The Stability of Two-Station Multitype Fluid Networks

Dai, J. G.; Vate, John H. Vande

doi:10.1287/opre.48.5.721.12408

Cited by 119 publications

(96 citation statements)

References 28 publications

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“…This result opens up an opportunity for using methods from continuous-time, continuous-state processes for stability analysis of adversarial networks. Such methods include Lyapunov functions [5], [8], [10], [11], [13] and trajectory decomposition [2], [14].…”

Section: Discussionmentioning

confidence: 99%

Using fluid models to prove stability of adversarial queueing networks

Gamarnik

2000

IEEE Trans. Automat. Contr.

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741 REFERENCES[1] J. Sun, A. W. Olbrot, and M. P. Polis, "Robust stabilization and robust performance using model reference control and modeling error compensation," IEEE Trans. Automat. Contr., vol. 39, pp. 630-635, 1994 Automat. Contr., vol. 35, pp. 356-361, 1990. Using Fluid Models to Prove Stability of Adversarial Queueing Networks David GamarnikAbstract-A digital communication network can be modeled as an adversarial queueing network. An adversarial queueing network is defined to be stable if the number of packets stays bounded over time. A central question is to determine which adversarial queueing networks are stable under every work-conserving packet routing policy. Our main result is that stability of an adversarial queueing network is implied by stability of an associated fluid queueing network.

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Section: Discussionmentioning

confidence: 99%

Using fluid models to prove stability of adversarial queueing networks

Gamarnik

2000

IEEE Trans. Automat. Contr.

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“…This reduces the aggregate network's effective capacity in the sense that the network can become instable, even though each server is less than 100% utilized. (Dai and Vande Vate 2000 review the recent surge in the study of stability conditions for multiclass queueing networks. )…”

Section: Canonical Capacity Models In An Iidmentioning

confidence: 99%

Commissioned Paper: Capacity Management, Investment, and Hedging: Review and Recent Developments

Mieghem

2003

M&SOM

512

240

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T his paper reviews the literature on strategic capacity management concerned with determining the sizes, types, and timing of capacity investments and adjustments under uncertainty. Specific attention is given to recent developments to incorporate multiple decision makers, multiple capacity types, hedging, and risk aversion. Capacity is a measure of processing abilities and limitations and is represented as a vector of stocks of various processing resources, while investment is the change of capacity and includes expansion and contraction. After discussing general issues in capacity investment problems, the paper reviews models of capacity investment under uncertainty in three settings:The first reviews optimal capacity investment by single and multiple risk-neutral decision makers in a stationary environment where capacity remains constant. Allowing for multiple capacity types, the associated optimal capacity portfolio specifies the amounts and locations of safety capacity in a processing network. Its key feature is that it is unbalanced; i.e., regardless of how uncertainties are realized, one typically will never fully utilize all capacities. The second setting reviews the adjustment of capacity over time and the structure of optimal investment dynamics. The paper ends by reviewing how to incorporate risk aversion in capacity investment and contrasts hedging strategies involving financial versus operational means.

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“…Production systems modeling has been analyzing so called fluid models for a long time (see e.g. [29]). They are coupled ODEs that mimic the behavior of queues in front of machines.…”

Section: Discussionmentioning

confidence: 99%

Control of Continuum Models of Production Systems

Marca

Armbruster

Herty

et al. 2010

IEEE Trans. Automat. Contr.

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Abstract-A production system which produces a large number of items in many steps can be modelled as a continuous flow problem. The resulting hyperbolic partial differential equation (PDE) typically is nonlinear and nonlocal, modeling a factory whose cycle time depends nonlinearly on the work in progress. One of the few ways to influence the output of such a factory is by adjusting the start rate in a time dependent manner. We study two prototypical control problems for this case: i) demand tracking where we determine the start rate that generates an output rate which optimally tracks a given time dependent demand rate and ii) backlog tracking which optimally tracks the cumulative demand. The method is based on the formal adjoint method for constrained optimization, incorporating the hyperbolic PDE as a constraint of a nonlinear optimization problem. We show numerical results on optimal start rate profiles for steps in the demand rate and for periodically varying demand rates and discuss the influence of the nonlinearity of the cycle time on the limits of the reactivity of the production system. Differences between perishable and non-perishable demand (demand versus backlog tracking) are highlighted.

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The Stability of Two-Station Multitype Fluid Networks

Cited by 119 publications

References 28 publications

Using fluid models to prove stability of adversarial queueing networks

Using fluid models to prove stability of adversarial queueing networks

Commissioned Paper: Capacity Management, Investment, and Hedging: Review and Recent Developments

Control of Continuum Models of Production Systems

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