# Refined large deviations asymptotics for Markov-modulated infinite-server systems

@article{Blom2017RefinedLD, title={Refined large deviations asymptotics for Markov-modulated infinite-server systems}, author={Joke G. Blom and Koen De Turck and Michel Mandjes}, journal={Eur. J. Oper. Res.}, year={2017}, volume={259}, pages={1036-1044} }

## 14 Citations

### Analysis of the infinite server queues with semi-Markovian multivariate discounted inputs

- MathematicsQueueing Syst. Theory Appl.
- 2020

The present model is demonstrated by showing how it allows us to study semi-Markovian modulated infinite server queues where the customers (claims) arrival and service times depend on the state of the process immediately before and at the switching times.

### UvA-DARE (Digital Academic Repository) An Infinite-Server System with Lévy Shot-Noise Modulation Moments and Asymptotics

- Mathematics
- 2019

We consider an inﬁnite-server system with as input process a non-homogeneous Poisson process with rate function Λ( t ) = a (cid:124) X ( t ) . Here { X ( t ) : t ≥ 0 } is a generalized multivariate…

### Rare-event analysis of mixed Poisson random variables, and applications in staffing

- MathematicsPerform. Evaluation
- 2017

### Analysis of the incurred but not reported/infinite server queue process with semi-Markovian multivariate discounted inputs

- Mathematics
- 2018

We consider a general k dimensional discounted innite server queues process (alternatively, an Incurred But Not Reported (IBNR) claim process) where the multi-variate inputs (claims) are given by a k…

### Linear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation

- Mathematics, Computer ScienceMethodology and Computing in Applied Probability
- 2018

The main objective is to develop efficient importance sampling algorithms with provable performance guarantees for linear stochastic fluid networks under Markov modulation, and it is proved that the number of runs needed increases polynomially as the probability under consideration decays essentially exponentially.

### Stationary analysis of the infinite-server queue modulated by a multi-phase Markovian environment

- Mathematics
- 2018

We consider an infinite-server queue, where the arrival and service rates are both governed by a continuous-time Markov chain that is independent of all other aspects of the queue. Through…

### Stationary analysis of certain Markov-modulated reflected random walks in the quarter plane

- MathematicsAnn. Oper. Res.
- 2022

In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node…

### Linear stochastic fluid networks

- Mathematics, Computer Science
- 2018

The main objective is to develop efficient importance sampling algorithms with provable performance guarantees for linear stochastic fluid networks under Markov modulation, and it is proved that the number of runs needed increases polynomially as the probability under consideration decays essentially exponentially.

### UvA-DARE ( Digital Academic Repository ) Linear Stochastic Fluid Networks

- Computer Science, Mathematics
- 2018

The main objective is to develop efficient importance sampling algorithms with provable performance guarantees for linear stochastic fluid networks under Markov modulation, and it is proved that the number of runs needed increases polynomially as the probability under consideration decays essentially exponentially.

### Monitoring and control of stochastic systems

- Computer Science
- 2017

This thesis provides performance evaluation techniques for call centres based on queuing models and model control problems in telecommunications such as the problem of dynamically selecting transmission channels, and investigates novel criteria for the false alarm performance of sequential tests.

## References

SHOWING 1-10 OF 24 REFERENCES

### ANALYSIS OF MARKOV-MODULATED INFINITE-SERVER QUEUES IN THE CENTRAL-LIMIT REGIME

- MathematicsProbability in the Engineering and Informational Sciences
- 2015

This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix Q≡(q ij ) i,j=1 d . Both arrival rates and…

### Tail asymptotics of a Markov-modulated infinite-server queue

- MathematicsQueueing Syst. Theory Appl.
- 2014

This paper analyzes large deviation probabilities related to the number of customers in a Markov-modulated infinite-server queue, with state-dependent arrival and service rates. Two specific scalings…

### Rare Event Analysis of Markov-Modulated Infinite-Server Queues: A Poisson Limit

- Mathematics
- 2013

This article studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process.…

### Large deviations of an infinite-server system with a linearly scaled background process

- MathematicsPerform. Evaluation
- 2014

### A Functional Central Limit Theorem for a Markov-Modulated Infinite-Server Queue

- Mathematics
- 2013

We consider a model in which the production of new molecules in a chemical reaction network occurs in a seemingly stochastic fashion, and can be modeled as a Poisson process with a varying arrival…

### Functional central limit theorems for Markov-modulated infinite-server systems

- MathematicsMath. Methods Oper. Res.
- 2016

The Markov-modulated M/M/$$\infty $$∞ queue is studied, with a focus on the correlation structure of the number of jobs, and the system’s asymptotic behavior under a particular scaling of the model parameters is described under a functional central limit theorem.

### An infinite-server queue influenced by a semi-Markovian environment

- Mathematics, Computer ScienceQueueing Syst. Theory Appl.
- 2009

This work derives a system of equations that are satisfied by various “parts” of the generating function of the steady-state queue-length, while assuming that all arrivals bring an amount of work to the system that is either Erlang or hyperexponentially distributed.

### A large-deviations analysis of Markov-modulated infinite-server queues

- MathematicsOper. Res. Lett.
- 2013

### M/M/∞ queues in semi-Markovian random environment

- MathematicsQueueing Syst. Theory Appl.
- 2008

An M/M/∞ queue whose parameters depend on an external random environment that is assumed to be a semi-Markovian process with finite state space is investigated and a recursive formula is shown that allows to compute all the factorial moments for the number of customers in the system in steady state.