A special transport mechanism must be designed for the mTAS to move samples and reagents through the system’s microchannels for medical and biomedical applications. A bi-directional microfluidic driving system was developed numerically and experimentally in this work. This pneumatic system is an on-chip planar structure without moving parts and does not require microfabricated heaters or electrodes. The pumping actuation is introduced to the microchannel fabricated in chip by creating an airflow through this device. The bi-directional driving module combines two individual components for suction and exclusion. The velocity at the microchannel can be adjusted by varying the inlet velocities for the suction and exclusion components. The individual components can be combined either by using a T-shape connection or parallel connectors. This paper explores the behavior of three differently designed parallel connectors. The width of the horizontal microchannels at the junction is 600 mm while the width of the vertical is 300 mm in parallel connector A. The widths of both the horizontal and vertical microchannels are 600 mm in parallel connector B and 300 mm parallel connector C, respectively. It was observed that the narrow microchannels 2 at the junction synthesized the suction and exclusion effects and avoided the “crossalk” of the two individual components. The results indicated that the operating range of the driving module with narrow microchannels at the junction (parallel connector C) was widest and the output velocities for this design exhibited good linearity for the application of specific biochemical analysis.