Analysis of Fleet Management and Network Design for On-Demand Urban Air Mobility Operations
AAnalysis of Fleet Management and Network Design forOn-Demand Urban Air Mobility Operations
Sheng Li ∗ Stanford University, Stanford, CA, 94305, USA
Maxim Egorov † Airbus UTM, Sunnyvale, CA, 94086, USA
Mykel J. Kochenderfer ‡ Stanford University, Stanford, CA, 94305, USA
A significant challenge in estimating operational feasibility of Urban Air Mobility (UAM)missions lies in understanding how choices in design impact the performance of a complexsystem-of-systems. This work examines the ability of the UAM ecosystem and the operationswithin it to meet a variety of demand profiles that may emerge in the coming years. We performa set of simulation driven feasibility and scalability analyses based on UAM operational modelswith the goal of estimating capacity and throughput for a given set of parameters that representan operational UAM ecosystem. UAM ecosystem design guidelines, vehicle constraints, andeffective operational policies can be drawn from our analysis. Results show that, while criticalfor enabling UAM, the performance of the UAM ecosystem is robust to variations in groundinfrastructure and fleet design decisions, while being sensitive to decisions for fleet and trafficmanagement policies. We show that so long as the ecosystem design parameters for groundinfrastructure and fleet design fall within a sensible range, the performance of the UAMecosystem is affected by the policies used to manage the UAM traffic.
I. Introduction T echnological advances in electrical vertical takeoff and landing (eVTOL) aircraft have enabled a variety of newmissions that could soon be feasible including cargo delivery and passenger transportation. Some estimates showthat by the year 2035, the hourly demand for passenger carrying urban flights could be as large as 2,500 in metropolitanareas like Paris [1]. Passenger carrying Urban Air Mobility (UAM) operations would ultimately try to capture somefraction of this demand. However, designing a system capable of safe and efficient UAM operations at such a scale is amajor challenge. While certain aspects of eVTOL vehicle design and requirements have become more concrete in recentyears [2, 3], the uncertainty surrounding what the UAM ecosystem as a whole will look like still exists.For UAM operations and its supporting systems, the majority of design decisions will be driven by the safety andbusiness cases. However, it is difficult to evaluate the implications of a design choice on these two factors withoutexamining the UAM ecosystem as a whole. Specifically, understanding how various constraints and design choicesinteract with one another is critical to understanding the performance of the system. For example, decisions on thecapacity of an in-demand vertiport, the size of a fleet used to serve a region, and the choice of policies used to managetraffic all have a crucial impact on performance metrics like vehicle throughput and demand fulfillment rate of the UAMecosystem in a given region. Understanding how these decisions impact the overall performance of the system caninform a more efficient design process for UAM, leading to a safer, healthier, and more sustainable ecosystem.The UAM ecosystem is comprised of a number of independent but interconnected systems, including the supportingground infrastructure like a network of vertiports, the UAM vehicle fleet, and the system used to manage UAM traffic.These systems, like management and coordination of UAM traffic, can be further divided into systems responsible formanaging an operator’s fleet and the system responsible for coordination between various stakeholders in the system,such as a UAM equivalent to UTM [4]. Relationships between these systems are difficult to evaluate and an accurateanalysis generally requires a comprehensive view of all the systems functioning together, which is usually not feasible ∗ Ph.D. Candidate, Department of Aeronautics and Astronautics, AIAA Student Member, [email protected] † Research Scientist, Autonomy at Airbus UTM, [email protected] ‡ Associate Professor, Department of Aeronautics and Astronautics, AIAA Associate Fellow, [email protected] a r X i v : . [ c s . OH ] A ug ntil the ecosystem is operational. Challenges also emerge from the on-demand nature of UAM operations. It isexpected that some operators will not follow fixed schedules, as in current commercial air transportation systems, whichcan result in load imbalance problems. Accounting for the requirements, constraints, and inter-relationships imposedby these systems is difficult, and analyzing one of the parts in isolation could lead to poor estimates of overall systemperformance.In this work, we perform a number of quantitative analyses using a macroscopic scenario simulator of UAMoperations. We focus on the interactions between UAM operations, the underlying infrastructure, the traffic managementsystem, and any constraints imposed on the operations to extract emergent, system-level quantitative results likethroughput and demand fulfillment. Through careful choice of design variables, we are able to formulate the UAMecosystem design problem as an optimization. By performing a variety of analyses, we are able to both identifythe design variable regions that lead to solutions from which feasible UAM operations emerge, and to quantify therelationships between critical design variables like vertiport capacity and operational fleet sizes. Lastly, we investigatethe sensitivity of the critical design variables on system performance, and demonstrate how careful choice of fleet andtraffic management policies can compensate for sub-optimal design decisions related to vertiport capacity and fleet size.We conclude by drawing UAM ecosystem design guidelines from our analysis. II. Related Work
The design of requirements and constraints for UAM systems has become a widely explored topic in recent years.Kohlman and Patterson [5] describe a system-level model of a UAM network and explored energy-related constraintssuch as battery life of eVTOL aircraft as well as the number of charging stations that are part of the ground infrastructure.Vascik and Hansman [6] separately discuss scaling constraints for UAM operations from air traffic control, groundinfrastructure, and noise, with additional highlights on the additional congitive loads for air traffic control that comefrom UAM [7]. Mueller et al. [8] provide a conceptual description of the methodologies for enabling the integration ofon-demand operations with the existing commercial transportation airspace. While these works provide a glimpse intorequirements for UAM operations, they generally lack analysis of their feasibility in a broader UAM ecosystem.The topic of traffic management in UAM has also gained traction recently. New approaches for traffic managementhave been proposed for terminal area scheduling that account for UAM constraints [9], and for managing dense trafficflows in unstructured airspace [10]. Fleet management rules and ground infrastructure constraints have been evaluatedand found to result in limitations on the operation of UAM ecosystems [6]. More generally, analyses of dense and highlyutilized airspace have shown a need for strategic traffic management to minimize risk [11]. The topic of fairness and itsrelation to traffic management has shed light on the importance of designing proper traffic management policies in afederated system with a number of self-interested stakeholders [12].System level studies have been done for networked transportation ecosystems in the past. The problem of fleetmanagement and the associated behaviors in the system that emerge has been examined in on-demand autonomouscar networks [13, 14], for autonomous drone fleets with delivery applications [15], and in multi-modal transportsystems [16, 17]. These approaches consider a number of system-level constraints that may be applicable to UAMoperations. However, they provide limited analysis of design system-of-system wide design decisions and theirrelationships in the broader transportation ecosystem. Certain frameworks do examine the transportation network designproblem from an optimization perceptive [18], and consider how the impact of constraints and design decisions impactemergent, system-wide performance characteristics [19]. The design objectives generally do not consider characteristicsof interest typical to UAM such as on-demand operations and limited constraints at network nodes, leaving feasibilityand performance of an urban air transportation systems poorly understood. Approaches for maximizing throughputin transportation networks have been proposed as well [20, 21], however little work has been done on analyzing theconstraints that are critical to UAM related to vertiports and the on-demand nature of the operations. A recent collectionof system-levels analysis for UAM [22] is perhaps the most closely related work to what is presented in this paper.While that work provides a comprehensive analysis of operation scaling constraints for UAM, it provides quantitativesimulation results at a single vertiport level and does not evaluate performance of the UAM ecosystem as a whole.Overall, a system level quantitative analysis and design of the UAM ecosystem is not widely covered in existing literature,and this work aims to fill that gap. 2 able 1 UAM ecosystem design variables considered in this work and whether they are frozen or varied in ouranalyses.
Design Variable Variable Type Variable FrozenVertiport Capacity Long-Term Strategic VariedVertiport Locations Long-Term Strategic FrozenVertiport Ops Constraints Long-Term Strategic FrozenFleet Size Short-Term Strategic VariedUAM Route Network Short-Term Strategic FrozenFleet Management Policy Tactical Varied
III. Problem Formulation
In this work, we are interested in the problem of UAM ecosystem design. To that end, we want to evaluate theperformance of the UAM ecosystem with respect to a number of design variables that correspond to critical ecosystemcomponents. Specifically, we want to evaluate the impact that design variables of interest have on performance metricssuch as demand throughput, average passenger delay, and design variable sensitivities. We focus on nominal operationsthat are disturbance free. Additionally, we model stochastic demand profiles, and uncertainty driven properties of thevariables of interest such as vehicle turn-around time at vertiports. We leave system degradation events that couldemerge from vehicle system failures or weather events for future work. We organize the design variables into threecategories, roughly based on the time-horizon from the start of a UAM operation when these variables must generallybe chosen. The categories are illustrated in Fig. 1 and are described further below.
Fig. 1 UAM design decision variables and the associated time-horizon for when these decisions may be made.
We split the design variables into long-term strategic, short-term strategic, and tactical categories. The long-termstrategic variables are those that take on the order of years to modify and are most commonly related to the infrastructureof a UAM ecosystem. The short-term strategic variables are attributed to the UAM fleet and the route design in anetwork, requiring months to change. The tactical decisions are related to the fleet and traffic management componentsand may be made on the order of days or even hours. The above categorization of the variables helps shed light onthe impact of long-term, short-term, and tactical decision on the performance of the UAM ecosystem, with the goalof understanding at which point in the design cycle certain decisions must be made, and at which point they begin toimpact decisions downstream. We describe the design variables that are appropriate for each category in the sectionsbelow, and summarize them in Table 1. In the following sub-sections, we describe the design variables analyzed in thiswork and the time categories they fall into, as well as their associated modeling assumptions.
A. Long Term Strategic Design Variables
We consider a design variable to be long-term strategic when it would take on the order of years to modify itsubstantially. While all of of the variables in the long-term strategic category considered in this work are related to theUAM ecosystem infrastructure, such as the design decisions related to vertiports, a number of other critical designvariables exist in this category. For example command and control (C2) communication links are a critical componentof the UAM ecosystem that may require years of design and approval time due to it’s safety critical nature and thecomplexity of the problem [23]. However, these types of design decision are typically difficult to put into variable form,3nd we leave their analysis and how they fit into the larger UAM ecosystem as part of future work.
1. Vertiport Capacity
UAM vehicles need vertiports to land, recharge or refuel, await passengers and at times perform maintenance. Thetotal capacity of vertiports in a UAM network determines the maximum fleet size that can serve that network whichultimately determines the maximum demand rate the network can serve. Furthermore, we introduce a variable callednormalized vertiport capacity, which quantifies the relationship between the total capacity of the vertiports in a UAMnetwork and the total fleet size used to service it. Given the total size of a fleet serving a UAM network f , and the totalcapacity of all the vertiports that comprise the network c , the normalized vertiport capacity takes the following form: c n = cf . (1)This metric can capture a simple measure of the available space in a UAM network for a given fleet. For example, anetwork with c norm = c norm = c norm >
1, the UAM network has capacity that is greater than the size of the fleet using it. On the other hand c norm <
2. Vertiport Geographical Locations
Deciding geographical locations for vertiports is a challenging problem [24]. The location choice of vertiports musttypically consider trade-offs between passenger demand and noise concerns in addition to other critical factors, andcan be typically parameterized by a latitude and longitude value. Ultimately, the geographical locations of vertiportsdetermine demand rates and aircraft travel time which are critical operational factors within the UAM ecosystem. Dueto their cost and complexity, it may take years to build or relocate a vertiport. The constraints brought by vertiportgeographical locations are, thus, considered long term.
3. Vertiport Operation Constraints
Vertiport operations can be a complex process with a number off critical factors that must be considered. In thiswork, we focus on constraints related to arrival and departure procedures, in and out of vertiports, and constraintsassociated with the design decisions on maintenance, recharging or battery-swaps, and passenger loading. Becausethese constraints are closely tied to the vertiport design, they are considered long term. Fig. 2 shows the notional modelused to represent a vertiport in this work. It is based on commonly found models in literature [6]. In the model, avertiport consists of landing and takeoff zones and a location for maintenance and passenger loading. For vertiportswhere maintenance and passenger loading can be performed directly or nearly directly to the landing zones, ∆ t taxi times may be negligible and can be set to zero. The airspace near a vertiport can be structured into approach fixesand departure fixes which are fixed approach and departure waypoints the aircraft must use. Upon arrival, aircraftapproach a vertiport through its approach fixes. Then aircraft land in the landing and takeoff zones, may taxi to anotherarea, unload passengers, and may require maintenance procedures such as battery replenishment and safety inspections.Once the aircraft are ready for flight, they depart from the vertiport through the departure fixes. To maintain sufficientseparation in the vertiport airspace, only a limited number of approach fixes and departure fixes can be implemented.They can limit the number of aircraft landing or taking-off. Metering can be applied at the fixes to control the trafficflow through a vertiport [25]. We consider the times outlined in Fig. 2 to be long-term design variables due to theirstrong link to the underlying vertiport infrastructure. Additionally, the separation standards around vertiports are oftenset in place by regulators and are enforced the traffic management system and the participating operators [24]. Theydirectly guide the design of approach and departure fixes, which are also considered long-term design variables . B. Short Term Strategic Design Variables
Short-term strategic design variables can be modified on the order of months.4 anding& TakeoffZone(s)ApproachFix(es) DepartureFix(es)PAX Loading,Maintenance,Recharge ∆ t landing ∆ t takeoff ArrivalTraffic ∆ t arrival separation DepartureTraffic ∆ t departure separation Taxi in ∆ t taxi in Taxi out ∆ t taxi out Turnaround ∆ t turnaround Fig. 2 Vertiport abstract structure and operation flow.
1. Fleet Size
The UAM vehicle fleet is a critical component in the UAM ecosystem. The fleet size, denoted by f , can dictate anumber of critical UAM operational characteristics including the maximum demand rate d max a UAM ecosystem canserve. The choice of fleet management policies may also be dictated by the size of the fleet serving the UAM ecosystem.To more directly tie this design variable to others, we derive a simple upper bound ˆ d max for the maximum demandrate a fleet of size f may fulfill. It is expected that beyond this demand rate, the passenger delay times in the UAMecosystem will increase exponentially [6, 26]. This rate can be represented by a ratio between the total time resource ofa fleet T available , which represents the net time the fleet is available for UAM operations, and the average end-to-end timerequired to complete an operation T operation by a single vehicle in the fleet. An estimate of the maximum demand rate isgiven by d max ≤ ˆ d max = T available / ∆ tT operation = fT operation , (2)where ∆ t is a unit time period and T available = f ∆ t . While we refer to ˆ d max as the maximum demand rate a UAM networkand the fleet operating within it can serve, it can also be considered a maximum capacity determined by the long-termand short-term strategic design variables. In this paper, the limiting design variables dictating Eq. (2) are the vertiportgeographic locations, vertiport capacities, and the fleet size. Because the maximum demand rate is estimated usingstrategic design variables, it can also be considered the maximum throughput an effective fleet management policy canachieve in a fixed UAM network with a fixed fleet size. We assume fleet size to be a short term strategic constraint sinceit can take on the order of months to permanently increase or reduce the size of a fleet.
2. UAM Route Network
The underlying routes that UAM vehicles can use to fly between vertiports comprise the UAM route network. Theplacement of a route between two vertiports can depend on a number of factors such as demand, vehicle performancecapability, noise considerations, and the avoidance of no-fly zones [24]. Because the UAM route network ultimatelydetermines where and how vehicles can fly, a given route structure can drive a number of critical UAM operationalcharacteristics including the maximum demand rate d max a UAM ecosystem can serve. For a fixed set of vertiports in aUAM network, it is assumed that creation or removal of routes would be possible but may require substantial efforts andapprovals that could require extensive time, making this design variable short-term strategic In this work, we assume aroute network can be modeled as a graph with vertiports represented by graph nodes and the routes that connected bygraph edges.i 5 . Tactical Design Variables Tactical design variables in the UAM ecosystem are those that can be characterized as dynamic, and can be alteredon the order of days or hours.
1. Fleet Management and Re-balancing
The traffic management strategies primarily considered in this work are related to fleet re-balancing. The primaryfunction of fleet re-balancing lies in ensuring that the vehicle fleet is distributed at appropriate nodes of a transportationnetwork in a way that enables efficient fulfillment of demand. Vehicle re-balancing has been well studied in groundtransportation systems and networks. Smith et al. [27] propose an optimal re-balancing strategy to ensure the stability ofthe on-demand taxi transportation system by modeling traffic flow as fluid. Rossi et al. [28] model a traffic congestionproblem within a network flow framework and show a computationally efficient routing and re-balancing algorithmfor autonomous vehicles in on-demand operation. While fleet management and planning has been well studied incommercial aviation [29–31], literature for on-demand operations like UAM is limited and fleet re-balancing has notbeen deeply examined at the time-scales relevant to UAM.The on-demand nature of emerging transportation systems has transformed mobility in recent years. It is likely thatsome users of the UAM ecosystem will prefer to request operations in an on-demand way as well. Such on-demandsystems can lead to downstream problems requiring fleet re-balancing. Specifically, a fleet that does not follow a fixedand optimized schedule, can end up distributed through the transportation network in a way where it can not meet thedemand in the system. This can lead to poor system performance and significant inefficiencies. Practically, this meansthat in extreme cases, some vertiports may be at capacity with no room left for incoming flights; while other vertiportsmay be empty and have no idle aircraft to carry out an incoming operation request. Effective fleet re-balancing can helpmitigate and, in some cases, prevent these issues in the UAM ecosystem.While a number of re-balancing strategies are possible, in this work, we consider the following:•
Space-driven re-balancing works by trying to keep the fleet evenly distributed within the UAM network. Thisalso allows congested vertiports to be naturally freed up when the strategy is applied, creating a free landingspace for the departing flight at its destination, and potentially minimizing any air-holding. An example scenariowhere space-driven re-balancing is useful is when a large number of flights arrive at a vertiport and take up all ofthe landing spaces. With space-driven re-balancing, flights that landed at this vertiport will takeoff to nearbyvertiports with free landing spaces even if no operation request exists for that flight.•
Demand-driven re-balancing attempts to re-balance the fleet in order to meet anticipated demand in the UAMnetwork. An example scenario where demand-driven re-balancing is useful is when a customer requests a flightat a vertiport with no available aircraft. Instead of passively waiting for the next aircraft to arrive according toincoming demand, the strategy routes an idling aircraft, which may be empty, from a nearby vertiport to carry outthe operation request.Look-ahead adjustment can be made to the two re-balancing strategies by tuning the numeric threshold used to trigger are-balancing operation. A naive strategy may include simple thresholds on when the re-balancing flights take place.In this work, we improve on this heuristic and show that it significantly improves performance. For example, forspace-driven re-balancing, a naive threshold triggers a re-balancing flight when a vertiport is full. The look-aheadadjustment triggers re-balancing flights prior to the vertiport filling up completely, creating a buffer for emergentconditions. For demand-driven re-balancing, a naive threshold is triggering re-balancing flights when a vertiport isempty. The look-ahead adjustment triggers re-balancing flights when the number of idling aircraft at a vertiport dropsbelow some threshold. In general, we expect re-balancing flights to be empty (not carrying passengers), so it is criticalthat they are kept to a minimum.
2. Operation Rule: On-demand versus Scheduling
Operating on-demand is a natural way to answer stochastic requests for UAM missions, particularly when thoserequests are sparse [5, 32]. Its counterpart is a scheduled operation where flights depart at predetermined times [33].Both strategies have to consider a number of trade-offs, and one may be more appropriate for a certain operationalprofile than another. For example, on-demand operations generally require fleet re-balancing which consumes a portionof fleet resource; while scheduled operation can lead to long delays especially when requests are sparse.6 . Design as Optimization
Using the design variables described in the previous sections, we can formulate UAM ecosystem design problem asan optimization. While a number of critical design choices exist in the UAM ecosystem, we chose the following inthis work: the UAM fleet represented by a set of UAM vehicles f , the design choices of individual vertiports in theecosystem V , vertiport network configuration N , and the fleet management policy Π . For a given demand model D ,we want to minimize the a cost J with respect to the design variables, and subject to constraints on design variables, aswell as constraints on UAM ecosystem performance such as customer satisfaction, energy and safety as given in Eq. (3).minimize f , V , N , Π J ( f , V , Π , N , D) subject to feasible vehicle design ( f , V , N ) , feasible infrastructure cost ( f , V , N ) , separation ( f , V , Π , D , N ) ≥ minimum safe separation requirements . (3)In the following sections, we consider the various properties of a cost function appropriate for such an optimization.Typical cost profiles could include operational metrics such as system wide delay or average monetary cost of a flight.Additionally, the monetary costs of infrastructure related to f , V , and N could be considered. Constraints of theoptimization problem include but are not limited to feasible vehicle design, feasible infrastructure cost, and minimumseparation between vehicles for safety consideration. In this work, we consider constraints for a minimum separationrequirement and constraints that bound UAM vehicle range within expected bounds [34]. By ensuring that distancesbetween vertiports fall within vehicle range bounds, we ensure that constraint is met. IV. Simulation Based Analysis for UAM Ecosystem Design
It is difficult to quantify the operational performance of the UAM ecosystem using a single mathematical model.By using simulation, we are able to model individual components of that ecosystem and evaluate its performancemetrics through emergent operational properties. Using this approach, we are able to 1) analyze the feasibility of UAMecosystem operations, 2) analyze the impact of demand-capacity balancing on operational performance, 3) analyze theimpact of infrastructure and fleet constraints on the ecosystem, and 4) optimize the performance of the network withrespect to design parameters.
A. Simulation Modeling Assumptions
We use an event driven simulator in this work. The simulator models high-level operational states a vehicle mightfind itself in under a nominal operational profile such as takeoff, landing, and maintenance. We represent each entityusing a probabilistic model known as a Markov process, where each transition between states and the times spent ineach state are governed by a probabilistic model. Uncertainties regarding state transitions or times of transition can beincorporated directly into the probabilistic representation used in this work.Aircraft Event CycleArrival DepartureReady ∆ t takeoff ∆ t en − route ∆ t landing ∆ t turnaround ∆ t idling until operationrequest received ∆ t ground − holding untildeparture fix available ∆ t air − holding untillanding spaceand approach fixavailable Operation Center Fig. 3 Markov process for UAM operation simulation.
Fig. 3 shows the simulation event cycle for a single operation as a Markov chain. In this formulation, an operationcan be represented as a Markov chain ( Fig. 2). Starting from the “Ready” state, an aircraft idles for ∆ t idling untilreceiving an operation request. An operation request is generated by sampling a random distribution, and passed intothe model through an operation center. Then the aircraft enters the “Departure” state, holding for ∆ t ground-holding until adeparture slot is available. Then it takes-off with ∆ t takeoff , and spends ∆ t en-route to fly towards the destination vertiport.7pon arrival at destination, the aircraft is held airborne for ∆ t air-holding until a landing space and an approach fix areavailable. Then it lands with ∆ t landing . After spending ∆ t turnaround for turnaround procedures, the aircraft will be in the“Ready” state again.We make a number of simplifying assumptions to ensure that the event-driven simulation is tractable and can scale.In the context of our framework, these assumptions can be considered frozen design variables. We leave the analysis oftheir impact on the performance of the UAM ecosystem as future work. The assumptions are as follows:1) Concept of operations and configurations of vertiports:• a single operator is using the airspace and vertiports in the region• operations are in the nominal range, and disturbances such as weather and aircraft system failures are notconsidered• dynamic interactions with manned traffic are not explicitly considered, with UAM operations assumed touse dedicated corridors that do not interfere with manned traffic• all the vertiports and their properties are the same in a UAM network• a vertiport has the ability to accept a single arrival or departure if available capacity exists• preparation (turnaround of aircraft) for flight happens in a location in the vertiport separate from thelanding and take-off zone2) Airspace structure:• flight corridors are pre-defined in the UAM network to avoid collisions [35]• no hard limit is placed on how many aircraft can be placed in an air-holding pattern at the same time• the airspace of a vertiport has one approach fix and one departure fix• appropriate separation requirements are assumed to be met when an aircraft is using the defined approachand departure fixes3) Rules of sequencing and spacing:• “first come, first served” for demand dispatching, landing and takeoff sequencing• separation is enforced pre-flight through time based deconfliction B. Time Utilization in the UAM Ecosystem
The primary measures used to quantify the operational performance of the UAM ecosystem considered in this workare based on time utilization of the aircraft. The level of passenger satisfaction, the energy consumption requirementsof the fleet, the monetary cost of the operation, and the operation capacity can all be expressed in terms of a timevalued measure. Specifically, we consider the average time a vehicle spends in a given state or set of states as part of anominal operation profile (as shown in Fig. 3). The times of interest for this work are outlined in Table 2 along withtheir definitions. We assume the time metrics are random variables, with expected values computed empirically usingthe statistical averages for those times in simulation.
Table 2 Segments for time utilization analysis of a UAM ecosystem.
Metric Starting time Ending time ∆ t demand delay Operation request submitted Aircraft carrying out the request takes-off ∆ t idling Aircraft is prepared for flight Request is matched with a readied aircraft ∆ t ground-holding Aircraft is mission ready Aircraft takes-off ∆ t en-route Aircraft takes off Aircraft lands at destination vertiport ∆ t air-holding Aircraft enters the destination airspace Aircraft starts landing ∆ t re-balancing Re-balancing aircraft takes-off Re-balancing aircraft lands
C. Stochastic Demand Models
Operation requests are the driving force of the UAM ecosystem. One way of modeling request generation ismodeling it as a Poisson process. We can sample the number of requests generated in a time period from a Poissondistribution, which we refer to as the temporal demand model. A trivial model is a temporally uniform demand modelwhere demand rate is time independent [24]. A uniform model is not realistic, but useful for examining the steady-stateperformance of a UAM ecosystem. Due to the time-varying nature of UAM demand, we are interested in modeling time8 able 3 Design variables used in the system performance analysis.
Vertiport Capacity Fleet Size Fleet Management PolicyVariable Value Varied 36 Varied dependent demand rate as well. A more realistic model includes a time modulated demand rate, where demand ratechanges with respect to time. Using a Gaussian mixture model [5], we are able to emulate peaks and lows in demand forUAM operations. We then generate operation requests using a time-varying Poisson process parameterized by demandrates sampled from the Gaussian mixture model. By shifting the center and height of Gaussian mixture peaks, we cancreate geographically imbalanced demand rates for different vertiports to emulate load imbalance among routes which isa common phenomenon seen in ground transportation. From left to right in Fig. 4 shows examples of a temporallyuniform demand model, temporally modulated demand model and imbalanced demand model for vertiports.0 10 200510 Time (hours) D e m a nd R a t e ( / hou r) Fig. 4 From left to right 1) temporally uniform demand model, 2) temporally modulated demand modelusing Gaussian mixture, and 3) geographically imbalanced demand models using Gaussian mixture for a three-vertiport UAM network, three different colors indicate the different demand profiles associated with each ofvertiport.
V. System Performance Analysis
In this work, we consider a conceptual UAM ecosystem in the San Francisco Bay Area. For simplicity, we assumethere are three vertiports located near three major airports in the area (SFO, SJC and OAK). All the vertiports are directlyconnected by UAM routes, and are within the operational range of the UAM vehicles serving them on a single batterycharge. We leave more complex vertiport configuration optimization, and route structure analyses for future work. Fig. 5shows the vertiport locations and connected routes in the UAM network. We configure the mean turnaround time to 10min, with a standard deviation of 5 minutes based on average times a vehicle may spend between landing and beingoperation ready [36]. We set the average aircraft cruise speed to 140 km/h, with a nominal operational profile followingthe Markov process outlined in Fig. 3. In this analysis, we fix the fleet size, but vary the vertiport constraints and the fleetmanagement policy (see Table 3). We examine the delays, time utilization, and throughput metrics for time-independentand time-modulated demand models. Additionally, we analyze the results in the context of the UAM network capacitywhich is a function of fleet size and average operation time computed in Eq. (2), it is found to be ˆ d max = . A. Temporally Uniform Demand Model
First, we analyze operational performance under a time-independent uniform demand model where the averagedemand rate is a constant with respect to time. Fig. 6 shows the demand delay, or the time delay between the desired9FO OAK SJC
Fig. 5 A conceptual UAM network in the San Francisco Bay Area where three vertiports are located near threemajor airports. All vertiports are connected. and the actual start times of an operation as the average demand rate in the ecosystem increases. We see little impactof increasing vertiport capacity on the demand delay metric in the emergent system. However, the choice of fleetmanagement policy has significant effects on the delay metric. We observe that the on-demand + re-balancing policyleads to shorter demand delays at all demand rates evaluated. This is expected as the policy accounts for the stochasticnature of passenger demand in the system, and attempts to uniformly distribute the UAM fleet reducing delay times. Alack of a re-balancing policy leads to larger delays, as an imbalanced fleet can both create congestion at vertiports wherevehicles are idle and lack of readied vehicles for operations when requests come into the system. The relatively largedelays at lower demand rates for scheduled operations are surprising, and lead to a U shaped curve for the scheduled fleetmanagement policy. This can be explained by the very low frequency of scheduled flights that occur at lower demandrates. There is a natural analogy in ground transportation in for this phenomenon. A bus schedule in rural areas leads torelatively infrequent bus runs, and showing up at a random time of day to ride it can lead to long wait times; however thebus schedule in busy urban area can be lead to more frequent bus runs, leading to a shorter wait time for passengers.
10 20 30 40 50 60 700204060 Demand per Hour D e m a nd D e l a y ( m i n ) On-demand w/o re-balancing On-demand w/ re-balancing Scheduled Estimated ˆ d max
10 20 30 40 50 60 70Demand per Hour a Normalized Vertiport Capacity = 1 b Normalized Vertiport Capacity = 2Fig. 6 Demand delay analysis of UAM ecosystems with normalized vertiport capacity set to 1 and 2 under auniform demand model.
15 21 30 45 60 750100200 Demand per Hour A v e r a g e T i m e U tili za ti on ( m i n ) Passenger/En-route Air-holding TurnaroundIdling Re-balancing or Over-scheduled Scheduled operationOn-demand operation w/o re-balancing On-demand operation w/ re-balancing9 15 21 30 45 60 75Demand per Hour a Normalized vertiport capacity = 1 b Normalized vertiport capacity = 2Fig. 7 Time utilization analysis of UAM ecosystems with normalized vertiport capacity of 1 (left) and 2 (right)under a uniform demand model.
Fig. 7 shows a bar plot of time utilization for the three fleet management policies evaluated in this work as a functionof demand. We use time metrics introduced in Section IV.B to compare how much time a vehicle spends in various statesbetween operations. Specifically, we analyze the time a vehicle spends en-route, air-holding, idling, in a maintenance orturnaround state, and in a re-balancing or over-scheduled state. Time spent re-balancing or over-scheduled implies thata vehicle is flying empty to either re-balance the fleet or to perform its scheduled flight without a passenger. Largernormalized vertiport capacity significantly reduces and in certain cases eliminates the air-holding time of the on-demandpolicy with no re-balancing. This occurs because additional vertiport capacity allows more vehicles to idle at a vertiport.Without re-balancing and with limited vertiport capacity, en-route operations may enter an air-holding pattern whenthere is no room to accommodate them at the destination. Without re-balancing, the only mechanism that createsroom for an en-route operation in a full vertiport is an outgoing operation. We note that increased vertiport capacityhas negligible impacts on the other two fleet management policies. The results also show that fleet re-balancing isan effective way of preventing air-holding by freeing up used capacity at congested vertiports. As the demand rateincreases, air-holding time and re-balancing time both decrease. This occurs because a high demand rate drives trafficflow, and in a uniform demand setting can naturally re-balance the fleet.
Fleet re-balancing creates additional trafficflow that can geographically re-distribute a UAM fleet in a more uniform way . We note that when the demand rateexceeds the estimated capacity from Eq. (2), idling trends towards zero. At this stage the fleet is being fully utilized byeither carrying passenger or being prepped for carrying passengers in the turnaround state. We note that while fleetutilization is maximized, on an operation by operation basis, passengers experience large delays once the capacity of theUAM ecosystem is exceeded.Fig. 8 shows the throughput analysis for the temporally uniform demand model. Throughput is defined as theaverage hourly rate of completed operations in the ecosystem. The line marking unimpeded throughput indicates athroughput rate that is equal to the demand rate. The figure also shows per hour rates for operations completed within aspecific delay window ranging from 1 minute to 2 hours. From Fig. 8, we observe that normalized vertiport capacity haslittle impact on net average delay and the overall throughput of the system. Additionally, the average throughput beginsto flatten beyond ∼
75 operation requests per hour for all of the fleet management policies, which coincides with theestimated capacity bound for the UAM network, which was found to be 67.5 operations per hour. However, the delayperformance differs drastically between fleet management policies. Specifically, we observe increasing system-widedelays as the management policy changes from re-balancing, to non re-balancing, to scheduled.11 A vg . C o m p l e t e d O p e r a ti on s ( / h r) On-demand, w/ re-balancing, c n = < < <
15 minDelay <
30 min Delay <
60 min Delay <
120 min Estimated ˆ d max On-demand, w/o re-balancing, c n = c n =
10 20 40 60 80 100020406080100 Average Demand Rate (1/hr) A vg . C o m p l e t e d O p e r a ti on s ( / h r) On-demand, w/ re-balancing, c n = c n = c n = Fig. 8 Throughput analysis for the temporally uniform demand model with normalized vertiport capacity c n = and c n = .B. Temporally Modulated Gaussian Mixture Demand Model We perform similar analysis on a temporally modulated Gaussian mixture demand model with equally weightedcomponents where the time varying demand is proportional to d ( t ) ∝ Normal ( t ; 8 , ) + Normal ( t ; 12 , ) + Normal ( t ; 16 , ) where t is given in hours [5]. This demand model simulates peak hours at 8 AM and 4 PM, moderate demand rate atnoon and close to zero demand rate at midnight. The middle figure in Fig. 4 illustrates this Gaussian mixture modelwith 25% noise. We control the total demand rate by adjusting the peak demand rate of the model, and it is with respectto the peak demand rate that the results are presented. Fig. 9 shows the demand delay analysis of the conceptual UAMecosystem with normalized vertiport capacity of c n = c n =
2. A higher vertiport capacity is not shown to havemajor impacts on the delays. Additionally, we observe an improvement in the performance of the fleet managementpolicy without re-balancing and a worsened delay performance for the fixed schedule fleet management policy.Fig. 10 shows the time utilization as a function of peak demand rate. Similar to the results under a uniform demandmodel, a larger vertiport capacity significantly reduces air-holding time for on-demand operation without re-balancing,and we observe the policy with re-balancing avoiding air-delays while operating fewer empty flights than a fixed schedulepolicy. While the fixed schedule policy reduces idling time, it leads to the largest faction of operations flying emptypre-scheduled flights. In fact, a time varying demand model leads to a higher ratio of empty flights compared to the ratioof empty flights for a uniform demand model. Naive fixed scheduling approaches will be difficult to apply efficiently todynamic demand profiles, and we see significant gains in operating an on-demand policy in this work. However, it ispossible that demand may adjust to scheduled operations which could improve performance. While it is possible thatsystem performance under a scheduling policy can be improved, further analysis of scheduling optimization for UAMoperations is left as future work.Fig. 11 shows the throughput analysis for the temporally modulated Gaussian mixture demand model. Similarto the results for uniform demand model, vertiport capacity does not play a significant role on average net delays.12 D e m a nd D e l a y ( m i n ) On-demand w/o re-balancing On-demand w/ re-balancing Scheduled10 20 30 40 50 60 70Peak Demand per Hour a Normalized vertiport capacity = 1 b Normalized vertiport capacity = 2Fig. 9 Demand delay analysis of UAM ecosystems with normalized vertiport capacity of 1 and 2 under Gaussianmixture demand model. A v e r a g e T i m e U tili za ti on ( m i n ) Passenger/En-route Air-holding TurnaroundIdling Re-balancing or Over-scheduled Scheduled operationOn-demand operation w/o re-balancing On-demand operation w/ re-balancing9 15 21 30 45 60 75Peak Demand per Hour a Normalized vertiport capacity = 1 b Normalized vertiport capacity = 2Fig. 10 Time utilization analysis of UAM ecosystems with normalized vertiport capacity of 1 and 2 under aGaussian mixture demand model
The on-demand policy with re-balancing shows the best throughput profile overall with a large fraction of operationsseeing very low delays ( < >
30 min) as average demand rate increases over 30 per hour. The majority of operations undera fixed schedule policy tend to fall within delays 5 to 15 minutes. The throughput values for all policies plateau anddegrade at lower demand rates than those in temporally uniform demand analysis. This is because the temporallynonuniform demand rate can be low at non-peak hours and large at peak hours. The peak hour demand rate is higherthan the average demand rate (around twice of average in this particular Gaussian mixture demand model). The demandpeaks can cause cascading effects that makes the UAM ecosystem reach its capacity at a lower average demand rate thanwhen it is operated with a temporally uniform demand model. The estimate of capacity given by Eq. (2) is therefore anover-estimate for a more realistic time varying demand model.13 A vg . C o m p l e t e d O p e r a ti on s ( / h r) On-demand, w/ re-balancing, c n = < < <
15 minDelay <
30 min Delay <
60 min Delay <
120 min Estimated ˆ d max On-demand, w/o re-balancing, c n = c n =
10 20 40 60 80 100020406080100 Average Demand Rate (1/hr) A vg . C o m p l e t e d O p e r a ti on s ( / h r) On-demand, w/ re-balancing, c n = c n = c n = Fig. 11 Throughput analysis for the temporally modulated Gaussian mixture demand model with normalizedvertiport capacity c n = and c n = .Table 4 Design variables used in the ecosystem design optimization analysis. Vertiport Capacity Fleet Size Fleet Management PolicyVariable Value Varied Varied On-Demand + Re-balancing
VI. Ecosystem Design Optimization
In this section, we perform UAM design variable optimization with respect to a cost function that is based on systemwide performance metrics. We use a similar simulation configuration as in Section V, with a three vertiport network,operations cruising at 140 km/h, and mean turnaround time at vertiports of 10 minutes. However, we fix the fleetmanagement policy to be the best performing policy we found in the previous section, on demand with re-balancing.We vary both the fleet size and the vertiport capacity. The goal of this analysis is to determine the sensitivities of systemperformance to strategic design variables like vertiport capacity and fleet size, when a performant fleet managementpolicy is used (see Table 4).
A. Cost Function Design
A cost aware decision process has been used in a number of application in aviation, including in green airline fleetplanning [31]. We extend the formulation to consider variables and metrics of interest for UAM. We denote the cost J marginal , which quantifies the overall performance of the UAM ecosystem, and use it to guide the choice of designvariables relevant to UAM. We consider the cost J marginal to be “marginal” because it is the result of subtracting thenominal operation cost from the total operation cost, where the nominal operation cost only includes the basic cost forfulfilling the demand that exists within the ecosystem. The cost from any unfulfilled demand is reflected in the costassociated with delays. Additional cost induced by re-balancing or over-scheduled flights is also included in the cost14unction. Idling cost is added to represent the cost for fleet maintenance. The cost function J marginal is defined as follows J marginal = ( c idling T tot, idling + c ground-holding T tot, ground-holding + c air- holding T tot, air-holding + c cruising T tot, additional cruising + c takeoff T tot, additional takeoff + c landing T tot, additional landing + c demand delay T tot, demand delay )/ T simulation , (4)where the c ’s represent various cost coefficients or weights whose values are either roughly proportional to energyconsumption rates of different phases of operation [5], or to a rough estimate of the cost of incurred delays as in c demand delay . Subscript “additional” indicates that time is only accumulated for additional flights made in addition tocustomer requests (re-balancing or over-scheduled flights). Time T simulation stands for the total simulation time duration.The weight assignments of cost coefficients are list in Table 5. Table 5 Weight of cost coefficients
Cost coefficients Weight per time step c idling c ground-holding c air-holding c cruising c takeoff c landing c demand delay B. Ecosystem Design Optimization
We first evaluate the cost as a function of demand, and show only the results for the time varying demand model forbrevity. Fig. 12 shows the marginal operation cost as a function of peak demand with normalized vertiport capacity of 1and 2. Overall, on-demand operation with fleet re-balancing persistently performs better then the rest two operationrules. In Fig. 12b, on-demand operation without re-balancing performs as good as re-balanced on-demand operationunder high normalized vertiport capacity up until peak demand rate reaching 45 per hour.
We again find that increasingnormalized vertiport capacity leads to improved performance when no fleet re-balancing exists, but is not significantlyeffective when fleets are managed with a re-balancing policy or are under a schedule.
In the remainder of the section weconsider on the on-demand with re-balancing fleet management policy as it is shown to be the most pefromant.
10 20 30 40 50 60 7005001 ,
000 Peak Demand per Hour C o s t On-demand w/o re-balancing On-demand w/ re-balancing Scheduled10 20 30 40 50 60 70Peak Demand per Hour a Normalized vertiport capacity = 1 b Normalized vertiport capacity = 2Fig. 12 Marginal operation cost analysis of UAM ecosystem with normalized vertiport capacity of 1 and 2unde a temporally modulated Gaussian mixture demand model.
15e now examine, how the strategic UAM ecosystem design variables can be chosen in a way that minimizes themarginal operation cost J marginal . We fix the fleet management policy which is a tactical design variable, and vary boththe vertiport capacity, and the fleet size in this analysis. Fixing the tactical design variable, allows a simplification thegeneral optimization formulation Eq. (3) to a reduced optimization problem Eq. (5).minimize f , V J marginal ( f , V , Π , N , D) (5)Using simulation, we can approximately evaluate the whole design space using a discretized grid search. The vertiportconfiguration V we optimize over is the normalized vertiport capacity c n . We jointly optimize the cost with respect tofleet size f . We search over f ∈ { , , , . . . , } and c n ∈ { . , . , . . . , . } . F l ee t S i ze
15 21 27 33 39 45 51 57 N o r m a li ze d V e r ti po r t C a p ac it y C o s t (a) 3D surface plot.
15 21 27 33 39 45 51 573.02.82.62.42.22.01.81.61.41.21.0 Fleet Size N o r m a li ze d V e r ti po r t C a p ac it y C o s t (b) 2D heat map. Fig. 13 The results of UAM ecosystem design optimization through grid search under the Gaussian mixturedemand model with the peak demand at 30 flight per hour. The optimal point is indicated with the red dot.
The results of UAM ecosystem design optimization through grid search are plotted in Fig. 13 where Fig. 13a showsa 3D surface plot for the cost, and Fig. 13b shows a 2D heat map for the cost. The optimal design point through gridsearch is a fleet size of 36 and a normalized vertiport capacity of 2.0, with the optimal cost being 35.9. We can seefrom the landscape of the cost function that it is high under small fleet size and low vertiport capacity, where it ismore sensitive to the fleet size design variable. The cost is relatively flat as fleet size and vertiport capacity exceedssensible threshold levels. This relatively flat landscape in the cost function indicates that once reasonable values havebeen chosen for long-term strategic and short-term strategic design variables like vertiport capacity and fleet size, theperformance of the UAM ecosystem is most impacted by fleet management policy as highlighted in the previous section.We explore the sensitivities of the cost to each design variable further. Fig. 14 analyzes the sensitivity of eachvariable at the optimal point. We vary one of the design parameters while treating the other as a fixed value andevaluating the deviations from the optimal cost upon the variations of a single design variable. The results of sensitivityanalysis shed light on how designers of a UAM ecosystem can evaluate the risk of a potential wrong decision about adesign parameter. A design parameter that leads to less sensitivity in the cost may need minimal adjustment or none atall to improve the performance of the UAM ecosystem. Fig. 14a shows the sensitivity of the optimal cost and vertiportcapacity with respect to fleet size. Optimal cost is shown to have minimal sensitivity to changes in fleet size around itsoptimal value. We see a similar trend for changes in vertiport capacity, as the relatively large fluctuation in fleet sizedoes not lead to significant fluctuation in the cost. This indicates that the cost, and thus ecosystem performance haslow sensitivity for vertiport capacity values near the optimal point. Fig. 14b shows the sensitivity of the optimal cost16 ∆ O p ti m a l C o s t Vicinity boundOptimal point ∆ Optimal cost20 30 40 50 60 − − . . ∆ V e r ti po r t C a p ac it y ∆ Vertiport Capacity (a) Changes of the optimal cost and the correspondingoptimal normalized vertiport capacity as the fleet sizevaries from its optimal point. ∆ O p ti m a l C o s t Vicinity boundOptimal point ∆ Optimal cost1.0 1.5 2.0 2.5 3.0 − −
505 Normalized Vertiport Capacity ∆ F l ee t S i ze ∆ Fleet Size (b) Changes of the optimal cost and the correspondingoptimal fleet size as the vertiport capacity varies fromits optimal point.
Fig. 14 The sensitivity of the optimal point. and fleet size with respect to normalized vertiport capacity. The sensitivities to changes in the fleet size and vertiportcapacity design variables are again minimal. Both results imply that vertiport capacity and fleet size are low riskvariables in the UAM ecosystem design process for the configurations tested in this work. Once a sensible value forthese variables has been picked, the ecosystem is likely to be high performing even if the capacity value is not theoptimal for the configuration in question. We again note, that the performance of the ecosystem is tightly coupled to thefleet management policies, and the results shown here are valid when proper fleet re-balancing and management policiesare applied.
VII. Conclusion and Future Work
In this work, we examined the performance of a UAM ecosystem operating under nominal conditions using a varietyof UAM ecosystem design choices in simulation. We categorized these design variables into categories that representeddecisions on the strategic long-term, strategic short-term, and tactical time horizons. By evaluating the performancemetrics such as throughput and delay time in the ecosystem, we were able to quantify the impact of various designchoices on the operational ecosystem. We found that design variables that fall into the tactical time horizon categorysuch as choice of fleet and traffic management policies have a significant impact on system performance. While designvariable corresponding to long-term and short-term strategic decisions such as vertiport capacity and fleet size werefound to have less impact on system performance so long as they fell into a suitable range of values. The strategic designvariables are generally considered difficult to modify and typically represent design choices that must be made monthsor even years prior to seeing the design choice operational. In short, we show that it is possible to design a performantUAM ecosystem, even when the vertiport network and the fleet serving it have not been optimized for the emergentdemand profile. Instead, an effective fleet management policy can play a significant role in how the system performsoperationally, and must be optimized to .For future work, we plan to explore how our results generalize to more complex system disturbances and off-nominaloperational profiles. Specifically, we want to examine whether fleet and traffic management play as critical of a role17nder these conditions as they do during nominal operations. A wider range of design variables will also be exploredin future work such as more complex vertiport configurations. Additionally, we plan to explore more complex fleetmanagement policies, and derive their theoretical performance properties in the UAM ecosystem. Lastly, we would liketo consider how multiple operators that share resources in the UAM ecosystem impact the total system performance. Thedesign choices in a multi-operator UAM ecosystem would be driven by both the system managing coordination betweenoperators, such as a UTM, the resource allocation policies for resources that are shared, and the fleet managementpolicies each operator chooses to implement. Such design choices have been shown to have significant impact on theefficiency and the fairness of the ecosystem as a whole [12, 37], and must be better understood in the context of thebroader UAM ecosystem.
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