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Unloading of congestion in deterministic queueing networks
Author(s) -
Filipiak Janusz
Publication year - 1981
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660020104
Subject(s) - queueing theory , pontryagin's minimum principle , network congestion , computer science , mathematical optimization , uniqueness , node (physics) , tree (set theory) , layered queueing network , basis (linear algebra) , topology (electrical circuits) , mathematics , optimal control , computer network , engineering , network packet , mathematical analysis , structural engineering , combinatorics , geometry
The purpose of this paper is to find a control procedure which would efficiently unload the congestion in a queueing network. The congestion phenomenon is described by a dynamic deterministic model. The total waiting time of all entities in the overloaded region is assumed to be a performance index. The Pontryagin maximum principle is applied to show that for the optimal flow pattern cycles cannot exist and all routes leading from the given node to the outside of the overloaded region have to have the same length. These two properties are the basis for a construction of the algorithm. A topological optimization algorithm is used, since the solution must be a tree. The existence and uniqueness of the optimal solution are investigated.