⚡ electrical engineering

Vertiport Terminal Scheduling and Throughput Analysis for Multiple Surface Directions

This paper proposes a Mixed Integer Linear Program (MILP) to optimize vertiport scheduling across multiple surface directions and derives theoretical throughput equations, demonstrating that the approach reduces delays by up to 50% while achieving capacity levels consistent with theoretical maximums.

Original authors: Ravi Raj Saxena, T. V. Prabhakar, Joy Kuri, Manogna Yadav

Published 2026-06-05

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ravi Raj Saxena, T. V. Prabhakar, Joy Kuri, Manogna Yadav

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a bustling city where the roads are gridlocked, and the solution is to build a new network of highways in the sky. This is the promise of Urban Air Mobility (UAM): using electric "air taxis" (VTOL vehicles) to zip people and packages around. But just like cars need gas stations and parking lots, these flying cars need special places to land, pick up passengers, charge, and take off again. These places are called Vertiport Terminals (or "vertiminals").

This paper tackles a big problem: How do we schedule these flying cars so they don't crash, don't wait too long, and keep the sky moving efficiently?

Here is a simple breakdown of what the authors did, using everyday analogies.

1. The Big Difference: Helicopters vs. Air Taxis

Think of a traditional airplane like a race car. It needs a long, straight runway. It can only take off in one specific direction (down the track) and must land coming from that same direction. If two cars want to use the track, they have to wait for the first one to clear the whole length.

Now, think of these new VTOL air taxis like drones or helicopters. They can take off straight up and land straight down.

The Superpower: Once they leave the ground, they can fly in any direction immediately.
The Opportunity: If you have a landing pad, you don't just need one "exit ramp." You can have multiple "exit ramps" (called surface directions) fanning out in different directions. If one car leaves going North, another can leave going East immediately after, without waiting for the first one to clear the whole sky.

2. The Problem: The "Traffic Jam" in the Sky

The authors realized that while we know how to design these terminals, we didn't have a great way to schedule the traffic.

The Old Way (FCFS): Imagine a line at a coffee shop where everyone is served strictly in the order they arrived ("First Come, First Served"). This is simple, but it's inefficient. If the person at the front is slow, everyone behind them waits, even if the person behind them could have been served faster if the order was swapped.
The New Way (MILP): The authors created a smart computer brain (a Mixed Integer Linear Program, or MILP). Instead of just looking at who arrived first, it looks at the whole picture. It asks: "If I let this car go East and that car go North, can we get both through faster than if they both tried to go North?"

3. The Solution: The Smart Scheduler

The authors built a mathematical model that acts like a super-traffic controller.

What it does: It schedules when a plane leaves the gate, when it drives on the taxiway (the ground path), when it lands on the pad, and which "exit ramp" (surface direction) it takes to leave.
The Result: By using this smart scheduler and allowing planes to leave in different directions, they found they could cut delays by up to 50%. It's like finding a shortcut through a maze that everyone else was too busy to notice.

4. The "Bottleneck" Check (Throughput Analysis)

The authors didn't just build the scheduler; they also wanted to know: "What is the absolute maximum number of planes this terminal can handle?"

They broke the terminal down into three parts, like checking the capacity of a water pipe system:

The Landing Pads (TLOF): The actual spots where planes touch down.
The Taxiways: The roads on the ground connecting the pads to the gates.
The Gates: The parking spots where passengers board.

They wrote simple math equations to calculate the "speed limit" of each part.

The Finding: They discovered that the Landing Pads and the Gates are usually the bottlenecks (the narrowest parts of the pipe). The taxiways (the ground roads) are usually wide enough that they don't cause traffic jams.
The Proof: When they ran their smart scheduler, the number of planes it handled matched their theoretical math equations perfectly. This proved their scheduler was working as efficiently as physically possible.

5. The Real-World Test: The Gimpo Airport Case Study

To make sure this wasn't just theory, they tested it on a real-world design for a terminal at Gimpo Airport in Korea. They tried four different ways to organize the terminal:

Scenario A: Let everyone mix freely (Arrivals and Departures sharing everything).
Scenario B & C: Separate the arrivals and departures into different zones.

The Winner: The scenarios that separated arrivals and departures (like having a dedicated "Drop-off" lane and a dedicated "Pick-up" lane) worked the best. They reduced confusion and allowed more planes to move through per minute.

Summary

In short, this paper says:

Air taxis are flexible: They can leave in any direction, unlike airplanes.
We need a smart brain: A simple "first-come-first-served" line is too slow. We need a smart algorithm (MILP) to juggle the schedule.
It works: This smart schedule cuts wait times in half and pushes the terminal to its maximum possible capacity.
Separation is key: Keeping arriving planes and departing planes in different zones makes the whole system run smoother.

The authors have provided a "blueprint" and a "traffic controller" to ensure that when our cities fill with air taxis, the sky doesn't turn into a parking lot.

Technical Summary: Vertiport Terminal Scheduling with Multiple Surface Directions and Throughput Analysis

Problem Statement

Urban Air Mobility (UAM) systems aim to alleviate ground congestion by utilizing urban airspace for Vertical Take-Off and Landing (VTOL) vehicles. While Vertiport terminals (vertiminals) are critical hubs for these operations, they risk becoming bottlenecks similar to traditional airports under high traffic loads. Unlike fixed-wing aircraft that rely on runways with fixed approach and climb directions, VTOL vehicles possess the flexibility to utilize multiple surface directions for take-off and landing.

Current literature largely addresses vertiport design, air traffic control rules, or isolated ground operations. However, there is a lack of holistic optimization frameworks that integrate:

Multiple Surface Directions: Leveraging the ability of VTOLs to climb and approach in various directions to reduce separation constraints.
Integrated Ground Operations: Simultaneously scheduling taxiing, gate turnaround, TLOF (Touchdown and Lift-Off) pad occupancy, and climb/approach phases.
Throughput Analysis: Deriving analytical bounds for capacity without relying solely on computationally expensive simulations.

The core challenge is to minimize delays (waiting at gates, taxiing, OFV occupancy, and climb) while adhering to safety constraints such as wake vortex separation, minimum separation distances on taxiways, and obstacle-free volume (OFV) occupancy rules.

Methodology

1. Mixed Integer Linear Program (MILP) Formulation

The authors propose a novel MILP formulation to optimize vertiminal operations. The objective is to minimize the weighted sum of delays across all operational stages:

Departures: Gate waiting, taxiing to TLOF, climbing within the OFV, and climbing to the vertiexit.
Arrivals: Climbing from vertiexit to OFV, landing on TLOF, and taxiing to the gate.
Turnaround: Time spent at gates for boarding/deboarding.

Key Features of the Formulation:

Multiple Directions: The model explicitly allows VTOLs to select different surface directions for climb and approach. If consecutive aircraft use different directions, the separation distance constraint is relaxed (set to zero), reducing delays.
Optimization Improvements: Building on previous work, the authors eliminated the "immediate predecessor" binary variable, relying solely on a general predecessor variable. This reduced the number of constraints by over 90%, significantly decreasing both formulation and solver times.
Constraints: The model enforces physical constraints (speed limits, path continuity), separation requirements (wake vortex on TLOF pads, distance on taxiways/surface directions), and gate holding capacities.

2. Analytical Throughput Capacity Derivation

To evaluate the efficiency of the MILP scheduling, the authors derived analytical equations to compute the theoretical upper bounds of vertiminal throughput. The system is decomposed into three independent subsystems:

TLOF Pad System: Calculates capacity based on TLOF pad occupancy time, OFV travel time, and separation requirements (wake vortex and surface direction separation). It considers four movement sequences: Arrival-Arrival (AA), Departure-Departure (DD), Arrival-Departure (AD), and Departure-Arrival (DA).
Taxiway System: Modeled as a flow network. Dynamic capacity is calculated based on vehicle length, separation distance, and taxi speed using the max-flow min-cut theorem.
Gate System: Capacity is determined by the static number of parking slots and the dynamic turnaround time (TAT) of the fastest vehicle class.

The overall vertiminal throughput is defined as the minimum of the throughputs of these three subsystems ( $\mu_{vertiminal} = \min(\mu_{TLOF}, \mu_{taxi}, \mu_{G})$ ).

Key Contributions

Novel Operational Procedure: The paper introduces a scheduling framework that exploits multiple climb and approach surface directions. This flexibility allows for tighter sequencing of aircraft, reducing delays by up to 50% compared to single-direction or First-Come-First-Served (FCFS) approaches.
Enhanced MILP Efficiency: The revised formulation reduces computational complexity by more than 90% compared to previous models, making it feasible to solve larger instances involving arriving flights and gate turnarounds.
Analytical Throughput Bounds: The authors provide equations to calculate theoretical throughput limits based on specific operational parameters (separation times, TAT, OFV occupancy). These equations allow for capacity analysis without running extensive simulations.
Validation via Case Study: The framework is validated using the Gimpo Vertiminal topology (a pier-type design with 4 TLOF pads and 20 gates). The study compares different operational configurations (e.g., segregated vs. mixed arrival/departure pads) to identify optimal setups.

Results

Delay Reduction and Scheduling

Surface Direction Impact: Increasing the number of available surface directions from 1 to 2 resulted in approximately a 50% reduction in excess delay for departing flights.
MILP vs. FCFS: The MILP approach consistently outperformed FCFS scheduling. The mean and median delays for MILP were significantly lower. In FCFS, delays were uniformly distributed, whereas MILP skewed delays away from the maximum, prioritizing overall system efficiency.
Weighted Optimization: By assigning higher weights to constrained resources (TLOF pads, OFV) and lower weights to less constrained resources (gates), the MILP successfully minimized congestion on critical bottlenecks, preventing unnecessary taxiway delays.

Throughput Analysis

Bottleneck Identification: The analysis confirmed that the TLOF pad system and Gate system are the primary bottlenecks, while the taxiway system generally has sufficient capacity.
Multiple Directions Effect:
- In scenarios where the OFV occupancy time exceeded the separation time, multiple surface directions offered no throughput advantage.
- Conversely, when separation time exceeded OFV occupancy time (Set 2 in the study), utilizing multiple surface directions increased throughput significantly (e.g., from ~5.14 to ~9.41 VTOLs/min for specific configurations).
Configuration Optimization: In the Gimpo case study, configurations that segregated arrivals and departures to specific TLOF pads (Configurations 3 and 4) achieved higher throughput (9.25 and 9.54 VTOLs/min in Set 1) compared to fully mixed or partially segmented configurations. This highlights that reducing path conflicts is crucial for maximizing capacity.

Significance and Claims

The paper claims that its dual approach—combining an optimized MILP scheduler with analytical throughput equations—provides a comprehensive tool for vertiminal planning.

Practical Utility: The derived equations allow planners to estimate capacity limits and understand the impact of design parameters (like TLOF-to-gate ratios) without relying on time-consuming simulations.
Operational Efficiency: The study demonstrates that strategic allocation of TLOF pads (segregating arrivals and departures) and the utilization of multiple surface directions can significantly enhance vertiminal capacity and reduce delays.
Scalability: The reduction in computational complexity makes the MILP formulation suitable for real-time or near-real-time scheduling in future UAM networks.

The authors conclude that while the MILP formulation effectively identifies optimal configurations and schedules, future work will focus on further reducing computation time via rolling horizon methods and incorporating stochastic elements to handle operational uncertainties.