Finite-Time Distributed Flow Balancing

Christoforos N. Hadjicostis, Alejandro D. Dominguez-Garcia, Apostolos I. Rikos

Research output: Contribution to journalArticlepeer-review


We consider a flow network that is described by a digraph, each edge of which can admit a flow within a certain interval, with nonnegative end points that correspond to lower and upper flow limits. We propose and analyze a distributed iterative algorithm for solving, in finite time, the so-called feasible circulation problem, which consists of computing flows that are admissible (i.e., within the given intervals at each edge) and balanced (i.e., the total in-flow equals the total out-flow at each node). The algorithm assumes a communication topology that allows bidirectional message exchanges between pairs of nodes that are physically connected (i.e., nodes that share a directed edge in the physical topology) and is shown to converge to a feasible and balanced solution as long as the necessary and sufficient circulation conditions are satisfied with strict inequality. In case, the initial flows and flow limits are commensurable (i.e., they are integer multiples of a given constant), then the proposed algorithm reduces to a previously proposed finite-time balancing algorithm, for which we provide an explicit bound on the number of steps required for termination.

Original languageEnglish (US)
Pages (from-to)6926-6933
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number12
StatePublished - Dec 1 2022


  • Balancing
  • distributed algorithms
  • distributed balancing
  • feasible circulation
  • finite-time
  • flow networks

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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