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arxiv: 2408.01152 · v3 · pith:GCDGOAUDnew · submitted 2024-08-02 · 💻 cs.ET · cs.SY· eess.SY

Vertiport Terminal Scheduling and Throughput Analysis for Multiple Surface Directions

Ravi Raj Saxena , T.V. Prabhakar , Joy Kuri , Manogna Yadav This is my paper

Pith reviewed 2026-05-23 22:40 UTC · model grok-4.3

classification 💻 cs.ET cs.SYeess.SY
keywords vertiportvertiminalMILP schedulingthroughput analysisVTOL operationsurban air mobilitytaxiing optimizationmulti-directional approach
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The pith

Mixed integer linear programming optimizes vertiport operations with multiple surface directions to achieve theoretical throughput while reducing delays by up to 50 percent.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a mixed integer linear program that schedules taxiing, multi-direction climbing and approach, and gate turnaround for VTOL vehicles at vertiports. It also provides equations for the upper bounds on throughput capacity based on the TLOF pad, taxiway, and gate systems. Results show the MILP reaches throughput levels matching these theoretical maxima in a case study, suggesting it can determine optimal vertiport configurations without needing simulations.

Core claim

The authors formulate a MILP that holistically optimizes vertiminal operations including taxiing, climbing or approach using multiple directions, and turnaround at gates. This formulation reduces delays by up to 50% and achieves throughput consistent with the theoretical maximum derived from equations considering the TLOF pad system, taxiway system, and gate system. Validation through a case study on an established vertiminal topology confirms the approach.

What carries the argument

The mixed integer linear program (MILP) that integrates constraints for taxiing, multi-directional climbing/approach, and gate operations to minimize delays and maximize throughput.

If this is right

  • Vertiport throughput can be computed analytically from pad, taxiway, and gate capacities.
  • Scheduling can be optimized without simulation by solving the MILP.
  • Configurations can be chosen to reach the calculated maximum throughput.
  • Delays in operations can be cut by as much as 50%.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method might extend to dynamic real-time scheduling as traffic increases.
  • It could inform regulatory standards for vertiport design in urban air mobility.
  • Similar MILP approaches might apply to other multi-directional transport hubs like drone delivery stations.

Load-bearing premise

The MILP is assumed to include all relevant safety, operational, and physical constraints without missing important interactions.

What would settle it

Running the MILP on the case study topology and observing whether the achieved throughput equals the theoretical upper bound from the derived equations.

Figures

Figures reproduced from arXiv: 2408.01152 by Joy Kuri, Manogna Yadav, Ravi Raj Saxena, T.V. Prabhakar.

Figure 1
Figure 1. Figure 1: Comparison of flight paths 4 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Example of OFV with 2 approach and climb surface directions [ [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The nodes and link representation for the optimisation problem that are explained in Table [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: TLOF pad system with two surface directions ‘X-N’ and ‘X-E’ [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Taxiway system connecting TLOF pad and gates [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Gate system with 4 gates, each having 3 slots [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Sample topology with 4 gates, 3 parking slots each and 2 surface directions. [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Results from MILP overlapped with FCFS for multiple surface directions. The results are generated [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Distribution of delays of 40 flights among gate delay (blue bars), taxing delay (orange bars), OFV [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Set1: Throughput versus the number of directions for varying flight counts. There is no advantage of multiple surface directions since OFV occupancy time exceeds the separation time, i.e. t T OT i +t R−X i > tsep ij 5.2.2 Gate system Recall the topology shown in [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Set2: Throughput versus the number of directions for varying flight counts. Since the OFV occupancy time is less than the separation time, i.e., t T OT i + t R−X i < tsep ij , the benefit of multiple surface directions becomes evident as the flight count increases. • As discussed in previous subsection 5.2.1, Arrival rate is bounded by time parameters as can be seen from Figure 12b for single surface dire… view at source ↗
Figure 12
Figure 12. Figure 12: Gate system throughput versus arrival rate. Figure 12a (Set1) depicts conditions where OFV occupancy time is more than separation time and turnaround time (T T AT ) is 90 seconds, while in Figure 12b (Set2), OFV occupancy time is less than separation time and T T AT is 120 seconds. The Slope=1 line confirms that gate throughput remains consistently below arrival throughput. Notably, the gate throughput de… view at source ↗
Figure 13
Figure 13. Figure 13: Gimpo Vertiminal topology given by [22] 6.1 Setup We evaluated four different operational configurations of the vertiminal on the Gimpo topology shown in [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Gimpo Vertiminal topology with nodes(4 TLOF pads and 20 gates) and directions [PITH_FULL_IMAGE:figures/full_fig_p024_14.png] view at source ↗
read the original abstract

Vertical Take-Off and Landing (VTOL) vehicles are gaining traction in both the delivery drone market and passenger transportation, driving the development of Urban Air Mobility (UAM) systems. UAM seeks to alleviate road congestion in dense urban areas by leveraging urban airspace. To handle UAM traffic, vertiport terminals (vertiminals) play a critical role in supporting VTOL vehicle operations such as take-offs, landings, taxiing, passenger boarding, refueling or charging, and maintenance. Efficient scheduling algorithms are essential to manage these operations and optimize vertiminal throughput while ensuring safety protocols. Unlike fixed-wing aircraft, which rely on runways for take-off and climbing in fixed directions, VTOL vehicles can utilize multiple surface directions for climbing and approach. This flexibility necessitates specialized scheduling methods. We propose a Mixed Integer Linear Program (MILP) formulation to holistically optimize vertiminal operations, including taxiing, climbing (or approach) using multiple directions, and turnaround at gates. The proposed MILP reduces delays by up to 50%. Additionally, we derive equations to compute upper bounds of the throughput capacity of vertiminals, considering its core elements: the TLOF pad system, taxiway system, and gate system. Our results demonstrate that the MILP achieves throughput levels consistent with the theoretical maximum derived from these equations. We also validate our framework through a case study using a well-established vertiminal topology from the literature. Our MILP can be used to find the optimal configuration of vertiminal. This dual approach, MILP and throughput analysis, allows for comprehensive capacity analysis without requiring simulations while enabling efficient scheduling through the MILP formulation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a MILP formulation to jointly optimize vertiport (vertiminal) operations for VTOL vehicles—taxiing, multi-direction climb/approach, and gate turnaround—claiming up to 50% delay reduction versus baselines. It also derives closed-form upper bounds on throughput capacity from separate TLOF-pad, taxiway, and gate counts, then reports that the MILP solutions reach throughput levels consistent with these bounds on a literature case-study topology.

Significance. If the MILP is shown to be tight against a bound that properly incorporates direction-specific conflicts and turnaround-taxi coupling, the dual analytical-plus-optimization approach would be useful for UAM capacity planning without Monte-Carlo simulation. The work supplies an explicit scheduling model and capacity formulas rather than black-box results.

major comments (2)
  1. [Throughput analysis section] Throughput analysis section (equations for TLOF, taxiway, and gate bounds): the upper-bound expressions are stated as products of individual subsystem capacities (pad occupancy time, taxiway flow rate, gate turnaround time) with no cross terms for simultaneous multi-direction approach/climb paths or gate-to-taxiway blocking. The claim that MILP solutions are “consistent with the theoretical maximum” therefore rests on whether these independent bounds remain tight once direction conflicts are present; the manuscript does not demonstrate that the reported bound accounts for such interactions.
  2. [Results section] Results section (delay-reduction claim): the reported “up to 50%” delay reduction is presented without an accompanying table or figure that isolates the contribution of the multi-direction variables versus a single-direction baseline, nor is an error bar or sensitivity analysis supplied for the case-study demand profile. This makes it impossible to judge whether the improvement is limited by unmodeled interactions that the MILP itself cannot capture.
minor comments (2)
  1. [Abstract] Abstract and introduction use the neologism “vertiminal” without an explicit definition on first use.
  2. [MILP formulation] Notation table or list of symbols is missing; several MILP variables (e.g., binary direction indicators) are introduced only in the text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below, indicating the revisions that will be incorporated.

read point-by-point responses

  1. Referee: [Throughput analysis section] Throughput analysis section (equations for TLOF, taxiway, and gate bounds): the upper-bound expressions are stated as products of individual subsystem capacities (pad occupancy time, taxiway flow rate, gate turnaround time) with no cross terms for simultaneous multi-direction approach/climb paths or gate-to-taxiway blocking. The claim that MILP solutions are “consistent with the theoretical maximum” therefore rests on whether these independent bounds remain tight once direction conflicts are present; the manuscript does not demonstrate that the reported bound accounts for such interactions.

    Authors: The upper bounds are formulated as the minimum of the independent subsystem capacities to yield a simple closed-form estimate. The MILP explicitly encodes direction-specific conflicts, taxiway blocking, and gate-taxi couplings. Attainment of the bound by the MILP in the case-study topology shows that, for the demand and geometry examined, these interactions do not reduce throughput below the independent bound. We will revise the throughput section to state this explicitly and to delineate the conditions under which the bounds remain tight. revision: yes

  2. Referee: [Results section] Results section (delay-reduction claim): the reported “up to 50%” delay reduction is presented without an accompanying table or figure that isolates the contribution of the multi-direction variables versus a single-direction baseline, nor is an error bar or sensitivity analysis supplied for the case-study demand profile. This makes it impossible to judge whether the improvement is limited by unmodeled interactions that the MILP itself cannot capture.

    Authors: The 50 % figure is obtained by comparing the full multi-direction MILP against an otherwise identical scheduler restricted to a single surface direction. We will add a table that directly reports delay statistics for both configurations on the same demand instances. We will also include sensitivity plots versus demand intensity and timing parameters, together with error bars for any stochastic demand components. revision: yes

Circularity Check

0 steps flagged

No circularity: throughput bounds derived from independent capacity counts; MILP is a separate optimization compared against them.

full rationale

The paper derives throughput upper bounds directly from counts of TLOF pads, taxiways, and gates (abstract and § on throughput analysis) and presents the MILP as an optimization procedure whose achieved throughput is then compared to those bounds. No step reduces a claimed prediction or result to a fitted parameter, self-citation, or definitional equivalence; the bounds are constructed from subsystem capacities without the MILP outputs as inputs, and the MILP formulation is solved independently. This matches the default expectation of a self-contained derivation with no load-bearing circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; the MILP is a standard optimization technique whose constraints are not detailed here.

pith-pipeline@v0.9.0 · 5845 in / 1107 out tokens · 28045 ms · 2026-05-23T22:40:56.299730+00:00 · methodology

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