A robust stochastic design and signal control (RoSign) is considered for urban traffic network under uncertain travel demand. The optimal solutions for RoSign can be cast as a stochastic mathematical program with equilibrium constraints (SMPEC) and efficiently solved by a stochastic projected cutting plane (SPC) with global convergence. While robust optimization is considered a good alternative against high-consequence realization of uncertainty, a flexible signal timing using a budget of uncertainty in demand is investigated. Sensitivity analysis of SPC against budgeted uncertainty in travel demand is performed. Numerical computation and comparison are also made with other heuristics using real-data road networks. Results indicate that SPC enjoyed a greater gain of achieving road network robustness whilst incurring less sub-optimality loss against uncertain demand as compared to other alternatives.