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In a dense Low Earth Orbit (LEO) satellite constellation, using a centralized algorithm for minimum-delay routing would incur significant signaling and computational overhead. In this work, we exploit the deterministic topology of the constellation to calculate the minimum-delay path between any two nodes in a satellite network. We propose a distributed probabilistic congestion control scheme to minimize end-to-end delay, which is built on top of the existing Datagram Routing Algorithm (DRA). The decision to route packets is taken based on the latest traffic information received from neighbours. We provide an analysis of the congestion caused by a simplified DRA on a uniform infinite mesh of nodes. We compare the proposed congestion control mechanism with the existing congestion control used by the DRA via simulations, and show improvements over the latter.