Abstract
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 a shot-noise process. A shot-noise rate emerges naturally in cases where the arrival rate tends to exhibit 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 to analysis. In particular, we perform transient analysis on the number of jobs in the queue jointly with the value of the driving shot-noise process. Additionally, we derive heavy-traffic asymptotics for the number of jobs 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.
Highlights
IntroductionOne has traditionally studied queues with Poisson input. The Poisson assumption typically facilitates explicit analysis, but it does not always align well with actual data; see, for example, [11] and references therein
In the queueing literature, one has traditionally studied queues with Poisson input
We have considered networks of infinite-server queues with shot-noise-driven Coxian input processes
Summary
One has traditionally studied queues with Poisson input. The Poisson assumption typically facilitates explicit analysis, but it does not always align well with actual data; see, for example, [11] and references therein. A very recent effort to analyze ·/G/∞ queues that are driven by a Hawkes process has been made in [8], where a functional central limit theorem is derived for the number of jobs in the system In this model, obtaining explicit results (in a non-asymptotic setting), as we are able to do in the shot-noise-driven Cox variant, is still an open problem. In this paper we study networks of infinite-server queues with shot-noise-driven Cox input. The main result of the exact analysis is Theorem 4.6, where we find the joint Laplace transform of the numbers of jobs in the queues of a feedforward network, jointly with the shot-noise-driven arrival rates.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
