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Related papers: Infinite-server queues with Hawkes input

200 papers

The paper studies a multiserver retrial queueing system with $m$ servers. Arrival process is a point process with strictly stationary and ergodic increments. A customer arriving to the system occupies one of the free servers. If upon…

Probability · Mathematics 2021-07-01 Vyacheslav M. Abramov

The focus of this paper is on the asymptotics of large-time numbers of customers in time-periodic Markovian many-server queues with customer abandonment in heavy traffic. Limit theorems are obtained for the periodic number-of-customers…

Probability · Mathematics 2014-06-03 Anatolii A. Puhalskii

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…

Probability · Mathematics 2010-10-05 Haya Kaspi , Kavita Ramanan

We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal.…

Probability · Mathematics 2007-05-23 Rami Atar , Avi Mandelbaum , Martin I. Reiman

This paper studies statistical inference in a network of infinite-server queues, with the aim of estimating the underlying parameters (routing matrix, arrival rates, parameters pertaining to the service times) using observations of the…

Probability · Mathematics 2025-06-10 Hritika Gupta , Michel Mandjes , Liron Ravner , Jiesen Wang

We consider a Markovian many server queueing system in which customers are preemptively scheduled according to exogenously assigned priority levels. The priority levels are randomly assigned from a continuous probability measure rather than…

Performance · Computer Science 2017-01-06 Neal Master , Zhengyuan Zhou , Nicholas Bambos

The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has…

Probability · Mathematics 2025-09-04 Behzad Mehrdad , Lingjiong Zhu

In the present paper the infinite-server MMAPkGk queueing model with random resource vector of customers, marked MAP arrival and semi-Markov (SM) arrival of catastrophes is considered. The joint generating functions (PGF) of transient and…

Performance · Computer Science 2018-05-25 K. Kerobyan , R. Covington , R. Kerobyan , K. Enakoutsa

This paper considers population processes in which general, not necessarily Markovian, multivariate Hawkes processes dictate the stochastic arrivals. We establish results to determine the corresponding time-dependent joint probability…

Probability · Mathematics 2021-06-08 Raviar Karim , Roger J. A. Laeven , Michel Mandjes

We consider the $\Delta_{(i)}/G/1$ queue, in which a a total of $n$ customers independently demand service after an exponential time. We focus on the case of heavy-tailed service times, and assume that the tail of the service time…

Probability · Mathematics 2016-05-23 Gianmarco Bet , Remco van der Hofstad , Johan S. H. van Leeuwaarden

For a widely used hub-and-spoke closed product-form network consisting of an infinite-server node and several single-server queues, we characterize the maximum queue-length distribution in various operational regimes by leveraging a novel…

Probability · Mathematics 2025-12-09 Predrag Jelenkovic , Petar Momcilovic

In this paper we analyze a single server queue with batch arrivals and semi-Markovian service times. We also include the feature that the first service of each busy period might have a different distribution than subsequent service times.…

Probability · Mathematics 2018-12-07 Abhishek , Rudesindo Núñez Queija , Marko Boon

Two networks of queues models, presented initially by Jackson, in the open case, and Gordon and Newell, in the closed case, stochastic processes are presented and studied in some of their details and problems. The service times are…

Probability · Mathematics 2021-10-19 Manuel Alberto M. Ferreira

We consider a finite population processor-sharing (PS) queue, with Markovian arrivals and an exponential server. Such a queue can model an interactive computer system consisting of a bank of terminals in series with a central processing…

Probability · Mathematics 2013-09-12 Qiang Zhen , Johan S. H. van Leeuwaarden , Charles Knessl

We consider the so-called GI/GI/N queueing network in which a stream of jobs with independent and identically distributed service times arrive according to a renewal process to a common queue served by $N$ identical servers in a…

Probability · Mathematics 2017-12-06 Reza Aghajani , Kavita Ramanan

This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix $Q\equiv(q_{ij})_{i,j=1}^d$. Both arrival rates and service rates are depending on…

Probability · Mathematics 2015-06-17 Joke Blom , Koen De Turck , Michel Mandjes

In this paper, we consider the occupancy distribution for an open network of infinite server queues with multivariate batch arrivals following a non-homogeneous Poisson process, and general service time distributions. We derive a…

Probability · Mathematics 2023-03-29 Somya Mehra , Peter G. Taylor

We provide probabilistic and computational results on Markovian multivariate Hawkes processes and induced population processes. By applying the Markov property, we characterize in closed form a joint transform, bijective to the probability…

Probability · Mathematics 2025-08-08 R. S. Karim , R. J. A. Laeven , M , M. Mandjes

We are interested in a large queue in a $GI/G/k$ queue with heterogeneous servers. For this, we consider tail asymptotics and weak limit approximations for the stationary distribution of its queue length process in continuous time under a…

Probability · Mathematics 2017-03-10 Masakiyo Miyazawa

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…

Machine Learning · Computer Science 2021-06-10 Feng Zhou , Quyu Kong , Yixuan Zhang , Cheng Feng , Jun Zhu