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Related papers: On a fractional queueing model with catastrophes

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Recent studies indicate that in many situations service times are affected by the experienced queueing delay of the particular customer. This effect has been detected in different areas, such as health care, call centers and…

Probability · Mathematics 2025-04-25 Bernardo D'Auria , Ivo J. B. F. Adan , René Bekker , Vidyadhar Kulkarni

In this article statistical bounds for certain output characteristics of the $M/GI/1/n$ and $GI/M/1/n$ loss queueing systems are derived on the basis of large samples of an input characteristic of these systems, such as service time in the…

Statistics Theory · Mathematics 2021-06-30 Vyacheslav M. Abramov

IIn this paper, we consider an M^X/M/c queue with state-dependent control at idle time and catastrophes. Properties of the queues which terminate when the servers become idle are firstly studied. Recurrence, equilibrium distribution and…

Probability · Mathematics 2015-12-17 Junping Li , Lina Zhang

Weconsider Markov decision processes arising from a Markov model of an underlying natural phenomenon. Such phenomena are usually periodic (e.g. annual) in time, and so the Markov processes modelling them must be time-inhomogeneous, with…

Optimization and Control · Mathematics 2024-09-17 Arash Khojaste , Geoffrey Pritchard , Golbon Zakeri

In the present work we study Bayesian nonparametric inference for the continuous-time M/G/1 queueing system. In the focus of the study is the unobservable service time distribution. We assume that the only available data of the system are…

Statistics Theory · Mathematics 2017-09-22 Cornelia Wichelhaus , Moritz von Rohrscheidt

We introduce an extension of the M/M/1 queueing process with a spatial structure and excluded- volume effect. The rule of particle hopping is the same as for the totally asymmetric simple exclusion process (TASEP). A stationary-state…

Statistical Mechanics · Physics 2014-09-18 Chikashi Arita

Important models in insurance, for example the Carm{\'e}r--Lundberg theory and the Sparre Andersen model, essentially rely on the Poisson process. The process is used to model arrival times of insurance claims. This paper extends the…

Statistics Theory · Mathematics 2019-04-16 Arun Kumar , Nikolai Leonenko , Alois Pichler

We investigate the transient and stationary queue-length distributions of a class of service systems with correlated service times. The classical $M^X/G/1$ queue with semi-Markov service times is the most prominent example in this class and…

Probability · Mathematics 2018-01-19 Abhishek , Marko Boon , Onno Boxma , Rudesindo Núñez-Queija

Efficient use of call center operators through technological innovations more often come at the expense of added operation management issues. In this paper, the stationary characteristics of an $M/G/1$ retrial queue is investigated where…

Networking and Internet Architecture · Computer Science 2021-08-05 Muthukrishnan Senthil Kumar , Aresh Dadlani , Kiseon Kim

In this paper, we introduce a time-continuous production model that enables random machine failures, where the failure probability depends historically on the production itself. This bidirectional relationship between historical failure…

Probability · Mathematics 2019-12-13 Stephan Knapp , Simone Göttlich

We consider a stationary Markov process that models certain queues with a bulk service of a fixed number $m$ of admitted customers. We find an integral expression of its transition probability function in terms of certain multi-orthogonal…

Probability · Mathematics 2023-08-29 Ulises Fidalgo

We study the power spectral density of continuous time Markov chains and explicit its relationship with the eigenstructure of the infinitesimal generator. This result helps us understand the dynamics of the number of customers for a M/M/1…

Probability · Mathematics 2023-10-24 Thomas Vanderbruggen

The presented study elaborates a multi-server catastrophic retrial queueing model considering preemptive repeat priority policy with phase-type (PH) distributed retrial times. For the sake of comprehension, the scenario of model operation…

Systems and Control · Electrical Eng. & Systems 2022-04-13 Raina Raj , Vidyottama Jain

The paper deals with a sharing economy system with various management factors by using a bulk input G/M/1 type queuing model. The effective management of operating costs is vital for controlling the sharing economy platform and this…

Probability · Mathematics 2019-10-24 Song-Kyoo Kim , Chan Yeob Yeun

We consider an $M/M/1$ queueing system with impatient customers with multiple and single vacations. It is assumed that customers are impatient whenever the state of the server. We derive the probability generating functions of the number of…

Probability · Mathematics 2016-04-12 Assia Boumahdaf

We consider Poisson's equation for quasi-birth-and-death processes (QBDs) and we exploit the special transition structure of QBDs to obtain its solutions in two different forms. One is based on a decomposition through first passage times to…

Probability · Mathematics 2013-08-13 Sarah Dendievel , Guy Latouche , Yuanyuan Liu

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

The continuous time Markov process considered in this paper belongs to a class of population models with linear growth and catastrophes. There, the catastrophes happen at the arrival times of a Poisson process, and at each catastrophe time,…

Probability · Mathematics 2019-05-14 A. Logachov , O. Logachova , A. Yambartsev

In piecewise-deterministic Markov processes (PDMPs) the state of a finite-dimensional system evolves continuously, but the evolutive equation may change randomly as a result of discrete switches. A running cost is integrated along the…

Optimization and Control · Mathematics 2023-02-27 Elliot Cartee , Antonio Farah , April Nellis , Jacob van Hook , Alexander Vladimirsky

We study a generalization of the $M/G/1$ system (denoted by $rM/G/1$) with independent and identically distributed (iid) service times and with an arrival process whose arrival rate $\lambda_0f(r)$ depends on the remaining service time $r$…

Probability · Mathematics 2017-10-05 Benjamin Legros , Ali Devin Sezer