Queueing Networks and Markov Chains

Bolch, Gunter; Greiner, Stefan; Meer, Hermann de; Trivedi, Kishor S.

doi:10.1002/0471791571

Cited by 837 publications

(311 citation statements)

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“…These computations are described in eg. [17,18]. When we have calculated the distributions defined above, the most important steady-state system characteristics can be obtained in the following way:…”

Section: System Modelmentioning

confidence: 99%

Performance Modeling of Finite-Source Retrial Queueing Systems with Collisions and Non-reliable Server Using MOSEL

Bérczes

Sztrik

Tóth

et al. 2017

Communications in Computer and Information Science

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Abstract. In this paper we investigate a single-server retrial queueing system with collision of the customer and an unreliable server. If a customer finds the server idle, he enters into service immediately. The service times are independent exponentially distributed random variables. During the service time the source cannot generate a new primary call. Otherwise, if the server is busy, an arriving (primary or repeated) customer involves into collision with customer under service and they both moves into the orbit. The retrial time of requests are exponentially distributed. We assume that the server is unreliable and could be break down. When the server is interrupted, the call being served just before server interruption goes to the orbit. Our interest is to give the main steady-state performance measures of the system computed by the help of the MOSEL tool. Several Figures illustrate the effect of input parameters on the mean response time.

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Section: System Modelmentioning

confidence: 99%

Performance Modeling of Finite-Source Retrial Queueing Systems with Collisions and Non-reliable Server Using MOSEL

Bérczes

Sztrik

Tóth

et al. 2017

Communications in Computer and Information Science

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“…Instead, upon a jump to stage 2, the jobs quickly accumulate in the single-server queue. On models of this kind, decomposition is known to be accurate because the length of the transient period is quite short compared to the overall holding time in a stage [7].…”

Section: Motivationmentioning

confidence: 99%

“…All stations have unbounded buffer capacity and FCFS service discipline. Service times are independent and identically distributed random variables following a Coxian distribution, which includes exponential, hyperexponential, and Erlang distributions as special cases [7]. We shall refer to the states of the Coxian service processes as phases.…”

Section: Modelmentioning

confidence: 99%

Blending randomness in closed queueing network models

Casale

Tribastone

Harrison

2014

Performance Evaluation

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Random environments are stochastic models used to describe events occurring in the environment a system operates in. The goal is to describe events that affect performance and reliability such as breakdowns, repairs, or temporary degradations of resource capacities due to exogenous factors. Despite having been studied for decades, models that include both random environments and queueing networks remain difficult to analyse. To cope with this problem, we introduce the blending algorithm, a novel approximation for closed queueing network models in random environments. The algorithm seeks to obtain the stationary solution of the model by iteratively evaluating the dynamics of the system in between state changes of the environment. To make the approach scalable, the computation relies on a fluid approximation of the queueing network model. A validation study on 1,800 models shows that blending can save a significant amount of time compared to simulation, with an average accuracy that grows with the number of servers in each station. We also give an interpretation of this technique in terms of Laplace transforms and use this approach to determine convergence properties.

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“…Queueing theory is widely used to model the performance of a web server [13,14]. In this paper, we use the M/M/n queueing model in queueing theory [40] to model the response time for a data center.…”

Section: Response Time and Power Modelsmentioning

confidence: 99%

GreenWare: Greening Cloud-Scale Data Centers to Maximize the Use of Renewable Energy

Zhang

Wang

2011

Lecture Notes in Computer Science

137

111

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Abstract. To reduce the negative environmental implications (e.g., CO2 emission and global warming) caused by the rapidly increasing energy consumption, many Internet service operators have started taking various initiatives to operate their cloud-scale data centers with renewable energy. Unfortunately, due to the intermittent nature of renewable energy sources such as wind turbines and solar panels, currently renewable energy is often more expensive than brown energy that is produced with conventional fossil-based fuel. As a result, utilizing renewable energy may impose a considerable pressure on the sometimes stringent operation budgets of Internet service operators. Therefore, two key questions faced by many cloud-service operators are 1) how to dynamically distribute service requests among data centers in different geographical locations, based on the local weather conditions, to maximize the use of renewable energy, and 2) how to do that within their allowed operation budgets.In this paper, we propose GreenWare, a novel middleware system that conducts dynamic request dispatching to maximize the percentage of renewable energy used to power a network of distributed data centers, subject to the desired cost budget of the Internet service operator. Our solution first explicitly models the intermittent generation of renewable energy, e.g., wind power and solar power, with respect to varying weather conditions in the geographical location of each data center. We then formulate the core objective of GreenWare as a constrained optimization problem and propose an efficient request dispatching algorithm based on linear-fractional programming (LFP). We evaluate GreenWare with realworld weather, electricity price, and workload traces. Our experimental results show that GreenWare can significantly increase the use of renewable energy in cloud-scale data centers without violating the desired cost budget, despite the intermittent supplies of renewable energy in different locations and time-varying electricity prices and workloads.

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Queueing Networks and Markov Chains

Cited by 837 publications

References 0 publications

Performance Modeling of Finite-Source Retrial Queueing Systems with Collisions and Non-reliable Server Using MOSEL

Performance Modeling of Finite-Source Retrial Queueing Systems with Collisions and Non-reliable Server Using MOSEL

Blending randomness in closed queueing network models

GreenWare: Greening Cloud-Scale Data Centers to Maximize the Use of Renewable Energy

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