×

zbMATH — the first resource for mathematics

Price co-ordination for a resource allocation problem in a large-scale system. (English) Zbl 0842.93007
The essential point of the theory presented is the assumption that the decision-makers have different information. The coordinator has the information essential for the whole system, whereas the local controllers have the more detailed information concerning particular subsystems. Owing to this, the amount of information transmitted to and processed by the coordinator can be significantly decreased.
The original global elastic constraint admits some freedom in allowing the local controllers to take decisions; this way, they can use more detailed information better.
The problem stated in the paper and the proposed price coordination method make it possible to obtain analytic control laws in the case of mutually correlated random variables.
The results of the control realized in the proposed two-level structure are better than those realized in the one-level structure, with the same information shared by the decision-makers and by the coordinator. For the realization of the control in the two-level structure, some resource reserves are needed to meet some randomly increased resource demands.
From the example it is seen that the relative amount of resource reserves decreases asymptotically to some value if the number of subsystems increases. It depends on the correlation of the random variables defined in the problem.

MSC:
93A15 Large-scale systems
93A14 Decentralized systems
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] ASTR”M K. J., Introduction to Stochastic Control Theory (1971) · Zbl 1191.93141
[2] DOI: 10.1109/TAC.1971.1099810 · doi:10.1109/TAC.1971.1099810
[3] DOI: 10.1109/TAC.1972.1099854 · Zbl 0259.93060 · doi:10.1109/TAC.1972.1099854
[4] DOI: 10.1080/0020718508961118 · Zbl 0581.93004 · doi:10.1080/0020718508961118
[5] GESSING R., IF AC Workshop on Automatic Control for Qualityand Productivity, ACQP ’92 pp 279– (1992)
[6] Ho Y. C., Proceedings of theInstitution of Electrical Engineers 68 pp 644– (1980)
[7] DOI: 10.1109/TAC.1972.1100016 · doi:10.1109/TAC.1972.1100016
[8] DOI: 10.1109/TAC.1978.1101704 · Zbl 0385.93001 · doi:10.1109/TAC.1978.1101704
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.