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Infinite-server systems with Hawkes arrivals and Hawkes services
Dharmaraja Selvamuthu1, Paola Tardelli2
1Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi, 110016 India.
Abstract:
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 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 characterized by a system of differential equations. Then, the time-dependent results are also deduced for the system.
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