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Recently, Non-Geostationary Earth Orbit (NGEO) satellite networks have gained research attention. Since they offer many features, e.g., extensive coverage, disaster-resistance, and efficient power consumption, they are considered as a good candidate for providing global communication services. Moreover, Multi-Layered Satellite Networks (MLSNs), which consist of layered NGEO satellite networks, have attracted much attention since they achieve excellent load distribution through bypassing traffic from the lower layer to upper layer. However, there is a possibility that traffic congestion may exist at a satellite on the upper layer because each satellite on the upper layer usually covers more than one satellite on lower layers in MLSNs. In this paper, we focus on traffic control in two-layered networks, especially on distributing the packet flow between the two layers in order to minimize the transfer delay of the network …