We model the functioning of real-time gross settlement systems for large-value transfers as a linear programming problem in which queueing arrangements, splitting of payments, and Lombard loans arise as primal solutions. Then we use the dual programming problem associated with the maximization of the total flow of payments in order to determine the shadow-prices of banks in the payment system. We use these shadow-prices to set personalized intraday monetary policies such as reserve requirements, availability of Central Bank credit to temporarilly illiquid banks, extension of intraday interbank credit exposures, etc., so as to make the use of systemic liquidity more efficient.
