Peñaloza (J. of Math. Econ., 2009) modeled the functioning of real-time gross settlement (RTGS) systems as an in nite dimensional linear programming prob- lem and used duality theory to determine the shadow-prices of banks. Though he proved the existence of optimal settlement rules in RTGS systems without cen- tralized queueing facilities, he did not show how optimal settlements can be imple- mented. In this paper, we show that the optimal settlement rule can be implemented by an optimization routine involving reordering and spliting of payments. Such op- timization routine is a no-queueing analog of the rst-in- rst-out (FIFO) rule with reordering used in many RTGS systems with queueing.
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