An optimal control approach to dynamic routing in networks

Moss, Franklin H.; Segall, Adrian

doi:10.1109/tac.1982.1102915

Cited by 113 publications

(53 citation statements)

References 5 publications

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“…preferable [1,13,14,19] to assure robustness against uncertain events such as failures or unknown demand rate. In this context, several authors deal with the problem of transient optimality (see, e.g., [2,17,19,22]) and nearoptimality (see, e.g., [25]).…”

Section: Introductionmentioning

confidence: 99%

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Robust Control Strategies for Multi–Inventory Systems with Average Flow Constraints

Bauso

Blanchini

Pesenti

2006

Analysis and Design of Hybrid Systems 2006

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In this paper we consider multi-inventory systems in presence of uncertain demand. We assume that i) demand is unknown but bounded in an assigned compact set and ii) the control inputs (controlled flows) are subject to assigned constraints. Given a long-term average demand, we select a nominal flow that feeds such a demand. In this context, we are interested in a control strategy that meets at each time all possible current demands and achieves the nominal flow in the average. We provide necessary and sufficient conditions for such a strategy to exist and we characterize the set of achievable flows. Such conditions are based on linear programming and thus they are constructive. In the special case of a static flow (i.e. a system with 0-capacity buffers) we show that the strategy must be affine. The dynamic problem can be solved by a linear-saturated control strategy (inspired by the previous one). We provide numerical analysis and illustrating examples.

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Section: Introductionmentioning

confidence: 99%

“…In this context, several authors deal with the problem of transient optimality (see, e.g., [2,17,19,22]) and nearoptimality (see, e.g., [25]). However, few of them explicitly consider uncertainties in the demand or supply flows (see, e.g., [4,6,7]).…”

Section: Introductionmentioning

confidence: 99%

Robust Control Strategies for Multi–Inventory Systems with Average Flow Constraints

Bauso

Blanchini

Pesenti

2006

Analysis and Design of Hybrid Systems 2006

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“…With such systems, here and in several other works [2,3,4,6,14,15,16], a typical goal is to find a control strategy that stabilizes in a robust sense (i.e., under any disturbance realization) the state. Motivations derive from the benefits associated to keeping the state and consequently also the inventory costs bounded.…”

Section: Introductionmentioning

confidence: 99%

“…Several authors use inventory costs to construct a performance index and then look for an optimal [16,17,18] or near-optimal [19] control strategy. The idea of a performance index and optimal control strategy is present also in this work.…”

Section: Introductionmentioning

confidence: 99%

Average flow constraints and stabilizability in uncertain production-distribution systems

Bauso¹,

Blanchini²,

Pesenti³

2007

2007 American Control Conference

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Consider multi-inventory systems with controlled flows and uncertain demands (disturbances) bounded within assigned compact sets. The system is modelled as a first order one integrating the discrepancy between controlled flows and demands at different sites/nodes. Thus, the buffer levels at the nodes represent the system state. Given a long-term average demand, we are interested in a control strategy that satisfies just one of the two requirements: i) meeting any possible demand at each time (worst case stability) or ii) achieving a pre-defined flow in the average (average flow constraints). Necessary and sufficient conditions * D. Bauso is with Dipartimento di Ingegneria Informatica, Universitàd iP a l e r m o ,P a l e r m o-I t a l ydario.bauso@unipa.it † F. Blanchini is with Dipartimento di Matematica e Informatica, Università di Udine, Udine -Italy blanchini@uniud.it ‡ R. Pesenti is with Dipartimento di Matematica Applicata, Università "Ca' Foscari" di Venezia -Italy pesenti@unive.it § Research supported by PRIN "Robustness optimization techniques for high performance control systems", and MURST-PRIN 2007ZMZK5T "Decisional model for the design and the management of logistics networks characterized by high interoperability and information integration".for the achievement of both goals have been proposed by the authors. In this paper we face the case in which these conditions are not satisfied. We show that if we ignore the requirement on worst case stability, we can find a control strategy driving the expected value of the state to zero. On the contrary, if we ignore the average flow constraints, we can find a control strategy that satisfies worst case stability while optimizing any linear cost on the average control. In the latter case we provide a tight bound for the cost.

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“…For example when the number of users -in the network is small but some of these users can overload the network if left uncontrolled to transmit at maximum rate, then a dynamic method of routing and flow control is needed. The ideas of this paper can provide an alternative to existing techniques [7], [8] in such situations.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Control of Session Input Rates in Communication Networks

Gafni

Bertsekas

1983

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An optimal control approach to dynamic routing in networks

Cited by 113 publications

References 5 publications

Robust Control Strategies for Multi–Inventory Systems with Average Flow Constraints

Robust Control Strategies for Multi–Inventory Systems with Average Flow Constraints

Average flow constraints and stabilizability in uncertain production-distribution systems

Dynamic Control of Session Input Rates in Communication Networks

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