Infinite-server systems with Hawkes arrivals and Hawkes services

Dharmaraja Selvamuthu () and Paola Tardelli ()
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Dharmaraja Selvamuthu: Indian Institute of Technology Delhi
Paola Tardelli: University of L’Aquila

Queueing Systems: Theory and Applications, 2022, vol. 101, issue 3, No 5, 329-351

Abstract: 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 $$\mathrm{Hawkes/sdHawkes/\infty }$$ Hawkes / sdHawkes / ∞ 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 $$\mathrm{M/sdHawkes/\infty }$$ M / sdHawkes / ∞ system.

Keywords: Infinite-server systems; Hawkes processes; State-dependent; Markov property; Self-exciting; 60K25; 60G55; 60K30; 60J75; 60G46 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11134-022-09813-3

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