IEEE-ITS, SPECIAL ISSUE ON UNMANNED AIRCRAFT SYSTEM

IEEE-ITS, SPECIAL ISSUE ON UNMANNED AIRCRAFT SYSTEM TRAFFIC MANAGEMENT 1

Efficiency and Fairness inUnmanned Air Traffic Flow Management

Christopher Chin, Karthik Gopalakrishnan, Maxim Egorov, Antony Evans,and Hamsa Balakrishnan, Member, IEEE

Abstract—As the demand for Unmanned Aircraft Systems(UAS) operations increases, UAS Traffic Flow Management(UTFM) initiatives are needed to mitigate congestion, and to en-sure safety and efficiency. Congestion mitigation can be achievedby assigning airborne delays (through speed changes or pathstretches) or ground delays (holds relative to the desired takeofftimes) to aircraft.

While the assignment of such delays may increase systemefficiency, individual aircraft operators may be unfairly im-pacted. Dynamic traffic demand, variability in aircraft operatorpreferences, and differences in the market share of operatorscomplicate the issue of fairness in UTFM. Our work considersthe fairness of delay assignment in the context of UTFM.To this end, we formulate the UTFM problem with fairnessand show through computational experiments that significantimprovements in fairness can be attained at little cost to systemefficiency. We demonstrate that when operators are not alignedin how they perceive or value fairness, there is a decrease in theoverall fairness of the solution. We find that fairness decreasesas the air-ground delay cost ratio increases and that it improveswhen the operator with dominant market share has a weakpreference for the fairness of its allocated delays. Finally, weimplemented UTFM in a rolling-horizon setting with dynamictraffic demand, and find that efficiency is adversely impacted.However, the impact on fairness is varied and depends on themetric used.

Index Terms—Air transportation; Unmanned Aircraft Systems(UAS); UAS Traffic Management (UTM); Traffic Flow Manage-ment; fairness; efficiency

I. INTRODUCTION

THE potential of Unmanned Aircraft Systems (UAS) todramatically transform societal applications (including

infrastructure and environment monitoring, agricultural sur-veys, communication services, cargo delivery, and even pas-senger mobility) is expected to lead to a significant increasein autonomous aircraft operations. It has been estimated thatby the year 2035, Paris may see as many as 2,500 UrbanAir Mobility (UAM) flights, 16,000 delivery drones, and 60inspection drones flying each hour of the day [1]. Otherurban areas are projected to see a 200-fold increase in thenumber of flights due to Unmanned Aircraft Systems (UAS)operations (autonomous drones for package delivery, sensormeasurements, surveillance, tracking, etc.), and a 30-fold in-crease from UAM operations (autonomous, semi-autonomous,or piloted air taxis) [1], [2]. These operations will be largely

C. Chin {chychin}, K. Gopalakrishnan {karthikg} and H. Balakrishnan{[email protected]} are with the Department of Aeronautics and Astronautics,Massachusetts Institute of Technology, Cambridge, MA, USA.

M. Egorov {maxim.egorov} and A. Evans {[email protected]} arewith Airbus UTM, Sunnyvale, CA, USA.

concentrated around dense urban regions, in the proximity ofexisting airports, and will involve significant investments intechnology and infrastructure [3].

The increase in UAS traffic demand will inevitably resultin congestion in the air as well as at vertiports (low footprintairports in urban areas designed to support vertical takeoffsand landings). The entire US National Airspace System (NAS)currently handles about 90,000 flights a day, whereas UAStraffic operations are projected to exceed 2.5 million flights perday in the US [4]. The resultant strain on the air transportationinfrastructure, if not managed, could result in decreased levelsof safety, and increased economic losses and emissions. Theincrease in vehicle- and system-level autonomy will enablethe better utilization of limited resources, but the need for aUAS traffic management system will remain, especially forlow-altitude operations. The development of a UAS TrafficManagement (UTM) architecture, and the associated proto-cols, strategies, and infrastructure, is essential for the safe andefficient operations of autonomous aircraft.

Despite the excitement surrounding UAS/UAM operations,several questions regarding UTM architectures remain unan-swered. These open problems include the choice between acentralized and a more federated or distributed architecture,the role of a UAS Service Supplier (USS) in managing trafficand interfacing with air traffic controllers, assurances on thequality of service provided to users of the airspace, andthe possible timelines for the deployment of UTM solutions[1]. The focus of this paper is the development of strategictraffic flow management techniques for UAS/UAM operations.Prior work has shown that tactical and decentralized conflictresolution protocols are effective at low traffic volumes [5]–[7]; however, they are likely to be less efficient as traffic levelsincrease. Our work is motivated by the recognition that inhigh-demand scenarios, centralized resource allocation has thepotential to increase overall efficiency and safety. Furthermore,by strategically planning ground holds and airborne trajectorymodifications, we can reduce the amount of tactical coor-dination required of UAS, remote pilots, and USS, therebyimproving predictability.

A. Motivation for UAS Traffic Flow Management (UTFM)

Our approach to UTFM is primarily motivated by fourobservations. Firstly, in order to scale UAS/UTM operationsto meet the increasing demand, it is important to operateefficiently and minimize delays (in this context, delay canbe defined as the difference between the desired and actual


times of operation). Secondly, the equitable and fair allocationof airspace resources is important, especially in the presenceof a large number of aircraft operators; yet, fairness is oftenthe first casualty in the quest for efficiency [8], [9]. Thirdly,UAS operations are likely to result in competing interestsand strategic behavior on the part of the various participants,including first-mover advantages and attempts to monopolizethe airspace by aircraft operators. It is essential that theairspace, as a public good, remains accessible to all. Finally,the lessons learned from conventional traffic managementshould be leveraged in the design of a flexible, future-proofnext generation aviation infrastructure.

The overarching goals of our approach to UTFM are to:1) Explicitly incorporate fairness into traffic flow man-

agement decisions while accommodating user-specificfairness requirements.

2) Support a range of aircraft operator preferences andvehicle capabilities, as reflected in their delay sensitivity,mission requirements, and operator utility functions.

3) Support dynamic traffic demand, thereby enabling novelapplications such as on-demand mobility, exploration,quick package delivery, etc.

B. Prior workThe UTFM problem is an extension of the conventional

Air Traffic Flow Management (ATFM) problem, which canbe used to assign ground delays and speed restrictions toscheduled flights, in order to mitigate congestion [10]–[12].The optimal assignment of ground delays and airborne delaysto flights can be formulated as a large-scale optimizationproblem. Recent efforts have resulted in tractable approachesto this classical problem [13], [14].

Fairness in allocating scarce airport resources has beenexplored in prior work [15], [16]. With regard to jointlyallocating airport and airspace resources (as in ATFM), threenotions of fairness have been defined: reversals [17], over-takings [17], and time-order deviation [18]. Related workin ensuring fair trajectory-based operations has consideredmax-min fairness [19], cost-penalty formulations [20], as wellas notions of accrued delay [21]. This extensive body ofwork emphasizes the importance that the aviation communityhas placed on fairness and the wide range of meaningfuldefinitions of fairness in this context. Our work considersthese different notions of fairness in the context of UTFMand highlights the differences between them.

The UTFM problem has been the topic of recent research[6], [14]. While [6] addresses the problem by assigning flightsto different “layers” of the airspace, [14] proposes a distributedsolution approach based on column generation. Althoughfairness has been widely recognized as an important criterion[1], [9], it has only recently been explored in the contextof UTM and, even then, only for decentralized operatingparadigms [5], [22]. The limited work on addressing fairnessin strategic UTFM has involved monetary transactions, whichraises other practical challenges [23]. Furthermore, challengessuch as individual vehicle or aircraft operator preferencesover delays, fairness, and the lead-time for filing preferredtrajectories, have not been previously explored.

C. Contributions and main findings

This paper makes two key contributions to UTM research.Firstly, we develop a UTFM framework that incorporatesfairness, user preferences, and dynamic trajectory requestsinto the decision-making process. Secondly, we evaluate ourUTFM formulation using UAS/UTM demand generated froman industry-developed simulator, identify appropriate metricsfor fairness, and quantify the efficiency-fairness tradeoffs, inthe presence of operator preference variability and dynamictraffic demand.

Our main insights on the interplay between fairness andefficiency in UTFM can be summarized as follows:

1) Although several reasonable notions of fairness can beproposed in a networked setting, they are not all equallyeasy to achieve in practice. More precisely, we show thatsome of the metrics may be orthogonal to each other andthat optimizing for one may adversely affect another.

2) The preferences of different operators can vary in arange of ways (e.g., their preferences may be alignedbut differ in magnitude, or they may be misaligned), andthe resulting impacts on system efficiency and fairnesscan differ. More specifically, for the case of two aircraftoperators, we find that:• As the ratio of the airborne holding cost to the

ground holding cost increases, the fairness of theUTFM solutions decreases.

• The greater the divergence between the fairnesspreferences of the two operators (both in terms ofthe fairness metrics and the weights given to them),the greater is the loss in both system efficiency andfairness.

• When the operator with a weak preference forfairness has a high market share, the fairness ofthe resulting solution improves for both operators,relative to the solution where both operators haveeven market share.

3) UTFM with a rolling horizon framework leads to lowerefficiency and higher time-order deviation; however, thenumber of reversals is similar.

D. Outline

In Section II, we define candidate notions of fairness in thecontext of UTFM and identify the challenges that need to beaddressed. Section III presents the mathematical formulationof the resulting optimization problem. In Section IV, wedescribe the setup for the simulations, while in Section V,we discuss the results and findings. Finally, our conclusionsand proposals for future work are discussed in Section VII.

II. UAS/UAM TRAFFIC FLOW MANAGEMENT (UTFM)

In this section, we highlight the three main features ofour proposed UTFM framework: the consideration of fairness,variable aircraft operator preferences and vehicle capabilities,and dynamic traffic demand.


A. Fairness considerations

The revision of trajectories to mitigate congestion re-quires assigning delays to each flight (i.e. the aircraft takesoff/lands/accesses a region of airspace at a different time thanis desired by its operator). Depending on the desired trajectoryof a flight and the capacities of the airspace sectors it traverses,the amount of delay assigned to each flight can be different.Consequently, the objective of maximizing system efficiencyis equivalent to minimizing the sum of delay costs for all theflights. The resulting solution, although efficient, could havean uneven distribution of delays across flights and aircraft op-erators, raising questions of fairness. Additional considerationsinclude ensuring fairness across flights of differing durations,flights traversing different regions of the airspace, and flightswith varying performance capabilities.

When there is only one constrained resource (airspace sectoror vertiport), First-Come-First-Served (FCFS) at that resourceis a reasonable definition of fairness. However, when a singleflight traverses multiple congested resources and FCFS isenforced at each of them, the flight may get excessivelypenalized as delays from the first resource get compoundedfurther downstream in the trajectory (see example in Fig. 1).

Fig. 1. The purple drone joins the end of the queue at every constrainedresource, following a First-Come-First-Serve policy. The dotted purple linedenotes the desired trajectory, while the solid purple line denotes the realizedone.

Other notions of fairness may be preferable in this net-worked resource allocation setting. A few examples, whichwe will describe in greater detail later are:

1) As much as possible, maintain the scheduled arrivalorder of flights at each resource. In other words, if flightf1 was scheduled to arrive at a resource before anotherflight f2, then we prefer that it does so in the revisedschedule. In this case, a reversal is when f2 arrives atthis resource before f1. We will formalize this metricof fairness as minimizing the total number of flight-reversals across all resources.

2) Find the most constrained resource in a flight’s tra-jectory. This resource would introduce the maximumFCFS delay if it were the only constrained resourcepresent in the trajectory. One could argue that this is theminimum delay that a flight on this trajectory ought toendure, and the optimization should try to minimize, or

at least equalize any delay beyond this minimum valueacross flights. We will formalize this notion of fairnessas minimizing the time-order deviation (TOD) for allflights in the schedule.

Several nuances need to be addressed when incorporatingfairness into UTFM. A direct consequence of having multiplecandidate metrics of fairness is that it is not apparent whichone is better, or more widely acceptable to UAS operators.Although intuition would suggest that enforcing some degreeof fairness would result in a loss in system efficiency (i.e., thesum of flight delay costs will increase), the nature of this trade-off is not well understood. Furthermore, higher traffic demand,especially in urban areas, would result in a larger number ofcongestion points (airspace sectors or vertiports) for each flighttrajectory. Without explicit planning, the presence of multiplecongested resources can significantly decrease the fairness ofthe UTFM solution (e.g., Figure 1). It is therefore imperativethat we incorporate fairness at an early stage of system design,as concerns of unfairness will only grow with traffic volume.

Fairness in the networked setting has been studied in thecontext of air traffic control flow management [17], [18]. InATFM, airports typically remain the primary choke points,and the FCFS schedule emerging from a congested airportis usually prioritized over other constraints. However, such apractical approach cannot be translated to UTFM, since thereare multiple choke points.

B. Aircraft operator preferences and vehicle capabilities

While implementing UTFM in practice, one must be cog-nizant of significant differences that may exist amongst differ-ent users of the system. Potential aspects of variability include:• Mission requirements. The file-ahead time is how far in

advance an operator files a flight plan before the sched-uled departure time. UTFM should support on-demandoperations with short file-ahead times (e.g., package-delivery or UAM) as well as scheduled operations withlong file-ahead times (e.g., planned video inspections orfixed-schedule air taxis). Similarly, some missions suchas UAM or package delivery could require flying theshortest path to a destination, while others (e.g., plumetracking or traffic surveillance) could involve hovering oractively sensing and exploring a region.

• Vehicle capabilities. Some vehicles may have a widerrange of feasible speeds, resulting in a larger potential forairborne holding. Fixed-wing vehicles may not be ableto reduce their speed below a certain critical thresholdwithout the risk of stalling, whereas rotary-wing vehicles(like quadcopters) may be able to hover at a particularlocation and reduce their lateral speed to zero if needed.Vehicles may also have different endurance times andabilities to operate safely when subject to delays.

• Preferred metrics of fairness. Certain aircraft operators,such as those running supply and logistics missions,may have coordinated flight operations. For instance, onevehicle may bring a certain package to a warehouse anda drone scheduled for later may transport that packageto a customer. For such an operator, reversals in the


order of arrivals may be of significant consequence, andthey may wish to minimize the number of reversals inthe UTFM solution. On the other hand, a point-to-pointUAM operator may only be concerned about their on-timeperformance relative to competitors. A fair allocationwould then be one that results in an equitable distributionof delays for any two flights that use the same set ofresources. In such cases, minimizing the TOD might bethe preferred metric of fairness, rather than minimizingthe reversals.

• Aircraft operator cost/utility functions. An operator trans-porting packages might be more sensitive to delays thana leisure drone photographer. Even among the flightsmanaged by the package delivery operator, an aircraftcarrying perishable goods may be more delay-sensitivethan one carrying non-perishable goods.

Different operator preferences and vehicle capabilities mayaffect the tradeoffs between fairness and efficiency. Further-more, the notion of what is considered fair for a pair ofoperators may be the same (i.e. aligned) or different (i.e.misaligned). This can affect not only the system efficiency,but also determine the extent to which efficiency must becompromised to satisfy fairness preferences of the operators.The challenge lies in developing a UTFM framework that cannot only support diverse user preferences and constraints, butalso equitably allocate resources. Such a framework would bea significant departure from ATFM, where the vehicle capabil-ities are relatively homogeneous, and the limited variability indelay costs due to airline-specific factors (such as connectingpassengers, crew time-outs, etc.) are handled post hoc via theCollaborative Decision Making (CDM) process [15].

In a marked departure from traditional ATFM research, ourwork quantifies the loss in efficiency and fairness for differentoperator traffic volumes and preferences (delay sensitivity andfairness requirements) using a UAS/UAM demand simulatordeveloped by Airbus.

C. Strategic planning with dynamic traffic demand

The last feature of our UTFM framework that we wish tohighlight is its ability to adapt to temporally dynamic trafficdemand. In particular, we note that the file-ahead times for anaircraft operator (or vehicle) to convey its demand for airspaceor airport resources may be very short. Low traffic demandpredictability could correspond to two scenarios: missions maybe initiated with short lead times (e.g., on-demand UAM orpackage delivery), or they could be inherently uncertain dueto a reactive sensing control loop (e.g., a car chase using adrone, air pollution monitoring, traffic surveillance, etc.). Inother words, the file-ahead times could range from a few weeksfor scheduled services, to a few seconds for reactive sensingmissions.

Unfortunately, strategic planning requires some look-aheadand visibility into future demand. It is challenging to efficientlymanage a mix of scheduled as well as dynamic traffic demand.Furthermore, the UTFM problem needs to be solved frequentlyat scale, in near-real-time, owing to the high volume ofUAS/UTM traffic and dynamically changing flight plans. We

address this concern by implementing the UTFM solutioniteratively with a receding horizon to account for dynamicdemand and variable file-ahead times.

III. MATHEMATICAL FORMULATION

In this section, we present the main formulation for theUTFM problem. We describe two metrics to measure fairnessand show how they can be incorporated in the optimization.We first build off of the classical traffic flow managementproblem (TFMP) formulation [11].

A. Setup and Notations

We consider a discrete-time traffic flow management prob-lem. The mathematical notations used in the formulation aredescribed below.

T : Set of time periods {1, . . . , T} of length ∆TA : Set of all airportsS : Set of all airspace sectorsF : Set of all flightsO : Set of all operatorsFo : Set of all flights by operator o ∈ O

C(s, t) : Capacity of sector s ∈ S at time tA(a, t) : Arrival capacity of airport a ∈ A at time tD(a, t) : Departure capacity of airport a ∈ A at time t

af : Scheduled arrival time for flight f ∈ Fdf : Scheduled departure time for flight f ∈ FSf : Sequence of sectors in flight f ’s scheduleSfj : Next sector after j in flight f ’s trajectoryPfj : Sector preceding j in flight f ’s trajectory

origf : Origin airport for flight fdestf : Destination airport for flight flf,s : Minimum time spent by flight f in sector sM : Maximum delay for each flightT fj : Set of feasible time periods for flight f to arrive

at resource j ∈ A ∪ S (airport or sector)T̄ fj : Latest time in the set T fjTfj : Earliest time in the set T fjwfj,t : A binary variable that is 1 when flight f ∈ F

has arrived at resource j ∈ A ∪ S at or beforetime t

B. Baseline TFMP

The objective function minimizes total delay cost (TDC).The expression for total delay cost (TDC) is assumed to be ofthe form TDC = β(GD1+ε+αAD1+ε), where GD is grounddelay, AD is airborne delay, β is delay to cost scale factor,and α ≥ 1 is the ratio of airborne delay cost to ground delaycost. Note that ε makes these costs super-linear in the delayduration, as we prefer even distribution of delays across flightsover skewed delay distributions. For example, setting ε to be asmall positive number (≤ 0.05) guides the optimization solverto allocate 2 minutes of delay each for two flights rather than 4minutes of delay to a single flight, even though the total delaywould be the same for both solutions. In other words, thissuper-linear cost structure helps break ties between multiple


solutions that result in the same total system delay. Withoutloss of generality, we set β = 1.

Since, TD = AD +GD, we have

TDC = αTD1+ε + (1− α)GD1+ε (1)

If the flight departs at time t, then the ground delay is GD =(t − df ). Also, if the flight lands at time t, the total delay isTD = (t− af ). Thus, TDC can be re-written in terms of thedecision variables w as

TDC =∑f∈F

(∑

t∈T fdestf

α(t− af )1+ε(wfdestf ,t − wfdestf ,t−1)

−∑

t∈T forigf

(α− 1)(t− df )1+ε(wforigf ,t − wforigf ,t−1)) (2)

The key aspect of the formulation that lends computationaltractability to larger-scale problems is the choice of the de-cision variable wfj,t, which is a binary variable that is non-decreasing in time (Constraints (3g) and (3h)). Flight f is saidto enter a resource i (which could be an airport or a sector)at time t if (wfi,t − w

fi,t−1) = 1.

The following constraints must be satisfied:∑f∈F : origf=k

(wfk,t − wfk,t−1) ≤ D(k, t), ∀k ∈ A, t ∈ T

(3a)∑f∈F : destf=k

(wfk,t − wfk,t−1) ≤ A(k, t), ∀k ∈ A, t ∈ T

(3b)∑f∈F : i∈Sf ,j=Sf

i

(wfi,t − wfj,t−1) ≤ C(j, t), ∀t ∈ T (3c)

wfi,t = 0, ∀f ∈ F , t = Tfj−1, i = S ∪ A (3d)

wfi,t = 1, ∀f ∈ F , t = T̄ fj , i = S ∪ A (3e)

wfi,t − wfj,t−lf,j ≤ 0, ∀f ∈ F , t ∈ T fi ,

i ∈ Sf : i 6= origf , j = Pfj(3f)

wfi,t−1 − wfi,t ≤ 0 ∀f ∈ F , i ∈ Sf , t ∈ T fi (3g)

wfi,t ∈ {0, 1} ∀f ∈ F , i ∈ Sf , t ∈ T fi (3h)

Constraints (3a), (3b), and (3c) enforce departure, arrival,and sector capacities, respectively. Constraint (3d) ensures thata flight does not reach a sector before the earliest feasible time.Analogously, constraint (3e) enforces that a flight must arriveat a sector before the latest feasible time. The minimum timeto be spent in each sector is described in Constraint (3f).

C. Fairness Metrics

We focus on two candidate notions of fairness, which wedescribe qualitatively below. We then incorporate them intothe baseline TFMP formulation.

1) Reversals [17]: According to this notion, a fair solutionis one in which the relative ordering of arrivals at any resourceis preserved according to published schedules. We want tominimize reversals in the ordering of flight arrivals at a sectoror an airport relative to the originally scheduled ordering.

A few additional variables for incorporating reversals aredefined below.

Rj : Pairs of reversible flightsT rf,f ′,j : Set of time periods common for flights f and

f ′ where a reversal could occur at resource jλor : Penalty factor for reversals for operator o

We define a new variable sf,f ′,j which is 1 if flight f ′

arrives before flight f at resource j, where f was scheduledto arrive before f ′, and 0 otherwise. Thus, flight f suffers fromthe reversal, but flight f ′ benefits. In the objective function,we sum the previously defined TDC with the total number ofreversals suffered by an operator multiplied by a weight λor.

min TDC +∑o∈O

λor∑

j∈S,(f,f ′)∈Rj ,f∈Fo

sf,f ′,j (4)

The following constraint must be satisfied:

sf,f ′,j = max (0, wf′

j,t − wfj,t) ∀t ∈ T

rf,f ′,j (5)

2) Time-order deviation [18]: In this section, we describethe time-order deviation metric used to quantify fairness.We calculate the first-come-first-serve (FCFS) arrival timeFCFSfi for each flight f at resource i that it goes through,assuming that i was the only constrained resource. WithFCFS, arrival slots are assigned to flights according to theoriginal schedule ordering. For each flight, we then calculatethe maximum FCFS delay dFCFSf .

FCFSfi : First-come-first-serve arrival time forflight f at resource i assuming that i wasthe only constrained resource (i ∈ S ∪A)

dFCFSf : Maximum FCFS delay for flight fcfTOD(t) : Additional delay cost when flight f is

delayed for time tλot : Penalty factor for time-order deviation for

operator oJust as with the penalty factor for reversals, λot is opera-

tor specific. The intuition behind time-order deviation is asfollows. When there are multiple constrained resources, eachflight should not expect to incur any less delay than it wouldincur as a result of only the most constrained resource alongits route. In other words, there is a notion of expected delay,that every flight is inherently entitled to be assigned, andonly delays beyond this expected delay should be equalizedamong the multiple flights. Thus, for every flight f ∈ F , themaximum delay that it would have been assigned as a resultof only the most constraining resource is

dFCFSf maxi∈S∪A

FCFSfi (6)

Thus, the modified optimization problem is

min TDC +∑o∈O

λot∑f

T∑t=af

cfTOD(t)(wfdestf ,t−wfdestf ,t−1),

where cfTOD(t) = (max{0, t−af−dFCFSf })1+ε. (7)


Fig. 2. Example of a four-operator scenario in a 16 km × 14 km region, withflight trajectories showing the operations flown, the colors denoting differentoperators, and axis ticks along the border denoting 1km sector boundaries.

IV. EXPERIMENTAL SETUP

A. Scenario generation

We use a package delivery scenario created by Airbuswhere four operators in Toulouse, France have warehouseson the outskirts of the city and make deliveries in locationsrandomly distributed around the city [24]. The demand isgenerated using a Poisson process. Each flight has a desired4D trajectory (three spatial dimensions with time as the fourthdimension). For simplicity, only the outbound flight segments,from the warehouse to the delivery site, are considered. Weused two demand scenarios: 50 flights/hour and 25 flights/hourper vertiport. Fig. 2 shows the scenario with 50 flights/hour.For some experiments, we use a two-operator scenario, whichis generated by combining the black and green operations intoone operator and the red and blue operations into anotheroperator.

One of the key requirements of the UTFM formulation isthat time is discretized into timesteps. We rounded sector entryand exit times to the nearest 60 s (the timestep size) whileensuring that each flight spent at least one timestep in eachsector. We set a sector time discretization threshold of 3 sand skip a sector if a flight spent less than 3 s in it. Anotherrequirement of the UTFM formulation is that a flight may onlytraverse through a sector once. There were 8 instances wherea flight entered a sector multiple times; for example, it wasinitially in sector A then briefly left to sector B then reenteredA. We eliminated repeated sectors by smoothing the trajectoryand forcing the flight to stay in one sector the whole time.

An additional factor that we accounted for was that flightshad limited battery capacity, which we assumed to be 20 min.Thus, we used the remaining battery life and the unimpededtime-to-destination to calculate the maximum time durationthat a given flight could hold at its current sector at any pointin time. This gave a useful upper-bound on airborne delay foreach flight at each sector. Table I lists additional parameters.

TABLE ILIST OF PARAMETERS

Parameter ValueTimestep Size 60 s

Sector X-Y Dimensions 1 km × 1 kmSector Z Dimension (Height) 65 m

Sector Capacity 1 per sectorDeparture Capacity 2 per timestep

Sector Discretization Threshold 3 sMaximum Battery Life 20 min

Airborne Delay Cost to Ground Delay Cost Ratio α = 3

B. Fairness-efficiency tradeoffsWe seek to evaluate the fairness-efficiency tradeoff when

incorporating one of two fairness metrics: reversals or time-order deviation. We assume that all four operators’ notionsof fairness are aligned and penalized the same (effectivelyequivalent to having one operator). Recall that the weight thata fairness metric is given is represented by λor or λot . We varythese values to generate fairness-efficiency curves. We use totaldelay cost as the efficiency metric, as shown in (2). Note thattotal delay cost is distinct from total delay, as it penalizesairborne delay α times more than ground delay.

C. Ratio of airborne to ground delay costsOne of the key parameters in the UTFM formulation is the

airborne to ground delay cost ratio, α. When α > 1, grounddelay is preferred over airborne delay. The assumption is thatairborne delay is more costly than ground delay because ofhigher fuel/energy costs. In practice, α could vary and havea significant impact on not only the split between airborneand ground delay, but also notions of fairness. We evaluatethe impact of α on the baseline UTFM and UTFM whenincorporating reversals and time-order deviation.

D. Alignment of notions of fairnessWe expect that operators will often have not only different λ

weights of fairness, but also different notions of fairness. Forexample, an operator conducting deliveries where the order ofoperations is very important may care about reversals muchmore than time-order deviation. The effect of a reversal maypropagate downstream to the operators’ later operations. Onthe other hand, an operator passing through multiple con-strained resources may care more about time-order deviation(additional delay beyond expected delay) than reversals. Weconsider a case with two operators where one operator’s notionof fairness associated penalty factor is fixed and the otheroperator’s notion of fairness and penalty factor are variable.

E. Effect of market shareThere is concern that the market share of operators may

lead to unfair allocations of delay. Smaller operators may beeffectively crowded out by larger operators. As an initial step,we evaluate the effect of market share on system and per-operator efficiency and fairness in a case with two operators.We keep the total number of flights constant and randomlyselect the appropriate number of flights to switch operators.We test several market share splits in a two operator scenario.


F. Rolling horizon implementation

The standard UTFM formulation assumes that the demandis not only deterministic, but also known well in advance.Given the on-demand nature of many UTM applications, thisis not a safe assumption. One way around this challenge isto implement a rolling horizon version of the UTFM. Witha rolling horizon of length n minutes long, we propose tosolve the UTFM once for every time-interval of that length(i.e., every n minutes). Each flight must file their flight planbefore the start of the time-interval that contains its scheduleddeparture time. For example, if n = 5 min, we solve the UTFMat 6:00, 6:05, 6:10, and so on. Flights departing between 6:05and 6:10 must file before 6:05. At 6:05, all flights scheduledto depart between 6:05 and 6:10 are considered for planning(from takeoff to landing), and their revised schedule constrainsflights and resource capacities in subsequent time-intervals.For comparison, we also solve the baseline UTFM in an on-demand fashion such that one flight is scheduled at a time,in order of their scheduled departure time. We use a scenariowith four operators in this case.

V. RESULTS

A. Fairness-efficiency tradeoffs

In the baseline formulation, the objective function consistssolely of the total delay cost. When incorporating reversalsor time-order deviation in the objective function, we expecta trade-off between fairness and efficiency (measured withtotal delay cost). The total delay cost should either remainunchanged or increase as the fairness terms are added to theobjective and drive the solution away from the optimal totaldelay cost. In return, we expect fairness to increase.

The following figures evaluate two different fairness metricsand two different demand scenarios. Results are shown for ahigh demand scenario (vertiport demand of 50 flights/hour)and a low demand scenario (25 flights/hour). For each sce-nario, there is one data point in black for the baseline case,but several data points for reversals and TOD, correspondingto different λr and λt values, respectively. For this section, weassume that all operators have the same notion of fairness anddegree of preference. To conserve space, specific λ values areonly shown for one curve in Fig. 3, but the arrow shows thedirection in which λ increases.

Fig. 3 plots the average number of reversals and averagetotal delay cost per flight when solving the baseline UTFM(“Baseline”) and when incorporating reversals or time-orderdeviation (“Reversals” or “TOD”). Two baselines are shown,corresponding to the low demand (black square) and high de-mand scenario (black circle). We first look at the low demandscenario. The blue curve shows the results of incorporatingfairness to varying degrees, with the corresponding λr valueshown next to each point. As λr increases, the number ofreversals decreases and the total delay cost increases relativeto baseline. For small λr values, it is possible to reduce thenumber of reversals with no increase in total delay cost. Forexample, when λr = 0.4, the number of reversals per flightdecreases to 0.23 (compared to 0.54 in the baseline) withno increase in total delay cost. With further increases in λr,

Fig. 3. Reversals vs. Total Delay Cost (TDC) when incorporating differentfairness metrics. (The hourly demand level is shown in parentheses.)

decreases in reversals are smaller and become increasinglyexpensive in terms of the total delay cost. At λr = 10, theoptimal solution has only 3 reversals (equivalent to an averageof 0.03 reversals per flight) but an average delay cost per flightof 1.86 (a 19% increase compared to 1.56 in the baseline).Overall, the average number of reversals decays exponentiallywith increasing total delay cost. This is because to prevent apair of flights from being reversed, it may be necessary forone flight to incur excess delay. In the absence of limitationson the maximum delay that a flight can endure, the numberof reversals could be driven to zero at the cost of very hightotal delay.

For small λt, incorporating time-order deviation can leadto a decrease in the average number of reversals with littleto no increase in the total delay cost, especially for the highdemand scenario. However, incorporating time-order deviationdoes not decrease the average number of reversals as much asexplicitly incorporating reversals. For larger λt, the optimalsolution does not change and no further reductions in reversalsare apparent.

In the high demand scenario, the new baseline (shown asa black circle) has a higher average number of reversals andaverage total delay cost than the previous baseline correspond-ing to a demand of 25 flights/hour. This is expected, as morecongestion leads to more flight interactions and potential forreversals. Incorporating reversals in the objective has a similareffect as doing so with lower demand. The tradeoff curve hasa similar shape, and for very high λr, the average number ofreversals approaches zero while the average total delay costincreases substantially.

Fig. 4 is similar to Fig. 3 but shows the effect on time-order deviation. While penalizing reversals can drive its valueto zero, it is not possible to drive the average time-orderdeviation to zero when minimizing time-order deviation, nomatter how large λt gets. Recall that time-order deviation isdefined as assigned delay minus maximum expected delay (7).There are two ways to reduce system time-order deviation: 1)reduce system total delay or 2) shift delay from flights with


Fig. 4. Time-Order Deviation vs. Total Delay Cost (TDC).

positive time-order deviation to flights with delay less thantheir maximum expected delay. Thus, when the total delayhas been minimized and all flights have delay assigned thatis greater than or equal to their maximum expected delay, thetime-order deviation has been minimized. This appears to bethe case here, as minimizing only the total delay rather thantotal delay cost in the objective function in the high demandscenario leads to an optimal solution with the same 201 minof total delay seen with λt = 2. Whereas incorporating time-order deviation can slightly decrease reversals, incorporatingreversals results in up to a 17% increase in average time-orderdeviation in the low demand scenario and up to a 13% increasein the high demand scenario.

While the improvement in the average time-order deviationwhen penalizing time-order deviation may appear modest,there is another benefit. Since the cost coefficient for time-order deviation is a super-linear function, evenly distributedtime-order deviation is preferred over lopsided distributions.As such, incorporating time-order deviation also reduces thestandard deviation of time-order deviation across flights. As λtincreases, the standard deviation decreases; λt = 2 results in a27% decrease in the standard deviation of time-order deviationrelative to the baseline. As mentioned above, incorporatingtime-order deviation bounds the loss in efficiency (i.e., increasein total delay cost) while remaining robust to the choice ofλt. Note how much more total delay cost increases whenminimizing reversals compared to when minimizing time-order deviation in Fig. 3 and Fig. 4. These observations suggestthat time-order deviation may be a suitable fairness metric inpractice.

B. Effect of the airborne to ground delay cost ratio, α

Total Delay Cost (TDC) contains the parameter α, whichis the airborne to ground delay cost ratio. As α increases,airborne delay gets even more costly relative to ground delay,so ground delay is preferred over airborne delay. This can leadto an increase in total delay minutes, as one minute of airbornedelay may be replaced with two minutes of ground delay. We

confirmed this expected behavior. Less obvious is the impactof α on fairness.

Fig. 5. Impact of the airborne to ground delay cost ratio, α, on fairness whenλr = λt = 1.

Fig. 5 shows fairness/time-order deviation across differentα values when prioritizing different notions of fairness. λrand λt are both fixed to 1. For all prioritizations, increasing αgenerally leads to an increase in reversals and time-order de-viation. As delay is shifted from the air to the ground, grounddelays are assigned based on the most congested resourcein the trajectory. This conservative approach exacerbates theunfairness (e.g. reversals) for all the resources in the trajectoryrather than just remaining localized to the congested resource.Thus, when the system can afford airborne delays, there issignificant flexibility in assigning delays only when vehiclesinteract with congested resources. This helps improve thesystem fairness.

A UTFM solution prioritizing a particular fairness metricwill naturally perform the best with respect to that metric. Thisis highlighted in both the subfigures, where the fairest solution(lowest values) are for UTFM solutions incorporating reversals(top) and TOD (bottom), in terms of reversals and time-order deviation, respectively. Prioritizing time-order deviationperforms better (in terms of number of reversals) than thebaseline for α < 5 and slightly worse for α ≥ 5. Butprioritizing reversals performs worse than the baseline in termsof time-order deviation for all values of α.

C. Misaligned and imbalanced notions of fairness

The previous section described results when all operatorshave aligned notions of fairness and the same λ weight offairness. We refer to this scenario as a perfect alignmentof fairness. However, operators can have different efficiency-fairness trade-off preferences, as reflected by the λ valueor different notions of fairness itself (e.g. reversals or time-ordered-deviation). Whenever two operators have the samenotion of fairness, they are said to be aligned. Whenever twooperators have different notions of fairness (e.g., one prefers


Fig. 6. Operator efficiency and fairness with varying λ1t or λ1r , with fixedλ2t = 3. Operator 1 and 2 are misaligned when operator 1 prioritizes reversals,aligned when operator 1 prioritizes time-order deviation, and perfectly alignedwhen λ1t = λ2t = 3.

to minimize reversals while the other prefers to minimizeTOD), they are said to be misaligned. In this experiment,Operator 2 has the same λ weight of fairness for time-orderdeviation (λ2

t = 3), while Operator 1’s notion of fairness andλ weight vary, as shown in Fig. 6. Three subplots show thechange in total delay cost, number of reversals, and time-orderdeviation for each operator relative to a perfect alignment ofλ1t = λ2

t = 3. In this section, we refer to increases/decreasesrelative to perfect alignment as “increases” and “decreases”,respectively. Starting with the top subplot, we observe thatefficiency decreases in two cases: in the misaligned regionwith the operators having different notions of fairness andin the aligned region with λ1

t much higher than λ2t . In the

misaligned region, for λ1r ≤ 5 the decrease in total delay

cost from prioritizing time-order deviation for Operator 2is overridden by the worsening of total delay cost due tominimizing reversals for Operator 1. For λ1

r > 5, total delaycost increases for both operators. In the region near λ1 = 0,delay cost increases for Operator 1 and decreases for Operator2, but these mostly balance each other out. In the alignedregion where Operator 1 has a stronger fairness preferencethan Operator 2, Operator 1’s decrease in total delay cost isoutweighed by Operator 2’s increase.

As with efficiency, fairness decreases when one operator hasa much stronger notion of fairness than the other operator,in both the misaligned and aligned case. Looking at themiddle subplot of Fig. 6, for all misaligned cases, Operator1’s reversals naturally decrease since they are the only oneminimizing reversals, and Operator 2’s reversals increase. Forλ1r ≥ 10, the increase in Operator 2’s reversals outweighs

Operator 1’s decrease leading to an overall increase in numberof reversals, but for smaller λ1

r the total number of reversalsdecreases. The increase in Operator 1’s (and the system)number of reversals peaks around λ1 = 0. This is becauseOperator 1 has weak fairness preferences for either reversalsor time-order deviation, and minimizing either could reducethe number of reversals. Moving onto the bottom subplot ofFig. 6, in the misaligned region, Operator 1’s preference ofminimizing reversals increases time-order for both operators.In the aligned region, Operator 1’s time-order deviation in-creases if its fairness weight is lower than Operator 2’s butdecreases if its fairness weight is higher.

D. Effect of market share

Fig. 7. Effect of market share on Time-Order Deviation, with fixed λ1t = 0.5,λ2t = 1.0.

To test the effect of market share on fairness, we fix thefairness parameters in a two-operator setting. In this scenario,both operators care about time-order deviation, but Operator 1has a weaker preference for fairness than Operator 2 (λ1

t = 0.5and λ2

t = 1). We then vary the market share of Operator 1from 0.2 to 0.8 in increments of 0.1, as seen on the x-axis ofFig. 7. We switch the designated operator of an appropriatenumber of random operations to create a scenario with anygiven market share split. We run 50 experiments for eachmarket share split, with each experiment having the samenumber of flights per operator, but different flights belongingto each operator. The y-axis of Fig. 7 shows the change inaverage time-order deviation relative to average time-orderdeviation with equal market share on the y-axis. Fairnessimproves for both operators when the operator with weakfairness preference (Operator 1) has a higher market shareand the operator with strong fairness preference (Operator 2)has a low market share. In contrast, the fairness of Operator1 deteriorates if its market share is reduced.

One way to rationalize this is as follows. If an operator hasa very high λ (e.g., Operator 2) but a low market share, itwill be relatively easy to accommodate their requests without


penalizing other operators. On the other hand, if the marketshare of this operator was high, then the overall solution wouldpreferentially satisfy the fairness requirements of this operatorand might have to impose excessive penalties (in terms ofefficiency and fairness) on others.

E. Rolling horizon implementation

In this section, we discuss the results when using a rollinghorizon of varying size for the high demand scenario (50flights/hour). In Fig. 8, the total number of reversals vs.the total delay cost is shown for the case with no rollinghorizon (“Deterministic”), identical to the previous section,and cases with 15-minute and 5-minute rolling horizons. Notethat fairness is only incorporated among the flights that areplanned in a given horizon. We also show the result for solvingthe UTFM such that one flight is scheduled at a time in orderof their scheduled departure time (“Myopic UTFM”).

We first look at the impact of the rolling horizon in thebaseline case (no fairness metric incorporated). Recall thatin our implementation of the rolling horizon, flights fromthe previous time step cannot be changed, eliminating theability to shuffle those flights with flights from the currenttime step. While this lowers the number of reversals, it comesat the expense of total delay cost. Thus, compared to thedeterministic baseline, both of the rolling horizon baselines(15-minute and 5-minute horizons) have a lower number ofreversals and a higher total delay cost. Flights are planned forthe 5-minute rolling horizon with even less information thanwith the 15-minute rolling horizon; thus, it is not surprisingthat the total delay cost for the 5-minute rolling horizon isgreater than that of the 15-minute rolling horizon. The on-demand case has, by far, the highest total delay cost, whichmakes sense given that UTFM is only solved for one flightat a time. The solution results in 67 reversals, higher than the15-minute rolling horizon but lower than the 5-minute rollinghorizon.

Fig. 8. Reversals vs. Total Delay Cost (TDC), by length of rolling horizon.“Myopic” is when flights are planned one-by-one in order of scheduled timeof departure.

The 15-minute rolling horizon (depicted with orangehexagon points) is similar to the deterministic case, exceptthe decrease in fairness (reversals) is not exponential but

Fig. 9. Time-Order Deviation vs. Total Delay Cost (TDC), by length of rollinghorizon.

close to a linear decrease. Incorporating time-order deviationgenerally increases the number of reversals. With the 5-minuterolling horizon, incorporating reversals (green hexagon points)follows the expected behavior: decreasing number of reversalsfor increasing total delay cost. Also, the number of reversalsplateaus after very little increase in total delay cost. This islikely since fewer flights in each time step results in lessleeway to adjust schedules to untangle reversals. The myopiccase again has the highest total delay cost but also has muchhigher time-order deviation than all other results.

Fig. 9 is similar to Fig. 8 but shows time-order deviationinstead of reversals on the y-axis. When comparing the base-line points (in black), time-order deviation increases as thehorizon size decreases. As seen before, incorporating reversalsincreases time-order deviation, and this trend is seen acrossall horizon sizes tested. On the other hand, incorporatingtime-order deviation decreases time-order deviation in thedeterministic case and has more mixed results with the 5-minute and 15-minute rolling horizons.

An important consideration of the rolling horizon imple-mentation is the runtime, which we define as the computationaltime to optimize all the traffic demand (flights). As the horizonsize increases, more flights are included in each time-interval,adding additional variables to the TFMP formulation andleading to a longer runtime. On the other hand, a larger horizonsize means that fewer subproblems need to be solved. Forexample, the simulation lasts 87 min, so with a horizon sizeof 45 min, just two horizons (with several flights) are needed.In contrast, with a horizon size of 5 min, 18 horizons (eachwith fewer flights) are needed.

Fig. 10 shows how runtime varies for different horizon sizeswhen incorporating either reversals or time-order deviation(TOD). The runtime for the deterministic solution (i.e., allflights are known in advance) is also shown. With time-orderdeviation, total runtime decreases exponentially as horizonsize increases. With reversals, runtime decreases as horizonsize increases from 5 to 25 min, but increases thereafter. TheTFMP formulation with reversals requires more variables thanthe formulation with time-order deviation, and therefore takeslonger to solve for a larger number of flights. For all scenariostested, the total runtime is reasonable (at most about 5 min)


considering that the simulation spans nearly 90 min.

Fig. 10. Runtimes for different rolling horizon sizes.

VI. DISCUSSION OF RESULTS

A. Other metrics of fairness

A metric of fairness closely related to reversals is overtak-ings [17]. It quantifies the magnitude of reversals, i.e. measuresthe minutes by which a flight f1 arrives before an earlierscheduled flight f2 at a particular airspace sector or vertiport.Qualitatively, minimizing the total overtakings in the systemis very similar to minimizing reversals; this is backed up withexperimental evidence, but is not shown in this paper forbrevity (see [25]). A consequence of these two metrics beingclosely related is that individually optimizing for either oneresults in improvements in the other metric also. Essentially,paying a price in efficiency for either of the metrics gets youthe other for “free”.

Reversals and overtakings are two fairness metrics that havethe potential to be achieved in an absolute sense. By that, wemean that the total number of system reversals or overtakingminutes can be driven to zero, if there were no constraints onthe maximum delay for each vehicle. This is in contrast with ametric like TOD, where even a massive loss in efficiency maynot result in a TOD value of zero. Thus, one could present thecase for using metrics similar to TOD in practice, since theyare more resilient to poor design choices of λ, and enable aframework that limits inefficiency while incorporating fairness.

Another approach is to perform a First-Scheduled-First-Served allocation for each flight arriving at a constrainedresource. Under this approach, when a flight is excessivelydelayed at its first constrained resource and reaches the secondresource, it does not simply join the end of the queue; instead,the scheduled time of arrival at that resource determines thepriority ordering at the queue. This reduces the occurrence of“double penalties” where flights are delayed at one sector andthen further delayed at downstream sectors.

Lastly, we would like to highlight another natural definitionof fairness, the minimization of the variance in delays acrossflights. This can be achieved by penalizing total delays expo-nentially by setting a high ε in the baseline UTFM formulation.When ε is high, the optimal solution will tend to achieve a min-max fair solution, where it attempts to minimize the maximum

delay. The key takeaway from this discussion is that whilethere are several reasonable notions of fairness, they can beeasily incorporated in the UTFM formulation.

B. Implementing UTFM in a receding horizon framework

There are several nuances to implementing UTFM in adynamic traffic demand scenario, as each trajectory requestcan come with a different file-ahead time. Such scenarios canlead to interesting questions regarding the extent to whichUTFM should aggregate the demand to improve efficiency andfairness, while at the same time not being too aggressive inthe aggregation such that it induces artificial inefficiencies.

One possible implementation framework would be to ag-gregate all requests within a fixed time interval, say Tplan,and solve the UTFM problem. However, in the extreme casethat a vehicle files a request right after an interval is planned,it would have to endure an artificial delay of Tplan evenbefore it is assigned a revised trajectory. However, if a vehiclealways files ahead, with at least Tplan buffer, then it requestedschedule is guaranteed to be considered by the UTFM asfiled (an assumption we make when presenting our results inSection V-E).

A possible modification to the above strategy to eliminatethe artificial delays would be to solve the aggregate UTFMproblem for flights that file sufficiently ahead, but then followa Myopic UTFM strategy for flights with low file-ahead times.While this sacrifices fairness and does not help capitalizeon the efficiency gain due to coordinated planning, it wouldeliminate adding artificial delays.

In our current implementation, once a flight is scheduled,its schedule is fixed and it acts as a constraint to subse-quent flights. If we allow flights to be re-planned (potentiallychanging delay assignments), we may be able to improveefficiency and fairness. In ATFM there are practical humanfactors limitations to how often flights can be re-planned;the increased autonomy of UAS is likely to eliminate theseconcerns.

C. Varying aircraft operator delay utility functions

Our method is also adaptable and can minimize any utilityfunction that represents flight delay costs. We have also shownin our experiments that it is easy to incorporate operator- oreven flight-specific utility functions for the delays. In SectionV, we used a marginally super-linear delay cost function (tobreak ties and prefer a delay of 3 min each to two flights overa delay of 6 min to a single flight), but that need not be themost representative for all operators.

One reasonable utility function Ui that an operator i withdelay Di would like to minimize is [22]:

Ui(Di) =

β1

√Di, if Di < Dindifferent

β2Di, if Dindifferent ≤ Di < Dintolerable

β3D2i , if Di ≥ Dintolerable

where β1, β2 and β3 are constants that ensure continuity of theutility function. Other possible options involve step functions(representing a sharp increase beyond a threshold which can


happen due to cancellations), constant utility function (repre-senting irrelevance of delays for applications such as aerialphotography), or exponential functions (for extremely time-sensitive missions).

The utility function is incorporated into the formulation byspecifying the total delay cost as cftotal(t) = Ui(t), α = 1 andeliminating the ground hold reduction cfg = 0. Although nothighlighted in our examples, the delay utility function can alsodepend on both the ground and the air delay. An interestingconsequence of this formulation is that the complexity ofsolving the optimization does not change depending on thenature (e.g. linear, non-linear, convex, non-convex etc.) of theutility function.

VII. CONCLUSIONS

This paper explored the UAS/UTM traffic flow managementproblem with a special emphasis on the efficiency and fairnessof the resultant solution. In particular, we focused on theimpact of aircraft operators’ preferences, airborne to grounddelay cost ratios, and market shares on fairness. We consideredtwo metrics of fairness: the number of reversals and time-order deviation. We found that it is possible to improveeither of these fairness metrics at little cost to efficiency(i.e. little increase in total delay cost). We also found thatwhile minimizing reversals, time-order deviation increases, butwhen minimizing time-order deviation, the number of reversalscould also decrease.

We also evaluated the impact of aircraft operator preferenceson fairness and showed that as the airborne to ground delaycost ratio increases, fairness decreases. In a two-operatorsetting, system efficiency and fairness are both at their bestwhen the two operators have the same notion of fairness andvalue them to similar degrees. Additionally, fairness improveswhen the operator with dominant market share has a weakpreference for fairness. Finally, we considered UTFM in arolling horizon setting with dynamic traffic demand, and foundthat efficiency and time-order deviation worsen at shorterhorizons, while the number of reversals is unaffected.

We are currently pursuing several extensions of this re-search. We are looking at how operator delay cost functionsimpact efficiency and fairness, particularly when operatorshave different delay costs. We are also adapting the rollinghorizon framework to include the re-planning of airborneflights that have already been scheduled. This approach wouldbe useful in scenarios where flights do not comply with theirassigned 4-D trajectories. We also intend to test scenarios withheterogeneous operators (e.g., simultaneous urban air mobilityand package delivery operations). Finally, we are interested ininvestigating the impacts of strategic (gaming) behavior on thepart of the aircraft operators on fairness.

ACKNOWLEDGMENTS

This work was supported in part by A3 by Airbus undercontract number 40008574, and by NASA under grant number80NSSC19K1607.

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