Controlling flow of gas in a gas pipeline network, wherein flow of gas within each pipeline segment is associated with a direction (positive or negative). Minimum and maximum delivery rates to each gas receipt facility are determined. Lower and upper flow bounds of gas delivery rate are created by bounding minimum and maximum signed flow rates using minimum and maximum delivery rates, respectively, for each pipe segment. A pressure drop relationship for each pipeline segment within the lower and upper flow bounds is linearized to create a linear pressure drop model for each pipeline segment. A network flow solution is calculated, which includes flow rates for each pipeline segment and pressures for each network nodes to satisfy the lower and upper flow bounds on the gas delivery rate. The network flow solution is associated with control element setpoints used by a controller to control one or more control elements.