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• W2759162801 abstract "Abstract In this paper we study the number of customers in infinite-server queues with a self-exciting (Hawkes) arrival process. Initially we assume that service requirements are exponentially distributed and that the Hawkes arrival process is of a Markovian nature. We obtain a system of differential equations that characterizes the joint distribution of the arrival intensity and the number of customers. Moreover, we provide a recursive procedure that explicitly identifies (transient and stationary) moments. Subsequently, we allow for non-Markovian Hawkes arrival processes and nonexponential service times. By viewing the Hawkes process as a branching process, we find that the probability generating function of the number of customers in the system can be expressed in terms of the solution of a fixed-point equation. We also include various asymptotic results: we derive the tail of the distribution of the number of customers for the case that the intensity jumps of the Hawkes process are heavy tailed, and we consider a heavy-traffic regime. We conclude by discussing how our results can be used computationally and by verifying the numerical results via simulations." @default.
• W2759162801 created "2017-10-06" @default.
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• W2759162801 date "2018-09-01" @default.
• W2759162801 modified "2023-10-16" @default.
• W2759162801 title "Infinite-server queues with Hawkes input" @default.
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• W2759162801 doi "https://doi.org/10.1017/jpr.2018.58" @default.
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