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We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by shot noise. A shot-noise rate emerges as a natural model, if the arrival rate tends to display sudden increases (or: shots) at random epochs, after which the rate is inclined to revert to lower values. Exponential decay of the shot noise is assumed, so that the queueing systems are amenable for analysis. In particular, we perform transient analysis on the number of customers in the queue jointly with the value of the driving shot-noise process. Additionally, we derive heavy-traffic asymptotics for the number of customers in the system by using a linear scaling of the shot intensity. First we focus on a one dimensional setting in which there is a single infinite-server queue, which we then extend to a network setting.
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
We study many-server queues with abandonment in which customers have general service and patience time distributions. The dynamics of the system are modeled using measure- valued processes, to keep track of the residual service and patience times of
A many-server queueing system is considered in which customers with independent and identically distributed service times enter service in the order of arrival. The state of the system is represented by a process that describes the total number of cu
This work considers a many-server queueing system in which customers with i.i.d., generally distributed service times enter service in the order of arrival. The dynamics of the system is represented in terms of a process that describes the total numb
In this paper, we study an $N$ server fork-join queue with nearly deterministic arrival and service times. Specifically, we present a fluid limit for the maximum queue length as $Ntoinfty$. This fluid limit depends on the initial number of tasks. In