TY - JOUR

T1 - A mean field absorbing control model for interacting objects systems

AU - Martínez-Manzanares, M. Elena

AU - Minjárez-Sosa, J. Adolfo

N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.

PY - 2021/9

Y1 - 2021/9

N2 - We study a class of discrete-time stochastic systems composed of a large number of N interacting objects, which are classified in a finite number of classes. The behavior of the objects is controlled by a central decision-maker as follows. At each stage, once the configuration of the system is observed, the controller takes a decision; then a cost is incurred and there is a positive probability the process stops, otherwise the objects move randomly among the classes according to a transition probability. That is, with positive probability, the system is absorbed by a configuration that represents the death of the system, and there it will remain without incurring cost. Due to the large number of objects, the control problem is studied according to the mean field theory. Thus, instead of analyzing a single object, we focus on the proportions of objects occupying each class, and then we study the limit as N goes to infinity.

AB - We study a class of discrete-time stochastic systems composed of a large number of N interacting objects, which are classified in a finite number of classes. The behavior of the objects is controlled by a central decision-maker as follows. At each stage, once the configuration of the system is observed, the controller takes a decision; then a cost is incurred and there is a positive probability the process stops, otherwise the objects move randomly among the classes according to a transition probability. That is, with positive probability, the system is absorbed by a configuration that represents the death of the system, and there it will remain without incurring cost. Due to the large number of objects, the control problem is studied according to the mean field theory. Thus, instead of analyzing a single object, we focus on the proportions of objects occupying each class, and then we study the limit as N goes to infinity.

KW - Control problems

KW - Mean field theory

KW - Optimal policies

KW - Random horizon

KW - Systems of interacting objects

UR - http://www.scopus.com/inward/record.url?scp=85101837348&partnerID=8YFLogxK

U2 - 10.1007/s10626-021-00339-z

DO - 10.1007/s10626-021-00339-z

M3 - Artículo

AN - SCOPUS:85101837348

SN - 0924-6703

VL - 31

SP - 349

EP - 372

JO - Discrete Event Dynamic Systems: Theory and Applications

JF - Discrete Event Dynamic Systems: Theory and Applications

IS - 3

ER -