Related papers: Infinite-server queues with Hawkes input
Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result…
We consider a model for transitory queues in which only a finite number of customers can join. The queue thus operates over a finite time horizon. In this system, also known as the $\Delta_{(i)}/G/1$ queue, the customers decide…
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…
We study statistical aspects of state-dependent Hawkes processes, which are an extension of Hawkes processes where a self- and cross-exciting counting process and a state process are fully coupled, interacting with each other. The…
The Hawkes process has garnered attention in recent years for its suitability to describe the behavior of online information cascades. Here, we present a fully tractable approach to analytically describe the distribution of the number of…
Multivariate Hawkes processes are a widely used class of self-exciting point processes, but maximum likelihood estimation naively scales as $O(N^2)$ in the number of events. The canonical linear exponential Hawkes process admits a faster…
We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…
We consider an infinite-server queue into which customers arrive according to a Cox process and have independent service times with a general distribution. We prove a functional large deviations principle for the equilibrium queue length…
This paper analyzes a service system modeled as a single-server queue, in which the service provider aims to dynamically maximize the expected revenue per unit of time. This is achieved by constructing a stochastic gradient descent…
We consider exponential single server queues with state-dependent arrival and service rates which evolve under influences of external environments. The transitions of the queues are influenced by the environment's state and the movements of…
In this paper, we analyse a single server polling model with two queues. Customers arrive at the two queues according to two independent Poisson processes. There is a single server that serves both queues with generally distributed service…
This paper studies a service system in which arriving customers are provided with information about the delay they will experience. Based on this information they decide to wait for service or to leave the system. Specifically, every…
This paper studies the heavy-traffic (HT) behaviour of queueing networks with a single roving server. External customers arrive at the queues according to independent renewal processes and after completing service, a customer either leaves…
We develop a robust queueing network analyzer algorithm to approximate the steady-state performance of a single-class open queueing network of single-server queues with Markovian routing. The algorithm allows non-renewal external arrival…
We introduce a Markovian single point process model, with random intensity regulated through a buffer mechanism and a self-exciting effect controlling the arrival stream to the buffer. The model applies the principle of the Hawkes process…
This paper studies a diffusion model that arises as the limit of a queueing system scheduling problem in the asymptotic heavy traffic regime of Halfin and Whitt. The queueing system consists of several customer classes and many servers…
The Hawkes self-excited point process provides an efficient representation of the bursty intermittent dynamics of many physical, biological, geological and economic systems. By expressing the probability for the next event per unit time…
We investigate Markovian queues that are examined by a controller at random times determined by a Poisson process. Upon examination, the controller sets the service speed to be equal to the minimum of the current number of customers in the…
A service system with multiple types of customers, arriving according to Poisson processes, is considered. The system is heterogeneous in that the servers also can be of multiple types. Each customer has an independent exponentially…
This paper studies an infinite-server queue in a random environment, meaning that the arrival rate, the service requirements and the server work rate are modulated by a general c\`{a}dl\`{a}g stochastic background process. To prove a large…