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Vertiport Design Methodology and Capacity Analysis
Emin Burak Onat, Jean-Luc Lupien, Raja Sengupta
TL;DR
Vertiport capacity is difficult to assess because limited parking and uncertain, interacting TLOF and turnaround operations affect aircraft delays. The paper uses stochastic queueing models and simulation to analyze capacity under delay constraints. It finds that Markovian throughput is constrained to about half of departure capacity, while low-variance non-Markovian cases with enough pads can use the TLOF capacity.
Problem
Vertiport capacity analysis must account for interactions among stochastic queues, since analyzing individual processes separately misses the network structure.
Source: A. Literature Review · p. 2Method
The paper combines a finite-buffer two-node queueing network for mean queue lengths and delays with a simulator that examines vertiport capacity.
Source: §I · p. 1Results
Markovian vertiport throughput is constrained around 50% of departure capacity, while low-variance non-Markovian cases with many parking pads can use the TLOF capacity.
Source: B. Non-Markovian Model Results · p. 9, §V · p. 10Takeaways & Limitations
More deterministic TLOF and turnaround times can enhance capacity under strict delay constraints, and the methodology identifies parking-pad counts that maximize throughput gain per unit area.
Source: §I · p. 1
Abstract
from arXiv · showhide
This paper presents a comprehensive methodology for vertiport design and capacity analysis using stochastic queueing models. Vertiport capacity is defined as the maximum steady-state throughput of aircraft per hour while maintaining a specified maximum queuing delay with high probability. We introduce a two-node queueing network model with a finite buffer to analytically derive mean queue lengths and delays at singleTLOF vertiports, supported by a simulation model that validates these findings under various operational conditions. Our analyses reveal that vertiport capacity is significantly constrained by the interactions between takeoff/landing operations and turnaround activities. Capacity is further reduced by the variance in these operational parameters, with deterministic times substantially enhancing capacity. The study shows that vertiport throughput is typically around 50% of the theoretical maximum departure capacity in a Markovian model, decreasing sharply as confidence in maximum queuing delay increases. Non-Markovian models with adequate parking pads achieve full TLOF capacity. Additionally, our methodology identifies the optimal number of parking pads required to maximize throughput per unit area. The findings provide insights for designing vertiport infrastructure to support scalable and efficient UAM deployment.
I. INTRODUCTION
Vertiport capacity depends on stochastic interactions among TLOF operations, aircraft holding, and turnaround, making it important to model the system as a whole. The paper develops a queueing-based capacity methodology and reviews why earlier approaches do not capture these interactions.
I. INTRODUCTION
- Vertiport capacity analysis is complicated by limited urban footprint and charging uncertainty, while charging and takeoff/landing times are of similar duration.The paper cites approximately 6 minutes of charging for a typical 30-minute flight at low SoC, compared with about 1 minute each for takeoff and landing.Source: §I · p. 1
- The paper models vertiport capacity with stochastic queues and a finite buffer, deriving mean queue lengths and waiting times while accounting for high-probability delay constraints.The model assumes aircraft use the TLOF for takeoff or landing and parking pads for other operations, including charging.Source: §I · p. 1
- Capacity is substantially below the minimum of takeoff/landing and turnaround capacities when aircraft delays must remain small with high probability.The simulator reproduces the analytical model's relationships; more deterministic TLOF and turnaround times can increase capacity under strict delay constraints.Source: §I · p. 1
A. Literature Review
- Prior vertiport studies include deterministic capacity-envelope and queueing analyses,,, but deterministic estimates are upper bounds and may omit airspace holding delays.Airport-style single-node models commonly assume unlimited gate capacity –, unlike vertiports where gates may constrain operations,.Source: A. Literature Review · pp. 1–2
- The literature review identifies a gap in modeling the interactions among stochastic vertiport queues, arguing that queues should be analyzed as one network.The introduction frames this analysis as important to the operational viability and scalability of UAM.Source: §I · p. 1, A. Literature Review · p. 2
II. VERTIPORT QUEUEING NETWORK MODEL
The vertiport model represents aircraft moving between airspace, TLOF operations, and parking-pad servicing, with limited pad availability creating blocking. The analysis simplifies the feedback system into a finite-buffer two-node tandem network.
II. VERTIPORT QUEUEING NETWORK MODEL
- In the operational sequence, aircraft arrive through the TLOF, receive charging or other servicing at parking pads, then return to the TLOF for departure.When all pads are occupied, BBS-SNO blocking prevents an arriving aircraft from occupying or being serviced at the TLOF.Source: §II · p. 2
- The parking-pad node has c servers, no waiting room, and combined service rate µsurface = µpark · c; each pad’s turnaround includes taxiing, charging, and concurrent activities.Steady state requires the arrival and departure rates to match.Source: §II · p. 2
- The original feedback model tracks aircraft in the airspace buffer, at parking pads, and in the departure queue, with pad capacity constraining the latter two groups together.A tandem approximation halves the M/M/1 service rates and changes one queue to M/M/1/1 to reflect the reconfigured system.Source: §II · p. 3
- The final analytical network uses a finite-buffer M/M/1/K TLOF queue and an M/M/c/c parking-pad queue, with BBS-SNO blocking.Setting K to 100 limits the buffer to a finite state space while aiming for minimal impact on system dynamics; the model approximates the feedback system using separate arrival and departure TLOFs.Source: §II · p. 3, Figure 3 · p. 3
A. Notation
The notation describes system states using aircraft counts in the airspace buffer and at the surface, alongside the model's capacity and service-rate parameters.
A. Notation
- A system state is represented by (i, j), where i counts aircraft waiting in the airspace buffer and j counts aircraft at the surface.The counts are bounded by K and c, respectively.Source: A. Notation · p. 3
- The model parameters are λ for airspace-buffer arrivals, µcharge for a parking-pad charger, µTLOF for TLOF service, and c for the number of parking pads.K is the maximum airspace-buffer size.Source: A. Notation · p. 3
- p(i, j) denotes the probability that the system is in state (i, j).E is the set of all possible states.Source: A. Notation · p. 3
B. State Transition Rate Diagram
The state diagram represents vertiport operations with states labeled by airspace queue and occupied parking-pad counts. Its transitions encode arrivals, TLOF service, and departures after charging, while airspace capacity and pad count bound the state space.
B. State Transition Rate Diagram
- States are labeled by airspace queue length and occupied parking-pad count, with terminal airspace capacity and pad count constraining the possible state space.The diagram’s vertical and horizontal axes correspond to airspace capacity and parking pads, respectively.Source: B. State Transition Rate Diagram · p. 4
- Arrival transitions use λ, transitions from the buffer to a parking pad use µTLOF, and charged-aircraft departures use the adjusted rate µc.µc incorporates the subsequent departure TLOF service, which is needed because a single TLOF must be used for departure before the vacated pad can be occupied by a landing aircraft.Source: B. State Transition Rate Diagram · p. 4
- The average time before the departure TLOF is free is represented using the probabilities of having zero or one aircraft in the queue.The supplied equation relates tfree to p0 and p1, which are the respective probabilities of zero and one aircraft in the queue.Source: B. State Transition Rate Diagram · p. 4
C. Exact Analysis of Markovian Process
Under exponential charging times independent of arrivals, the vertiport is modeled as an ergodic continuous-time Markov chain. Its steady-state probabilities are obtained from global balance equations, including boundary cases imposed by finite airspace and parking capacity.
C. Exact Analysis of Markovian Process
- With exponential charging times independent of aircraft arrivals, the vertiport evolves as an ergodic continuous-time Markov chain with a unique steady-state distribution under irreducible routing.The state space is discrete, and the distribution is denoted by π over states (i, j).Source: C. Exact Analysis of Markovian Process · p. 4
- The steady-state probabilities are found by solving πQ = 0 together with the normalization condition that their sum over the state space equals 1.These global balance equations characterize the system’s steady-state behavior.Source: C. Exact Analysis of Markovian Process · p. 4
- The balance equations include edge cases where finite airspace or full parking pads constrain arrivals and service, as well as equations for interior states.For example, a full buffer rejects an incoming aircraft, while full pads with an empty buffer leave the TLOF blocked for service.Source: C. Exact Analysis of Markovian Process · p. 5
D. Performance Metrics
The analysis evaluates queue length and waiting time, including their variances, to characterize vertiport performance and the consistency of delays.
D. Performance Metrics
- The analysis evaluates mean airspace queue length, queue-length variance, mean queue waiting time, and waiting-time variance.Queue-length variance describes fluctuations in the number of aircraft waiting; lower variance indicates a more predictable queue for operations and planning.Source: D. Performance Metrics · p. 5
- Waiting time Wq is the main performance metric and is derived from mean queue length using Little’s Law.λ denotes the average aircraft arrival rate at the vertiport.Source: D. Performance Metrics · p. 5
- Waiting-time variance is used to assess the consistency of delays and the predictability of vertiport operations.The paper denotes this variance as σ²Wq.Source: D. Performance Metrics · p. 5
E. Interaction Between Queues
The parking-pad queue interacts with the TLOF queue, so blocking can remain substantial even when average delay is around ten minutes. The analysis also finds that this interaction becomes marginal only at a TLOF-to-pad service-rate ratio that the cited operational parameters do not attain.
E. Interaction Between Queues
- The finite-pad blocking mechanism is absent from the conventional M/M/c model’s infinite-buffer assumption.The paper identifies limited parking-pad availability as the reason the vertiport network requires a blocking mechanism.Source: E. Interaction Between Queues · p. 5
- Blocking is at least 30% across parking-pad configurations even with average queueing delay around 10 minutes, and exceeds 40% with one pad; arrivals reach only about 50% of designated surface capacity for most configurations.The findings show that the parking-pad queue affects the first queue before the arrival rate reaches full surface capacity.Source: E. Interaction Between Queues · p. 6
- Fig. 5 examines parking-pad blocking as arrival rates rise across pad counts at a charge rate of 6 aircraft per hour.The analysis reports increasing blocking with higher arrival rates, with fewer pads producing higher blocking.Source: E. Interaction Between Queues · p. 5, Figure 5 · p. 6
- With µcharge·c held at 30, blocking changes only marginally once µTLOF/(µcharge·c) exceeds 8, but the cited operational parameters do not attain that ratio.At that ratio the queues could be treated as sufficiently independent for separate M/M/1 and M/M/c analysis; otherwise, the system must be analyzed as a whole.Source: E. Interaction Between Queues · p. 6
III. SIMULATION MODEL
The simulator models aircraft movements through TLOF queues and parking-pad servicing, including waits for both a pad and TLOF access.
III. SIMULATION MODEL
- Aircraft wait in the arrival queue until they can secure both a parking pad and the TLOF.If no pad is available, they wait until another aircraft departs and frees space.Source: §III · p. 6
- After TLOF service and charging, aircraft queue for TLOF access to depart.This departure queue is represented in the simulator, unlike the analytical queueing model’s direct transition from pad service to TLOF service.Source: §III · p. 6
- VertiSim uses SimPy’s discrete-event framework to simulate arrivals, landings, charging completions, departures, and TLOF availability changes.Aircraft movements follow the BBS-SNO mechanism and a first-come-first-served process is not specified in this passage.Source: §III · p. 6
A. Simulation Validation
Simulation results closely match the analytical queueing model, supporting its use for studying vertiport operations; the simulator also approximates delay accurately in the stated scenarios.
A. Simulation Validation
- The largest simulated-versus-analytical queueing-delay difference was 5.9 seconds, or 3%.The validation used μTLOF = 30 aircraft/hr, μcharge = 6 aircraft/hr, and 1–10 parking pads.Source: A. Simulation Validation · p. 6
- The simulator’s approximation error was at most 18 seconds when queueing delay approached 10 minutes in the reported scenarios.The authors use this accuracy to support simulator analysis of more complex scenarios and non-Markovian distributions.Source: A. Simulation Validation · p. 7
- Table I compares analytical and simulation results; λ denotes arrival rate in aircraft per hour, and the reported times are in minutes.The difference column is the absolute difference between the models’ results.Source: Table I · p. 7, A. Simulation Validation · p. 7
IV. RESULTS
The results quantify throughput under a high-confidence queue-delay constraint and show how charge time, pad count, and operational variability shape capacity. They also reveal a trade-off between throughput and design flexibility.
IV. RESULTS
- The analysis selects maximum throughput subject to a queue-delay threshold and confidence level, estimating an upper confidence limit from mean and variance of Wq.It models Wq as normally distributed, uses the standard-normal Z-score, and iterates over arrival rates; simulations instead estimate the percentile directly from data.Source: §IV · p. 7
A. Queueing Model Results
- At a 5-minute charge time, the throughput gap between the fewest and most parking pads is 13 aircraft per hour; at 30 minutes, it is 9.Both comparisons use a 95% confidence requirement that Wq remain below 5 minutes.Source: A. Queueing Model Results · p. 7, Figure 7 · p. 8
- With seven effective parking pads, maximum capacity is about half the TLOF service rate or slightly below 20% of surface capacity.The reported maximum effective pad count is seven; the result describes capacity under the queueing-model analysis.Source: A. Queueing Model Results · p. 7
- The two-node queueing approximation closely follows the feedback simulation curves, with a maximum deviation of 10%.The validation used 200 distinct simulation seeds and reported configurations with five and ten parking pads.Source: A. Queueing Model Results · p. 8
- As arrival rates cross configuration-specific thresholds, confidence in keeping Wq below 5 minutes falls sharply, and further arrivals do not substantially increase throughput.The decline in controllability accompanies this confidence drop.Source: A. Queueing Model Results · p. 8, Figure 8 · p. 8
- At a vertiport, under the confidence constraint, reducing charge time and increasing parking pads yields higher throughput but restricts feasible design options; increasing charge time and reducing pads broadens flexibility at lower throughput.Source: A. Queueing Model Results · p. 8
B. Non-Markovian Model Results
The non-Markovian simulations examine three vertiport layouts with Poisson arrivals, deterministic TLOF service, and variable charging times. Under the stated low-variance charging scenario, throughput can reach TLOF capacity, and the dedicated takeoff/landing layout outperforms two independent TLOFs.
B. Non-Markovian Model Results
- The simulations use Poisson arrivals, deterministic TLOF service, normally distributed charging times with standard deviation at 20% of the mean, and first-come-first-served service.The layouts are a single TLOF surrounded by pads, two independent copies of that layout, and separate dedicated takeoff and landing TLOFs; the third is also called a pier layout.Source: B. Non-Markovian Model Results · p. 9, Figure 10 · p. 9, Figure 11 · p. 9
- With charging-time standard deviation set to 20% of its mean, throughput reaches full TLOF capacity for both the single-TLOF and doubled two-independent-TLOF layouts when pad counts are large.The authors characterize these simulations as a best-case scenario with minimal operational disruption.Source: B. Non-Markovian Model Results · p. 9, Figure 10 · p. 9, Figure 11 · p. 9
- The comparison with the Markovian results highlights the capacity cost of greater operational-parameter variance.The authors attribute the full-capacity outcome in these simulations to the smaller variance relative to the Markovian case.Source: B. Non-Markovian Model Results · pp. 8–9
- At six pads, Configuration 3 achieves 27 aircraft per hour per TLOF, versus 23 for Configuration 2.Configuration 3’s maximum effective pad count is five, compared with four for Configuration 2, per TLOF.Source: B. Non-Markovian Model Results · p. 9, Figure 14 · p. 9, Figure 13 · p. 9
1) Unit Throughput:
The paper combines a finite-buffer queueing model and simulation to analyze vertiport capacity and unit throughput. Results show capacity depends on operating assumptions and layout, with different parking-pad configurations favoring different throughput-per-area outcomes.
1) Unit Throughput:
- Configuration 1's area grows with added pads through nine, while Configuration 3 requires greater separation beyond four pads.Configuration 2 doubles Configuration 1's elements and uses at least 200-foot separation between FATOs for simultaneous TLOF operations; Configuration 3 maintains 200-foot TLOF separation and expands horizontally.Source: 1) Unit Throughput · p. 10
- Configuration 1 has an optimal six parking pads before unit throughput stabilizes and is most efficient through nine pads; Configuration 3 scales best when land is not constrained.Configuration 2 remains effective through 12 pads and outperforms Configuration 3 at or below four pads.Source: Figure 15 · p. 10, 1) Unit Throughput · p. 10
V. CONCLUSION
- The finite-buffer two-node queueing model and simulation estimate sustainable departures as structural and operational parameters vary.The listed parameters include parking pads, TLOFs, charger capacity, aircraft holding times, confidence levels, and energy consumption.Source: §V · p. 10
- Markovian vertiport throughput is around 50% of departure capacity, while non-Markovian operation reaches full TLOF capacity with adequate parking pads.The conclusion also reports that two independent TLOFs perform less effectively than separate TLOFs designated for takeoff and landing.Source: §V · p. 10
- Higher confidence in maximum aircraft holding time sharply reduces throughput, and exponential parameter variance significantly reduces system capacity.For the single-TLOF configuration, unit throughput does not increase beyond six parking pads.Source: §V · p. 10
- Two isolated TLOFs have lower throughput per unit area than separate takeoff and landing TLOFs because of the larger footprint requirement.The conclusion reports this comparison for two-TLOF systems under different operational rules.Source: §V · p. 10