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Stochastic fluid flow models for determining optimal switching thresholds

V. Aggarwal, N. Gautam, S.R.T. Kumara, M. Greaves
2005 Performance evaluation (Print)  
In order to do that, we use a stochastic fluid-flow model with two buffers, one for the agent that runs the routine tasks and the other for the remaining non-routine jobs at the CPU.  ...  We use the QoS performance measures to formulate and solve an optimization problem to design an optimal threshold value.  ...  The authors thank the editor and the anonymous reviewers for their comments and suggestions that led to considerable improvements in the content and presentation of this paper.  ... 
doi:10.1016/j.peva.2004.06.002 fatcat:pk5splf4mvbhnm7gcmhegajzdq

Optimal dispatching in a tandem queue

D. van Leeuwen, R. Núñez Queija
2017 Queueing systems  
This model can be formulated as a Markov Decision Process (MDP) for which the optimal strategy has nice structural properties.  ...  The fluid approach provides excellent approximations, and thus understanding, of the optimal MDP policy.  ...  In the next section we will exploit this description to determine a switching curve k(·) that approximates the optimal switching curve. x 1 (t) = λ − b(k Fluid-based approximations of the optimal policy  ... 
doi:10.1007/s11134-017-9554-x fatcat:ka6n7trsjnb7nex6hip7gnzexi

Page 4273 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
The authors consider a model with two queues served by a sin- gle server with switch-over times. The server operates under a Bernoulli-threshold schedule.  ...  Summary: “We focus on window flow control as used in packet- switched communication networks.  ... 

Efficient resource allocation in bandwidth-sharing networks

Maaike Verloop, Rudesindo Núñez-Queija
2007 Performance Evaluation Review  
Optimizing the "drain time" under a fluid scaling gives a simple linear switching strategy, which turns out to accurately approximate the numerically found optimal strategy in the stochastic model when  ...  For example, when µ1, µ2 ≥ µ0, the switching curves in the fluid model are both equal to zero, and hence the fluid policy gives preemptive priority to classes 1 and 2.  ... 
doi:10.1145/1328690.1328711 fatcat:5l2ugws27bg2zakw4ounawuche

Asymptotically optimal parallel resource assignment with interference

I. M. Verloop, R. Núñez-Queija
2010 Queueing systems  
Acknowledgment The authors are grateful to Sem Borst for valuable discussions and comments. References  ...  The optimal switching curves in the fluid regime can be used to determine asymptotically fluid optimal strategies for the stochastic model.  ...  In Section 4.1 we determined the optimal trajectory for the fluid control model, n * (t).  ... 
doi:10.1007/s11134-010-9171-4 fatcat:iuyjao36fffzlci5b5ldc5pb7y

Page 3907 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
The author then studies the correspondences between the stochastic network problems with an associated fluid problem, proving that the value function of the fluid problem provides a lower bound for the  ...  control of queueing networks: an approach via fluid models.  ... 

Dynamic server allocation at parallel queues

Susan E. Martonosi
2011 IIE Transactions  
Moreover, we find that intuitive switching strategies that are optimal for queues with homogeneous entry rates are not optimal in this setting.  ...  We use approximate dynamic programming methods to determine when servers should be switched, and we compare the performance of such dynamic allocations to that of a pre-scheduled deterministic allocation  ...  We now present our optimization models for this problem.  ... 
doi:10.1080/0740817x.2011.564602 fatcat:4c2r6ghv2nayfgjrdgd7qagk2y

Achieving Rapid Recovery in an Overload Control for Large-Scale Service Systems

Ohad Perry, Ward Whitt
2015 INFORMS journal on computing  
lengths crosses an activation threshold (with ratio and activation threshold parameters for each direction).  ...  The target ratio is chosen to be optimal in a deterministic fluid approximation, assuming a convex holding cost is incurred on the two queues during the overload incident.  ...  The stochastic AP determines when SSC occurs, and how the fluid evolves during periods of SSC; see §5.3 below. Time-Varying Models.  ... 
doi:10.1287/ijoc.2015.0642 fatcat:yrtxa2pombb2jhrp5m7glud47i

Applications of Markov Decision Processes in Communication Networks [chapter]

Eitan Altman
2002 International Series in Operations Research and Management Science  
We survey both the different applications areas in communication networks as well as the theoretical tools that have been developed to model and to solve the resulting control problems.  ...  Another example of this approach is the reference [246] where the authors consider a fluid model for the optimal flow control.  ...  and of a stochastic fluid, respectively.  ... 
doi:10.1007/978-1-4615-0805-2_16 fatcat:wwfp5ccqfng7dghdpffcfnfzsa

Large-deviations analysis of the fluid approximation for a controllable tandem queue

Ad Ridder, Arie Hordijk, Alexander Gajrat
2003 The Annals of Applied Probability  
A fluid approximation gives the main term in the asymptotic expression of the value function for a controllable stochastic network.  ...  Key words and phrases. stochastic network, fluid optimal control problem, asymptotic optimality, large deviations.  ...  Acknowledgement The authors would like to thank an anonymous referee for his valuable remarks that have improved the paper.  ... 
doi:10.1214/aoap/1069786504 fatcat:jlovjpl5jbhuroblhmx6cdf4pu

Stochastic Analysis and Optimization of Multiserver Systems [chapter]

Mark S. Squillante
2010 Run-time Models for Self-managing Systems and Applications  
Our primary focus is on multiserver systems in general, since this research provides the mathematical methods and results that have been and will continue to be used for the stochastic analysis and/or  ...  Motivated by emerging trends and applications such as autonomic computing, this paper presents an overview of some research in the stochastic analysis and optimization of multiserver systems.  ...  He also thanks Alan Hoffman, Yingdong Lu, Baruch Schieber, Mayank Sharma and Shmuel Winograd for helpful comments on an earlier version of the paper, as well as Dan Prener for fruitful discussions regarding  ... 
doi:10.1007/978-3-0346-0433-8_1 fatcat:7ddyzwfwebhfrdkb5in4ylkcee

Optimal Scheduling Control in Fluid Models of General n× n Input-Queued Switches [article]

Yingdong Lu and Mark S. Squillante and Tonghoon Suk
2020 arXiv   pre-print
To gain fundamental insights into these very difficult problems, we consider a fluid model of n × n input-queued switches with associated fluid-flow costs, and we derive an optimal scheduling control policy  ...  Computational experiments demonstrate the benefits of our optimal scheduling policy over variants of max-weight scheduling within fluid models of input-queued switches.  ...  Fluid Models is section introduces a deterministic process that represents our uid models for input-queued switches, describes the scaled processes of the original stochastic process, and relates them  ... 
arXiv:1910.13657v2 fatcat:5am3gattt5cg3fuwrnl5tfrvsa

Perturbation analysis for online control and optimization of stochastic fluid models

C.G. Cassandras, Y. Wardi, B. Melamed, Gang Sun, C.G. Panayiotou
2002 IEEE Transactions on Automatic Control  
This paper uses stochastic fluid models (SFMs) for control and optimization (rather than performance analysis) of communication networks, focusing on problems of buffer control.  ...  Index Terms-Communication network, perturbation analysis, stochastic fluid network.  ...  The fluid-flow worldview can provide either approximations to queuing-based models or primary models in their own right.  ... 
doi:10.1109/tac.2002.800739 fatcat:erx2u5fcjvagfct5n6kwy6prfe

Rare Event Simulation [chapter]

Søren Asmussen, Paul Dupuis, Reuven Y. Rubinstein, Hui Wang
2013 Encyclopedia of Operations Research and Management Science  
The underlying model for an ATM reference connection consists of a network with a sequence of */D/1/N 5 queues and an extra delay (propagation and switching) between these queues.  ...  Examples are given for the loss probability of ATM cells in G/G/1/N 4 type systems as well as certain tandem networks that represent a model for ATM reference connections.  ...  Several approaches have been used for modeling network traffic sources, including fluid-flow sources [30] [42], on-off sources [41] , MPEG coded video sources [2] , Composite Source Models [26] ,  ... 
doi:10.1007/978-1-4419-1153-7_1188 fatcat:qc4mcfmojvesvdeee7mzrhtxby

Page 3282 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
In a number of these cases, the thresholds that optimize performance measures such as overall average sojourn time are determined.” 2001¢:60194 60K25 90B22 Dudin, Alexander [Dudin, Aleksandr] (BE-BEL-AMI  ...  Summary: “A second-order fluid flow model of a queue with finite capacity buffer and variable net input process is presented, based on the previous work of R. L. Karandikar and V. G. Kulkarni.  ... 
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