Related papers: Queues Driven by Hawkes Processes
HTTP Adaptive Streaming (HAS) is becoming the de-facto video delivery technology over best-effort networks nowadays, thanks to the myriad advantages it brings. However, many studies have shown that HAS suffers from many Quality of…
A key operational challenge for call centers is to decide, in real time, which waiting customer should be served by which available agent. This is known as skill-based routing, and the decision becomes especially difficult in large systems…
Time spent in processing zones at an airport are an important part of the passenger's airport experience. It undercuts the time spent in the rest of the airport, and therefore the revenue that could be generated from shopping and dining. It…
We consider hyperbolic partial differential equations (PDEs) for a dynamic description of the traffic behavior in road networks. These equations are coupled to a Hawkes process that models traffic accidents taking into account their…
We consider a generalized processing system having several queues, where the available service rate combinations are fluctuating over time due to reliability and availability variations. The objective is to allocate the available resources,…
A classical queuing theory result states that in a parallel-queue single-server model, the maximum stability region does not depend on the scheduling decision epochs, and in particular is the same for preemptive and non-preemptive systems.…
The growth of Machine-Type Communication (MTC) increases the relevance of queuing scenarios with deterministic service times. In this letter, we present a model for queues without waiting lines and with degenerate service time distributions…
Polling systems have been widely studied, however most of these studies focus on polling systems with renewal processes for arrivals and random variables for service times. There is a need driven by practical applications to study polling…
We investigate how the properties of inhomogeneous patterns of activity, appearing in many natural and social phenomena, depend on the temporal resolution used to define individual bursts of activity. To this end, we consider time series of…
Hawkes processes are point process models that have been used to capture self-excitatory behavior in social interactions, neural activity, earthquakes and viral epidemics. They can model the occurrence of the times and locations of events.…
Emergence of various types of services has brought about explosive growth of traffic as well as diversified traffic characteristics in the cellular networks. To have a comprehensive understanding of the influences caused by various traffic…
We generalise the construction of multivariate Hawkes processes to a possibly infinite network of counting processes on a directed graph $\mathbb G$. The process is constructed as the solution to a system of Poisson driven stochastic…
We investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatiotemporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In…
The infinite-server queueing models with homogeneous and non-homogeneous arrivals of customers and catastrophes are considered. The probability generating functions of joint distributions of numbers of busy servers and served customers, as…
We consider a multi-class single server queueing network as a model of a packet switching network. The rates packets are sent into this network are controlled by queues which act as congestion windows. By considering a sequence of…
We study a model of a polling system, that is, a collection of $d$ queues with a single server that switches from queue to queue. The service time distribution and arrival rates change randomly every time a queue is emptied. This model is…
This is an expository review paper illustrating the ``martingale method'' for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximations. Careful treatment is given to an…
Consider an M/M/$s$ queue with the additional feature that the arrival rate is a random variable of which only the mean, variance, and range are known. Using semi-infinite linear programming and duality theory for moment problems, we…
We propose a novel probabilistic framework to model continuous-time interaction events data. Our goal is to infer the \emph{implicit} community structure underlying the temporal interactions among entities, and also to exploit how the…
We investigate congestion-aware control of quantum repeater nodes operating under stochastic traffic and finite memory coherence. Entanglement generation is modeled as a probabilistic process producing Werner states subject to depolarizing…