To mediate a gate dispute effectively, first acknowledge the importance of both airlines' operations and the tight schedules they maintain. Facilitate an impartial discussion, focusing on flight timing, passenger impact, and operational constraints. Propose a solution that prioritizes minimal delays for passengers while suggesting alternative gates or sharing the gate within a defined timeframe. Highlight the importance of collaboration for smoother operations and offer to review gate allocation procedures to avoid future conflicts, fostering long-term cooperation between the airlines.

As an efficient and authoritative airport manager, such conflicts should be resolved by patiently listening to both the sides and giving a definite & fair decision on the basis of routine gate allocation policy as well as the situational consideration to priorities for on time performance. Other possibilities like allocation of alternate available nearest gate and facilitating for consequential change arrangements can facilitate an acceptable resolution.