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We consider the distributed weight balancing problem in networks of nodesthat are interconnected via directed edges, each of which is able to admit apositive integer weight within a certain interval, captured by individual lowerand upper limits. A digraph with positive integer weights on its (directed)edges is weight-balanced if, for each node, the sum of the weights of theincoming edges equals the sum of the weights of the outgoing edges. In thiswork, we develop a distributed iterative algorithm which solves the integerweight balancing problem in the presence of arbitrary (time-varying andinhomogeneous) time delays that might affect transmissions at particular links.We assume that communication between neighboring nodes is bidirectional, butunreliable since it may be affected from bounded or unbounded delays (packetdrops), independently between different links and link directions. We showthat, even when communication links are affected from bounded delays oroccasional packet drops (but not permanent communication link failures), theproposed distributed algorithm allows the nodes to converge to a set of weightvalues that solves the integer weight balancing problem, after a finite numberof iterations with probability one, as long as the necessary and sufficientcirculation conditions on the lower and upper edge weight limits are satisfied.Finally, we provide examples to illustrate the operation and performance of theproposed algorithms.

Distributed Integer Balancing under Weight Constraints in the Presence of Transmission Delays and Packet Drops