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

Turck, K.E.E.S. De; Mandjes, Michel

doi:10.1016/j.peva.2014.01.001

Cited by 7 publications

(6 citation statements)

References 21 publications

(21 reference statements)

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“…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%

Scaling Limits for Infinite-server Systems in a Random Environment

2017

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Abstract. This paper studies the effect of an overdispersed arrival process on the performance of an infinite-server system. In our setup, a random environment is modeled by drawing an arrival rate Λ from a given distribution every ∆ time units, yielding an i.i.d. sequence of arrival rates Λ 1 , Λ 2 , . . .. Applying a martingale central limit theorem, we obtain a functional central limit theorem for the scaled queue length process. We proceed to large deviations and derive the logarithmic asymptotics of the queue length's tail probabilities. As it turns out, in a rapidly changing environment (i.e., ∆ is small relative to Λ) the overdispersion of the arrival process hardly affects system behavior, whereas in a slowly changing random environment it is fundamentally different; this general finding applies to both the central limit and the large deviations regime. We extend our results to the setting where each arrival creates a job in multiple infinite-server queues.

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Section: Introductionsupporting

confidence: 85%

Scaling Limits for Infinite-server Systems in a Random Environment

2017

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“…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%

A large deviations principle for infinite-server queues in a random environment

et al. 2016

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This paper studies an infinite-server queue in a random environment, meaning that the arrival rate, the service requirements, and the server work rate are modulated by a general càdlàg stochastic background process. To prove a large deviations principle, the concept of attainable parameters is introduced. Scaling both the arrival rates and the background process, a large deviations principle for the number of jobs in the system is derived using attainable parameters. Finally, some known results about Markov-modulated infinite-server queues are generalized and new results for several background processes and scalings are established in examples.

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“…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%

A Markovian analytical framework for public‐safety video sharing by device‐to‐device communications

Zhao

Han

Mao

et al. 2017

Concurrency and Computation

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Monitoring video of city surveillance camera plays an important role in public security and disaster relief, which is often used by first responder teams, such as firefighters and police officers.The first responders in emergency situations require consistent connection with one another and request the remote real-time monitoring video for effective cooperation and coordination.However, the capacity and privacy of public wireless networks fail to satisfy the requirements in many emergency scenarios, which often leads to exceptionally high traffic loads and insecurity.Device-to-device (D2D) communications have been deemed a key solution for this problem, as responders can use D2D links for traffic offloading and secure communications. To investigate the D2D-based solution for public safety video sharing, this paper focuses on the Focus Geographical Area (FGA) video consisting of multiple camera streams requiring higher bandwidth consumption than that of the traditional single-camera stream, which attracts a large number of contents delivery requests in emergency situations. This paper develops a new Traffic Burden Switching Markovian (TBSM) model to evaluate the performance of transmitting real-time FGA video in wireless networks with D2D communications. First, a novel D2D area model is introduced to characterize link-switching in wireless D2D communication networks. Based on the proposed D2D area model, the state and transition matrix of TBSM model are then derived by jointly considering user mobility, link-switching, and FGA video view-switching. Thereafter, some key performance metrics including system offloading ratio, D2D link-switching ratio, and view-switching ratio are derived on the basis of coverage probability and ergodic rate. The performance results show the significant varying performance among D2D areas with different geographical locations in D2D enabled wireless networks, which is referred to as multi-D2D-area diversity. The excellent match between simulation and model results validates the accuracy of the TBSM model, which can be used to provide guidelines for the deployment and optimization of future wireless video networks with D2D communications. KEYWORDS Device-to-device area, Camera view switching, Markovian model, Traffic burden switching 1 tional bandwidth-limited wireless networks with the following characteristics: (1) provision of more than one camera stream, (2) permission Concurrency Computat: Pract Exper. 2017;29:e4078.wileyonlinelibrary.com/journal/cpe

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

Cited by 7 publications

References 21 publications

Scaling Limits for Infinite-server Systems in a Random Environment

Scaling Limits for Infinite-server Systems in a Random Environment

A large deviations principle for infinite-server queues in a random environment

A Markovian analytical framework for public‐safety video sharing by device‐to‐device communications

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