# Centralized Versus Decentralized Control - A Solvable Stylized Model in Transportation

## Details

Download: 2010_PhysA_Hongler_Gallay_Hulsmann_Cordes_Colmorn.pdf (355.62 [Ko])

State: Public

Version: Author's accepted manuscript

State: Public

Version: Author's accepted manuscript

Serval ID

serval:BIB_656E229AC67D

Type

**Article**: article from journal or magazin.

Collection

Publications

Institution

Title

Centralized Versus Decentralized Control - A Solvable Stylized Model in Transportation

Journal

Physica A: Statistical Mechanics and its Applications

ISSN

0378-4371

Publication state

Published

Issued date

10/2010

Peer-reviewed

Oui

Volume

389

Number

19

Pages

4162-4171

Language

english

Abstract

Today's supply networks consist of a certain amount of logistics objects that are enabled to interact with each other and to decide autonomously upon their next steps: in other words, they exhibit a certain degree of autonomous cooperation. Therefore, modern logistics research regards them as complex adaptive logistics systems. In order to analyze evolving dynamics and underlying implications for the respective systems' behavior as well as the potential outcomes resulting from the interaction between autonomous decision-making "smart parts", we propose in this contribution a fully solvable stylized model. We consider a population of homogeneous, autonomous interacting agents traveling on R with a given velocity that is itself corrupted by White Gaussian Noise. Based on real time observations of the positions of his neighbors, each agent is allowed to adapt his traveling velocity. These agent interactions are restricted to neighboring entities confined in finite spatial clusters (i.e. we have range-limited interactions). In the limit of a large population of neighboring agents, a mean-field dynamics can be derived and, for small interaction range, the resulting dynamics coincides with the exactly solvable Burgers' nonlinear field equation. Explicit Burgers' solution enables to explicitly appreciate the emergent structure due to the local and individual agent interactions. In particular, for strongly interactive regimes in the present model, the resulting spatial distribution of agents converges to a shock wave pattern. To compare performances of centralized versus decentralized organization, we assign cost functions incurred when velocity adaptations are triggered either by multi-agent interactions or by central control. The multi-agent cumulative costs are then compared with the costs that would be incurred by implementing an effective optimal central controller able, for a given time horizon, to reproduce an identical spatial probability distribution of agents. The resulting optimal control problem can be solved exactly and the corresponding costs can be expressed as the Kullback-Leibler relative entropy between the free and the controlled probability measures. This enables one to conclude that for time horizons shorter than a critical value, multi-agent interactions generate smaller cumulative costs than an optimal effective central controller.

Keywords

Transportation logistics, "Smart parts" dynamics, Multi-agent systems, Mean-field approximation, Burgers' nonlinear evolution, Emergent cooperative pattern, Optimal stochastic control, Kullback-Leibler relative entropy

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Create date

14/12/2016 17:59

Last modification date

20/08/2019 15:21