Search results for "Multi-commodity flow problem"
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A decentralized solution for the constrained minimum cost flow
2010
In this paper we propose a decentralized solution to the problem of network stabilization, under flow constraints ensuring steady—state flow optimality. We propose a stabilizing strategy for network flow control with capacity constraints which drives the buffer levels arbitrarily close to a desired reference. This is a decentralized strategy optimizing the flow via the minimization of a quadratic cost of the control. A second problem characterized by non-fully connected networks is also considered, for which an exact network equilibrium is not possible. Here, the strategy, in the absence of constraints leads to a least square decentralized problem, but, unfortunately, in the presence of con…
Finding all optimal solutions to the network flow problem
1986
The problem examined in this paper is as follows: Given a feasible optimum basic solution (f.o.b.s) of the minimum cost network flow problem, find all the f.o.b.s of this problem. The existence of alternative f.o.b.s is characterized by means of elementary circuits of zero cost and length greater than two in the incremental graph associated to the given f.o.b.s. It is shown that any alternative f.o.b.s. can be obtained from the original one by circulating flow through elementary circuits belonging to a succession of incremental graphs. This result leads to the construction of an efficient algorithm to obtain all f.o.b.s. of the network flow problem.