THE M/M/c QUEUE WITH (e, d) SETUP TIME*

Xu, Xiuli; Tian, Naishuo

doi:10.1007/s11424-008-9126-6

Cited by 29 publications

(34 citation statements)

References 3 publications

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“…Recent discoveries have shown the specific functions of several chlorophyll metabolites of developing in animal tissues, including the production of ATP, [44] the regulation of the redox status in plasma, [45] implications as visual pigments, [37,42,43] and activation of specific nuclear receptors that could control lipid abnormalities in common diseases such as obesity, diabetes, and hyperlipidemia [46] among others. Evidently, the origin of chlorophyll metabolites present in the animal body is circumscribed to the diet.…”

Section: Discussionmentioning

confidence: 99%

First‐Pass Metabolism of Chlorophylls in Mice

Viera

Chen

Ríos

et al. 2018

Molecular Nutrition Food Res

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Pheophorbide a absorption is, at least partly, protein-mediated through SR-BI. This active absorption process could explain the specific accumulation of pheophorbide a in the livers of animals fed a chlorophyll-rich diet. A complementary mechanism could be the de-esterification of pheophytin a in the liver, yielding pheophorbide a and phytol, which can explain the origin of phytol in the liver. Hence, the results suggest two molecular mechanisms responsible for the accumulation of the health-promoting compounds pheophorbide and phytol.

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Section: Discussionmentioning

confidence: 99%

First‐Pass Metabolism of Chlorophylls in Mice

Viera

Chen

Ríos

et al. 2018

Molecular Nutrition Food Res

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“…Many papers have been written about the M/M/k system with vacations, see for example [28,27,23,18]. While the Markov chain for the M/M/k with vacations looks similar to the M/M/k/setup, the dynamics of the two systems are very different.…”

Section: M/m/k With Vacationsmentioning

confidence: 99%

“…After solving for p L i→d ,Ṙ L i,k andṘ H i,j , we can deriveṘ, and consequently NQ(z), via Eq. (27). T (s) can then be derived by using the fact T (s) = TQ(s) · µ s+µ = NQ 1 − s λ · µ s+µ .…”

Section: Derivingṙ H Ij For the Non-repeating Portionmentioning

confidence: 99%

Exact analysis of the M/M/k/setup class of Markov chains via recursive renewal reward

GandhiAnshul¹,

Doroudi²,

Harchol-BalterMor³

et al. 2013

SIGMETRICS Perform. Eval. Rev.

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The M/M/k/setup model, where there is a penalty for turning servers on, is common in data centers, call centers and manufacturing systems. Setup costs take the form of a time delay, and sometimes there is additionally a power penalty, as in the case of data centers. While the M/M/1/setup was exactly analyzed in 1964, no exact analysis exists to date for the M/M/k/setup with k > 1.In this paper we provide the first exact, closed-form analysis for the M/M/k/setup and some of its important variants including systems in which idle servers delay for a period of time before turning off or can be put to sleep. Our analysis is made possible by our development of a new technique, Recursive Renewal Reward (RRR), for solving Markov chains with a repeating structure. RRR uses ideas from renewal reward theory and busy period analysis to obtain closed-form expressions for metrics of interest such as the transform of time in system and the transform of power consumed by the system. The simplicity, intuitiveness, and versatility of RRR makes it useful for analyzing Markov chains far beyond the M/M/k/setup. In general, RRR should be used to reduce the analysis of any 2-dimensional Markov chain which is infinite in at most one dimension and repeating to the problem of solving a system of polynomial equations. In the case where all transitions in the repeating portion of the Markov chain are skip-free and all up/down arrows are unidirectional, the resulting system of equations will yield a closed-form solution.

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“…Multiple server systems modelled as continuous time Markov chains have been studied in [7]- [9], [20], [22], [26]. Exact solutions for system metrics such as the expected response time and expected rate of energy consumption have been derived.…”

Section: Introductionmentioning

confidence: 99%

On Optimal Control for Energy-Aware Queueing Systems

Maccio

Down

2015

2015 27th International Teletraffic Congress

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Over the past few years, energy provisioning in server farms and data-centres has become an active area of research. As such, many models have been proposed where an individual server has setup times and can switch between two different energy states (on and off). To make such models tractable, assumptions are usually made on the type of policies the system can implement. However, it is often not known if such assumptions allow for the model to capture the optimal policy, or if such a model will be strictly suboptimal. In this work we model such systems using Markov Decision Processes (MDPs) and derive several structural properties which (partially) describe the optimal policy. These properties reduce the set of feasible policies significantly, allowing one to describe the optimal policy by a set of thresholds which have considerable structure. In addition to the analysis, we discuss the current literature in the context of our results.

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THE M/M/c QUEUE WITH (e, d) SETUP TIME*

Cited by 29 publications

References 3 publications

First‐Pass Metabolism of Chlorophylls in Mice

First‐Pass Metabolism of Chlorophylls in Mice

Exact analysis of the M/M/k/setup class of Markov chains via recursive renewal reward

On Optimal Control for Energy-Aware Queueing Systems

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