6533b826fe1ef96bd1283de7
RESEARCH PRODUCT
Optimization of Long-Run Average-Flow Cost in Networks With Time-Varying Unknown Demand
Dario BausoFranco BlanchiniRaffaele Pesentisubject
Flow control (data)Mathematical optimizationComputer scienceTime varying systemsFunction (mathematics)Optimal controlFlow networkMin-max optimalityAverage flow cost; Flow control; Gradient-based control; Min-max optimality; Uncertain demand; Time varying systems; Time varying networksComputer Science ApplicationsAverage flow costFlow controlControl and Systems EngineeringRobustness (computer science)Control theoryBounded functionProduction controlElectrical and Electronic EngineeringTime varying networksAverage flow cost flow control gradient-based control min-max optimality uncertain demandGradient-based controlAverage costUncertain demanddescription
We consider continuous-time robust network flows with capacity constraints and unknown but bounded time-varying demand. The problem of interest is to design a control strategy off-line with no knowledge of the demand realization. Such a control strategy regulates the flow on-line as a function of the realized demand. We address both the case of systems without and with buffers. The main novelty in this work is that we consider a convex cost which is a function of the long-run average-flow and average-demand. We distinguish a worst-case scenario where the demand is the worst-one from a deterministic scenario where the demand has a neutral behavior. The resulting strategies are called min-max or deterministically optimal respectively. The main contribution are constructive methods to design either min-max or deterministically optimal strategies. We prove that while the min-max optimal strategy is memoryless, i.e., it is a piece-wise affine function of the current demand, deterministically optimal strategy must keep memory of the average flow up to the current time.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-01-01 |