Seaplane Period Appointment with the Hangar: A Fluid Flow Approach

Seaplanes’ hangar appointments scheduling is emerging. There is a fixed number of staying slots in the station; hence there will be a waiting time in the hangar queue. This paper presents a queuing system optimization framework for allocating appointment slots across multiple periods, aimed at minimizing congestion and enhancing service efficiency. The objective function minimizes the total squared queue length, penalizing longer queues to reduce congestion and prevent service bottlenecks. Queue dynamics are modeled, accounting for seaplane arrival rates and adjustable service rates influenced by utilization. In particular, the hangar is modeled as a controlled multi-server queue with time-dependent arrival rated is utilised and it is handled using the pointwise stationary fluid flow approximation (PSFFA) technique. The service rate ensures dynamic adaptation, balancing load and maintaining system stability by reducing queues when service capacity exceeds demand. Constraints ensure feasibility by aligning appointment allocation with demand, enforcing non-negativity, and maintaining reasonable waiting times and queue lengths. This approach provides an efficient, adaptable solution for man- aging variable demand over time while respecting system constraints