system, the Markov property of the system is derived. The joint time-dependent distribution of the number of customers in the system, the arrival intensity and the server intensity is characterised by a system of differential equations. Then, the time-dependent results are also deduced for the M/sdHawkes/\infty system.

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