The s2s-OVCA is a cellular automaton (CA) hybrid of the optimal velocity (OV) model and the slow-to-start (s2s) model, which is introduced in the framework of the ultradiscretization method. Inverse ultradiscretization as well as the time continuous limit, which lead the s2s-OVCA to an integral-differential equation, are presented. Several traffic phases such as a free flow as well as slow flows corresponding to multiple metastable states are observed in the flow-density relations of the s2s-OVCA. Based on the properties of the stationary flow of the s2s-OVCA, the formulas for the flow-density relations are derived.