Despite the importance of controlling the inter-arrival times of flights to propose strategies for efficient arrival management by the Arrival Manager (AMAN), the specific guidelines of such adjustments and their effect on reducing delays have not been explicitly considered. Accordingly, this paper proposes a novel approach, which integrates the Gt/GI/st+GI time-varying fluid model and nonlinear integer programming to flatten the arrival rate at terminal gates. This, in turn, is achieved by minimizing the variance in inter-arrival times by penalizing any excessive change in arrival time, considering operational constraints. The results for Tokyo International Airport show potential to significantly reduce arrival traffic delays by minimizing said variance. This study may also spawn subsequent work, which builds a queuing network comprising upstream and terminal airspace and demonstrates the scope to reduce delays in the terminal airspace by controlling inter-arrival times at the upstream airspace.