2014
DOI: 10.1016/j.peva.2014.01.001
|View full text |Cite
|
Sign up to set email alerts
|

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

Abstract: ABSTRACT. This paper studies an infinite-server queue in a Markov environment, that is, an infiniteserver queue with arrival rates and service times depending on the state of a Markovian background process. We focus on the probability that the number of jobs in the system attains an unusually high value. Scaling the arrival rates λ i by a factor N and the transition rates ν ij of the background process as well, a large-deviations based approach is used to examine such tail probabilities (where N tends to ∞). T… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

1
5
0

Year Published

2014
2014
2021
2021

Publication Types

Select...
7

Relationship

0
7

Authors

Journals

citations
Cited by 7 publications
(6 citation statements)
references
References 21 publications
1
5
0
Order By: Relevance
“…Again, the value of α determines what type of tail behavior dominates: for α < 1 this is effect (i), for α > 1 effect (ii), and for α = 1 a combination of effects (i) and (ii). These findings complement similar results that have been established for an infinite-server system with Markov-modulated input, where it is noted that the slow regime (α ∈ (0, 1)) was not covered in that setting [3,6]. We conclude Section 4 by pointing out how the large deviations results can be extended to the multidimensional setting.…”
Section: Introductionsupporting
confidence: 85%
“…Again, the value of α determines what type of tail behavior dominates: for α < 1 this is effect (i), for α > 1 effect (ii), and for α = 1 a combination of effects (i) and (ii). These findings complement similar results that have been established for an infinite-server system with Markov-modulated input, where it is noted that the slow regime (α ∈ (0, 1)) was not covered in that setting [3,6]. We conclude Section 4 by pointing out how the large deviations results can be extended to the multidimensional setting.…”
Section: Introductionsupporting
confidence: 85%
“…This scaling resembles the scaling featured in [9]. There, the authors considered a modulated infinite-server queue under a linear scaling of both the arrival rate and the time scale of an irreducible Markov chain.…”
Section: Examples: Scaled Background Processesmentioning
confidence: 63%
“…There, the authors considered a modulated infinite-server queue under a linear scaling of both the arrival rate and the time scale of an irreducible Markov chain. The rate function obtained in [9] is given as the solution of a variational problem. We will obtain a similar result in this example.…”
Section: Examples: Scaled Background Processesmentioning
confidence: 99%
“…Due to memoryless properties, Markovian model is a widely used tool for the analysis of large‐scale systems . Markovian model has already been applied to characterize user mobility in simulation of large‐scale scenarios with traditional circle coverage base stations .…”
Section: Related Workmentioning
confidence: 99%