Related papers: Queues Driven by Hawkes Processes
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 the problem of staffing large-scale service systems with multiple customer classes and multiple dedicated server pools under joint quality-of-service (QoS) constraints. We first analyze the case in which arrival rates are…
A point process for event arrivals in high frequency trading is presented. The intensity is the product of a Hawkes process and high dimensional functions of covariates derived from the order book. Conditions for stationarity of the process…
Point processes are widely used statistical models for continuous-time discrete event data, such as medical records, crime reports, and social network interactions, to capture the influence of historical events on future occurrences. In…
Across a wide variety of applications, the self-exciting Hawkes process has been used to model phenomena in which the history of events influences future occurrences. However, there may be many situations in which the past events only…
Consider a population of customers each of which needs to decide independently when to arrive to a facility that provides a service during a fixed period of time, say a day. This is a common scenario in many service systems such as a bank,…
We study randomized experiments in a service system when stochastic congestion can arise from temporarily limited supply or excess demand. Such congestion gives rise to cross-unit interference between the waiting customers, and analytic…
Arrivals in queueing systems are typically assumed to be independent and exponentially distributed. Our analysis of an online bookshop, however, shows that there is an autocorrelation structure present. First, we adjust the inter-arrival…
The discrete time queueing system is highly applicable to modern telecommunication systems, where it provides adaptive packet handling, congestion controlled security/inspection, energy efficient operation, and supports bursty traffic…
We establish heavy-traffic stochastic-process limits for waiting times in many-server queues with customer abandonment. If the system is asymptotically critically loaded, as in the quality-and-efficiency-driven (QED) regime, then a bounding…
Modern Internet services, such as those at Google, Yahoo!, and Amazon, handle billions of requests per day on clusters of thousands of computers. Because these services operate under strict performance requirements, a statistical…
We study a make-to-order system with a finite set of customers. Production is stochastic with a nonlinear dependence between the ordered quantity and the production rate. Customers may have to queue until their turn arrives, and therefore…
This paper studies an infinite buffer single server queueing model with exponentially distributed service times and negative arrivals. The ordinary (positive) customers arrive in batches of random size according to renewal arrival process,…
In many different settings, requests for service can arrive in near or true simultaneity with one another. This creates batches of arrivals to the underlying queueing system. In this paper, we study the staffing problem for the batch…
In this work, several convergence results are established for nearly critical self-excited systems in which event arrivals are described by multivariate marked Hawkes point processes. Under some mild high-frequency assumptions, the rescaled…
In customer support contact centers, every service interaction involves a messaging dialogue between a customer and an agent; together, they exchange information, solve problems, and collectively co-produce the service. Because the service…
Discrete-time queueing models find huge applications as they are used in modeling queueing systems arising in digital platforms like telecommunication systems, computer networks, etc. In this paper, we analyze an infinite-buffer queueing…
This paper develops a theoretical mesoscopic model of the limit order book driven by multivariate Hawkes processes, designed to capture temporal self-excitation and the spatial propagation of order flow across price levels. In contrast to…
Queueing networks are typically modelled assuming that the arrival process is exogenous, and unaffected by admission control, scheduling policies, etc. In many situations, however, users choose the time of their arrival strategically,…
Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to…