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In a certain number of applicative situations, the control of a process with a random component consists in selecting one among different evolutions. Using the simplified model problem of choosing the line in a traffic jam, we set up this class of problems in the framework of stochastic hybrid optimal control, derive the dynamic programming equation and study an approximation scheme. Numerical tests are included to support the whole procedure. Mathematics Subject Classification: 34A38, 49L25, 65M06doi:10.12988/ams.2014.310579 fatcat:z4gtxv4vwfcxvdpdndfrrnccky