Exploratory Data Analysis for Airline Disruption Management
EExploratory Data Analysis for Airline DisruptionManagement (cid:63)
Kolawole Ogunsina ∗ , Ilias Bilionis , Daniel DeLaurentis Abstract
Reliable platforms for data collation during airline schedule operations havesignificantly increased the quality and quantity of available information for ef-fectively managing airline schedule disruptions. To that effect, this paper appliesmacroscopic and microscopic techniques by way of basic statistics and machinelearning, respectively, to analyze historical scheduling and operations data froma major airline in the United States. Macroscopic results reveal that majorityof irregular operations in airline schedule that occurred over a one-year periodstemmed from disruptions due to flight delays, while microscopic results val-idate different modeling assumptions about key drivers for airline disruptionmanagement like turnaround as a Gaussian process.
Keywords: airline disruption management, data analysis, machine learning
1. Introduction
Despite overcoming numerous financial and technical challenges over thelast century through continued drive towards innovation and productivity, acomplete solution to irregular operations in the airline industry has remainedelusive. A major driver that has significantly stunted the progress in developing (cid:63)
This article represents one full chapter from the corresponding author’s completed doctoraldissertation. ∗ Corresponding Author
Email addresses: [email protected] (Kolawole Ogunsina), [email protected] (Ilias Bilionis), [email protected] (Daniel DeLaurentis) School of Aeronautics and Astronautics, Purdue University, United States. Department of Mechanical Engineering, Purdue University, United States. School of Aeronautics and Astronautics, Purdue University, United States.
Preprint submitted to Machine Learning with Applications February 9, 2021 a r X i v : . [ s t a t . A P ] F e b full solution for airline disruption management is poor data integration andintegrity.Internal data containing real-time information about an airline’s resourcesand its scheduled utilization over time, and external data for factors such ascurrent and future weather forecasts, competitor activities, and air traffic con-trol are necessary for efficient operations (Nathans, 2015). These bits of infor-mation and data must be readily available and accessible to represent driversand constraints for scenarios induced by irregular operations, so as to facili-tate the development of effective self-governing platforms for airline disruptionmanagement. In addition, whenever a new airline system is replaced or up-graded, new data sources are typically integrated into the existing framework(Gershkoff, 2016). The new data must be maintained for both existing and newapplications, and thus present cost-intensive challenges for mitigating disruptionbecause many facets of the airline infrastructure are impacted.While there have been consistent improvements to the existing decision sup-port systems used by human controllers in the Airline Operations Control Center(AOCC), two factors have continued to limit the performance of the disruptionresolutions that are applied. First, the decision support systems do not ex-plicitly proffer solutions to specific schedule disruptions, and as such, humancontrollers in the AOCC are required to be reactive in addressing disruptionsby using their best judgement based upon their prior experience from resolv-ing the same (or similar) disruption. Second, majority of the decision support(computer) systems used by multiple departments in an airline (including theAOCC) and other air transportation stakeholders (e.g. airports) are not de-signed or developed at the same time nor by the same vendor (Nathans, 2015).As such, information and data are required to be entered into multiple computersystems thereby exposing human controllers in the AOCC to data input prob-lems and errors. As such, information entered into a decision support systemfor disruption management may be out of sync with other systems and yieldincorrect decisions due to lack of data integrity.In the bid to improve data integrity for existing decision support systems,2irlines have significantly invested in creating better localized data collectionplatforms within their respective organizations, which can amass informationfrom different sources within and outside the organization that is easily accessi-ble through a centralized data server (Amadeus IT Group, 2016). As such, thereis a need to fully leverage the ubiquity and accessibility of information (data)collected by existing platforms in the AOCC to enhance agile decision-makingcapabilities of the AOCC during airline disruption management. To this effect,this paper provides a comprehensive discussion on exploratory analysis adminis-tered on historical scheduling and operations recovery data supplied by a majorairline in the United States, which serves as the basis for the development ofcredible predictive and prescriptive models for airline disruption management.The next section in this paper provides an overview of the elements of his-torical scheduling and operations recovery data retrieved from a major U.S.airline, followed by a section that expansively discuses several relevant and in-terrelated processes for exploratory data analysis. We conclude with a sectionon a summary of pertinent findings.
2. Data Overview
The raw data utilized for demonstrating the exploratory analysis discussedin this paper was provided by Southwest Airlines. Like many major U.S. air-lines, Southwest Airlines employs an integrated AOCC organization whereinall functional roles share the same physical space (at the airline’s headquartersin Dallas) and are hierarchically dependent on AOCC Supervisors for multipleproblem dimensions in airline operations recovery (Hagel et al., 2017). As thelargest carrier in the United States in terms of originating domestic passen-gers boarded with more than 4,100 flight schedule operations daily to over 100destinations, the supervisors (and controllers) at Southwest Airlines NetworkOperations Control (SWA-NOC) seek to use technology to see the impact oftheir decisions to make better ones for improved disruption management. Formany years, the controllers at SWA-NOC relied on gut instincts to track and3nderstand how their disruption resolution actions cascaded throughout the air-line’s network, but could not inform their instincts with data. To address thisissue, upper management at SWA-NOC created the Baker workgroup; an in-tegrated team of supervisors and software developers dedicated to improvingdecision-making during disruption management by developing and enhancing asuite of computerized decision support systems called the Baker tool. In orderto better support the Baker tool, the workgroup created an autonomous datacollection platform to record flight schedules that are subject and not subjectto different disruption incidents in the Southwest Airlines route network.As such, the raw data generously provided to us for the research discussed inthis paper contains approximately 1.1 million instances of direct flight schedulesfrom the Southwest Airlines route network operations recorded from September2016 to September 2017; of which there are 620,000 flight schedules that were notsubject to disruptions, over 430,000 flight schedules that were subject to flightdelays, and approximately 26,000 flight schedules that were either cancelled ordiverted. The instances of disrupted flight schedules (i.e. delayed, cancelledor diverted flight schedules) are distributed across eleven separate functionalroles in SWA-NOC (i.e. the AOCC) that represent primary disruption reso-lution domains for aircraft, crew, and passenger problem dimensions in airlinedisruption management. Table 1 reveals a list of functional disruption resolu-tion domains in the Southwest Airlines Network Operations Control, includingthe corresponding problem dimensions they seek to address, and the class ofdisruption and the number of instances of different effects of a disruption classfor a specific functional domain. The disruption class defines the origination ofa specific disruption, and as such, disruptions resolved by functional domains inSWA-NOC with a “controllable” disruption class indicate that all instances ofdisrupted flight schedules associated with those domains were caused (or couldhave been avoided) by the airline. Conversely, disruptions resolved by functionaldomains in SWA-NOC with an “uncontrollable” disruption class indicate thatall instances of disrupted flight schedules affiliated with those domains were notcaused (nor could have been avoided) by the airline. A brief description of the4 a b l e : D i s r up t i o n o u t l oo k f o r f un c t i o n a l d o m a i n s i nS o u t h w e s t A i r li n e s n e t w o r k o p e r a t i o n s c o n t r o l f r o m S e p t e m b e r t o S e p t e m b e r F un c t i o n a l D o m a i n A ff e c t e d P r o b l e m D i m e n s i o n D i s r up t i o n C l a ss D e l a y e d F li g h t S c h e du l e I n s t a n c e s C a n c e ll e d F li g h t S c h e du l e I n s t a n c e s D i v e r t e d F li g h t S c h e du l e I n s t a n c e s C u s t o m e r H o l d A i r c r a f t a nd P a ss e n g e r C o n t r o ll a b l e , D i s pa t c h C S C A i r c r a f t a nd C r e wC o n t r o ll a b l e , F l i g h t O p e r a t i o n s C r e wC o n t r o ll a b l e , , F u e l M a n a ge m e n t A i r c r a f t C o n t r o ll a b l e , G r o u n d O p e r a t i o n s A i r c r a f t a nd P a ss e n g e r C o n t r o ll a b l e , I n fl i g h t C r e wC o n t r o ll a b l e , M a i n t e n a n ce A i r c r a f t C o n t r o ll a b l e , N A S A ll U n c o n t r o ll a b l e , , S ec u r i t y P a ss e n g e r C o n t r o ll a b l e , T ec h n o l o g y A ll C o n t r o ll a b l e , W e a t h e r A ll U n c o n t r o ll a b l e , , Customer Hold : This functional domain addresses disruptions relatedto holding aircraft for passengers on inbound flight connections and hold-ing aircraft to accommodate passengers off cancelled and delayed flights.As such, the customer hold functional domain resolves the aircraft andpassenger problem dimensions in airline disruption management. Disrup-tion instances for the customer hold domain accounted for about 11% ofdelayed flight schedules in the Southwest Airlines route network over theone-year period (i.e. September 2016 to September 2017).2.
Dispatch CSC : This functional domain manages disruptions related toflight dispatch activities by the airline that also includes holding flights toaccommodate international flight schedule slot times. To that effect, theDispatch CSC functional domain addresses the aircraft and crew problemdimensions during disruption management, and disruption instances re-lated to Dispatch CSC represented 4% of delayed flight schedules in theairline operations between September 2016 and September 2017.3.
Flight Operations : This functional domain resolves disruptions definedby Pilot (cockpit crew) scheduling activities as they relate to Pilot tar-diness and normal aircraft readiness, and addresses the crew problem di-mension of airline disruption management. Between September 2016 andSeptember 2017, disruption instances related to Flight Operations rep-resented about 8.5% of delayed flight schedules, 5.7% of cancelled flightschedules, and 13.5% of diverted flight schedules in Southwest Airlinesoperations.4.
Fuel Management : This functional role in SWA-NOC manages disrup-tions related to aircraft fueling and other energy administration activities,and addresses the aircraft problem dimension during disruption manage-ment. Disruption instances related to Fuel Management between Septem-6er 2016 and September 2017 represented 1.1% of delayed flight schedulesin Southwest Airlines operations.5.
Ground Operations : This functional domain in SWA-NOC managesdisruptions defined by several activities ranging from passenger boardingand aircraft provisioning to ramp services and aircraft towing, and as such,resolves the aircraft and passenger problem dimensions in airline disrup-tion management. Over the one year period of airline operations, disrup-tions related to Ground Operations accounted for the largest percentageof total flight schedule delays of 39%, and the third highest percentage oftotal flight schedule cancellations of 13%.6.
Inflight : Similar to Flight Operations, Inflight resolves disruptions de-fined by Flight Attendant (cabin crew) scheduling activities as they relateto Flight attendant tardiness and normal aircraft preparedness, and thusaddresses the crew problem dimension of airline disruption management.Between September 2016 and September 2017, disruption instances relatedto Flight Operations represented about 18.5% of delayed flight schedules,5.1% of cancelled flight schedules, and about 1% of diverted flight sched-ules in Southwest Airlines operations.7.
Maintenance : This functional domain resolves disruptions defined byaircraft maintenance and inspection activities, and as such, addresses theaircraft problem dimension of airline disruption management. Disruptioninstances related to Maintenance represented 7.8% of delayed flight sched-ules and about 0.3% of cancelled flight schedules during Southwest Airlinesoperations from September 2016 to September 2017.8.
NAS : This adopted functional role in SWA-NOC manages disruptionsdefined by air traffic control activities related to gate hold for congestionat departure and arrival airport stations. As such, the NAS functionaldomain addresses uncontrollable disruptions representing all problem di-mensions during airline disruption management. Disruption instances as-7ociated with NAS represented 5.3% of delayed flight schedules, 13.5%of cancelled flight schedules and 6.4% of diverted flight schedules duringSouthwest Airlines operations from September 2016 to September 2017.9.
Security : This functional domain addresses disruptions defined by secu-rity measures enforced to ensure the safety and convenience of passengersat airports prior to aircraft boarding. Its responsibilities includes manag-ing disruptions due to baggage screening by TSA (Transportation Secu-rity Administration) at the skycap or ticket counter. As such, the Securityfunctional domain resolves the passenger problem dimension during airlinedisruption management. Between September 2016 and September 2017,disruption instances related to Security represented the least percentagesof total delayed, cancelled, and diverted flight schedules of 0.7%, 0.03%,and 0.16%, respectively, in Southwest Airlines operations.10.
Technology : This functional role manages all disruption activities definedby system-wide technology outages, and thus aims to resolve all problemdimensions during airline disruption management. Disruption instancesrelated to Technology accounted for 2.1% of all delayed flight schedulesin Southwest Airlines operations between September 2016 and September2017.11.
Weather : Similar to NAS, this adopted functional domain in SWA-NOC manages all kinds of uncontrollable disruption defined by inclementweather activities. To that effect, the Weather functional role aims toresolve the aircraft, crew and passenger problem dimensions during dis-ruption management. Disruption instances associated with the Weatherfunctional domain accounted for the highest percentage of cancelled anddiverted flight schedules (62.6% and 72.8% respectively) among all func-tional domains in SWA-NOC between September 2016 and September2017. In addition, delayed flight instances related to Weather represented2.9% of the total delayed flight instances addressed by all functional do-mains in SWA-NOC over the one year data collation period.8 igure 1: Procedure for exploratory data analysis in a data-driven paradigm for airline dis-ruption management
3. Data Analysis
The previous section provided a macroscopic overview of disruption activitiesfor different functional roles in SWA-NOC and revealed that about 42% of allflight schedules for Southwest Airlines route network operations from September2016 to September 2017 were disrupted. As a result, the functional disruptionresolution domains in SWA-NOC were most likely to address irregular oper-ations due to delayed flight schedules, which represent approximately 94% ofall disrupted flight schedules recorded from September 2016 to September 2017.Furthermore, there are two separate chunks of data which are defined by the oc-currence of disruption during flight schedule execution. The first chunk, which9s known as the non-disrupted data set, represents the larger chunk that con-tains instances of flight schedules that executed without any disruption. Thesmaller chunk, also known as the disrupted data set, contains instances of flightschedules that executed with disruption, and thus represent instances of flightschedule execution due to irregular operations. As such, the major differencebetween the non-disrupted data set and disrupted data set is the existence ofadditional data features (i.e. disruption features) in the disrupted data set thatindicate different types of disruption. However, there is a small subset (6%) ofthe disrupted data set that represents instances of canceled and diverted flightschedules, which have less data fields with sparse data entries that present signif-icant challenges for machine learning applications. To that end, we restrict thescope of the research presented in this paper to irregular operations based upondelayed flight schedules and ignore flight cancellations and diversions which areprimarily limited to the Weather functional domain. Henceforth, irregular oper-ations only represent controllable and uncontrollable disruptions due to delayedflight schedules.Fine details that highlight pertinent high-level patterns for elements (or fea-tures) that define each flight schedule in the raw data set introduced in Section 2can not be readily observed nor acknowledged through macroscopic inspection.Hence, in order to mine relevant microscopic information from raw data, thissection elucidates the exploratory data analysis used to effectively generalizepattern-finding schemes for consistent flight schedule features that are appli-cable in all functional roles in SWA-NOC. Fig 1 shows the general procedureadopted for performing exploratory data analysis on the raw data set. The pro-cess commences by abstracting separate data features that represent distinctproperties of flight scheduling and operations, next raw data features are trans-formed into data forms that are readily decipherable by appropriate machinelearning algorithms. The data transformation is necessary for applying sepa-rate methods for identifying critical data features and reducing the dimensionspace of the data set achieved by the feature selection and dimensionality re-duction processes shown in Fig 1. The subsequent parts of this section provide10 igure 2: Sample knowledge abstraction of a basic flight schedule for airline disruption man-agement more insight into the aforementioned processes as they relate to the historicalscheduling and operations data adapted for the microscopic analysis techniquesdiscussed in this paper.
Feature abstraction (often referred to as data abstraction) is an effective tech-nique for accommodating semantic relationships between features in a database(Ramakrishnan & Ullman, 1995). Feature abstraction ensures that features thatdefine specific properties of fundamental tenets of flight scheduling and opera-tions (embedded in each flight schedule from the raw data set) is generalizedinto abstract values (Huh et al., 2000). As such, a specific property can beviewed as a specialized quality of an abstract value. The properties describingthe tenets of flight scheduling and operations are described by two separateprinciples of abstraction that represent a knowledge abstraction (Abbott, 1987;Huh et al., 2000; Liskov, 1988). These related feature abstraction principles ex-ist for creating semantic associations among data features for airline schedulingand disruption management and are namely: event abstraction and uncertaintyabstraction . 11
Event abstraction : Event abstraction serves two primary purposes. First,it characterizes the importance of planned airline activities and resourcesassociated with a specific flight schedule, and how their importance canbe subject to change prior to (or on) day of operation due to the riskof disruption from passenger-boarding at a departure station to aircraftgate-parking at an arrival station. Second, event abstraction defines themanner in which planned airline activities for a specific flight schedulevaries during schedule execution based upon the impact of irregular op-erations. As such, the event abstraction principle is synonymous to flightoperation value abstraction , wherein the specific value (or profit) that aparticular flight schedule in the airline route network provides is appraisedby how effectively the flight schedule features estimated prior to scheduleexecution align with flight schedule features that are realized during andafter schedule execution. To that effect, flight schedule features that aredetermined prior to schedule execution represent low-value features forevent abstraction, and flight schedule features estimated during and afterschedule execution represent high-value features for event abstraction. • Uncertainty abstraction : From an airline planning perspective, the uncer-tainty abstraction principle, also analogous to a functional domain plan-ning abstraction , defines the manner in which the uncertainty for the risk ofirregular operations during schedule planning and execution is quantifiedand propagated via various features in the data set. Most airlines, includ-ing Southwest Airlines, adopt a perspective on the scheduling process thataccentuates the internal planning approach of different planning depart-ments as an iterative cycle of flight schedule development and assessmentover a timeline horizon, such that the flight schedule is continually ad-justed and optimized until a suitable schedule is obtained or the planningperiod is over (Grosche, 2009a). Thus, the primary purpose of uncertaintyabstraction is to express the relationships among flight schedule featuresthat are representative of the transitions through three iterative and in-12erconnected airline planning phases namely: strategic planning, tacticalplanning and operational planning respectively (Grosche, 2009b). Strate-gic planning, otherwise known as “future scheduling”, focuses on long-term decision-making for the subsequent tactical and operational plan-ning phases, such that a generic service plan consisting of essential andviable sets of serviceable routes without specific aircraft and crew assign-ments and tentative departure and arrival times are determined. Tacticalplanning or “current scheduling” focuses on creating a refined schedule ofoperations for the service plan based upon the resources that are actu-ally expected to be available to the airline over a definitive time period.Lastly, the operational planning phase focuses on adjusting the schedulegenerated in the tactical planning phase with respect to changes in de-mand for air travel prior to executing the flight schedule, and also onexecuting the schedule with minimal penalty (cost) in the event of unex-pected disruptions on the day of operation (i.e. rescheduling for disruptionmanagement) (Mathaisel, 1997).By applying the event and uncertainty abstraction principles, we identify threeseparate classes of features in the raw data that can be used to enable robustairline disruption management and are described as follows:1.
Determinate aleatoric features : These represent flight schedule featuresthat are determined during the strategic planning phase of airline plan-ning and are required to remain unchanged during schedule execution onthe day of operation. Examples of determinate aleatoric features includeflight date, origin (departure) station, destination (arrival) station, routeoriginator indicator, route distance, etc. With respect to disruption man-agement, determinate aleatoric features represent flight schedule featureswhose alternatives do not differ considerably each time the AOCC invokesa disruption management initiative. Thus, from a statistical perspective,determinate aleatoric features are flight schedule features that are subjectto the least possible uncertainty for the risk of reassessment (or alteration)13uring irregular operations for disruption management, based upon in-herent randomness of disruption events. For instance, airport identifiersand exact longitude and latitude coordinates that provide specific infor-mation for origin and destination stations are always assumed to remainunchanged, by the AOCC, during the recovery of a delayed flight schedule.However, if a human specialist in the AOCC chooses to divert the samedelayed flight to another airport during schedule execution, then the air-port information for the destination station changes to that of the airportwhere the flight is to be diverted. It is important to note that this scenariois unlikely, based upon our research scope, because we consider irregularoperations for delayed flight schedules only.2.
Indeterminate aleatoric features : These are separate data features fromflight schedule features that represent disruption types for different func-tional domains, which occur randomly during schedule execution on dayof operation. Examples of indeterminate aleatoric features include delaycodes for uncontrollable inclement weather and controllable maintenanceinspections. From a disruption management perspective, indeterminatealeatoric features represent triggers for the need of the AOCC to addressa specific disruption. As such, indeterminate aleatoric features are datafeatures that can create the most uncertain responses in disruption man-agement initiatives employed by the AOCC during schedule execution.From a statistical perspective, indeterminate aleatoric features are datafeatures that are subject to the most possible uncertainty for the risk ofoccurrence (or instantiation) of irregular operations during schedule ex-ecution, due to inherent randomness of disruption events. For example,inclement weather at a particular airport may require a human specialistin the AOCC to delay the departure of a specific flight at the (origin)airport and reassign some or all of its passengers to another flight with alater departure, while also reallocating the arrival of the original delayedflight to a different gate at the destination airport.14.
Epistemic features : These represent flight schedule features that are de-termined during the tactical and operational phases of airline planningand can be subject to change during schedule execution on day of opera-tion. Examples of epistemic features include specific departure and arrivaltimes during the day, aircraft type, delay periods, actual turnaround andblock time periods. With regards to disruption management, epistemicfeatures represent flight schedule features with considerable amount of al-ternatives for every time the AOCC initiates a disruption managementplan. As such, from a statistical standpoint, epistemic features are flightschedule features that are subject to the most possible uncertainty for therisk of alteration during irregular operations for disruption management,due to lack of knowledge of the exact impact of their alteration. For in-stance, following a specific disruption like late arrival of flight crew for ascheduled flight, a human specialist in the AOCC may choose to delay thedeparture of the flight by a specific period of time after the original depar-ture time. However, most times, the human specialist can not guaranteethat the decision on applying a particular delay duration after scheduleddeparture will produce a specific recovery plan, due to the cascading effectof disruptions in large airline networks.Fig. 2 shows a generic knowledge abstraction for airline disruption managementbased upon some specific flight schedule features. The horizontal axis in Fig. 2represents event abstraction for defining the value of flight operations man-agement based upon the perishable nature of a flight service during scheduleexecution, while the vertical axis represents uncertainty abstraction for definingthe risk of disruption instances and schedule alteration during flight scheduleplanning.
While the abstraction of raw flight schedule data features provides an ex-cellent avenue for effectively representing latent planning capabilities in airline15perations control, the quality of the knowledge extracted from the raw datacan be enhanced through transformation to enable discernible representationand interpretation for machine learning algorithms (Kusiak, 2001; Liu & Mo-toda, 1998). These algorithms provide efficient means for easily recognizinguseful patterns and relationships amongst flight schedule features in a data set.To this end, feature transformation is the process of converting flight scheduleand disruption features in raw historical airline scheduling and operations datainto relevant mathematical properties (or functions) that can be readily under-stood by machine learning algorithms. Every direct flight schedule in the rawdata set is defined by forty separate data features (or attributes) that describedifferent resources, behaviors, and performance indicators that are observableduring airline scheduling and disruption management. As such, raw flight sched-ule features can be separated into four distinct categories namely: geographicalfeatures, temporal features, categorical features, and continuous features. • Geographical features : These are flight schedule features which representresources, behaviors, or performance indicators that require or enable theperception and property of geographic location (or position) during airlinedisruption management. Examples of geographical features in the rawdata set are International Air Transport Association (IATA) codes fordeparture and arrival airport stations, and the identifier for the origin ofthe first departure flight of the day. • Temporal features : These are flight schedule features that describe andenable the perception and property of time during airline scheduling anddisruption management. Temporal features are conceptualized by fourdifferent types of time (Shurkhovetskyy et al., 2018) namely:1. ordinal time : This represents time points that occur one after anotheron day of operation. Examples of flight schedule features defined byordinal time are time-of-day events such as aircraft pushback time,takeoff time, landing time, and aircraft gate-parking time.16. interval time : This represents time events that are measured on aninterval scale with a specific duration (or length). Examples of flightschedule features characterized by interval time include the durationbetween aircraft pushback and aircraft gate-parking otherwise knownas blocktime, the duration for boarding passengers and loading cargounto an aircraft also known as turnaround, and the duration of anyform of delay in airline operations during schedule execution.3. cyclic time : This describes cyclic or repeatable processes wherein theapplication of an ordered relation is inane. Flight date is an exampleof a flight schedule feature characterized by cyclic time.4. branching time : This represents time points that can occur in differ-ent branches or alternatives to describe several scenarios or processes.Thus, all temporal flight schedule features in the raw data set are de-fined by branching time. • Categorical features : These are flight schedule features that represent fieldsin the raw data defined by discrete values which belong to a finite set ofcategories or classes. Categorical features can be text or numeric, and areseparated into two classes namely nominal and ordinal, based upon theperception of ordering.1. nominal : Nominal categorical features represent flight schedule fea-tures for which there is no concept of ordering among different valuesof each feature. An example of a nominal categorical feature is A0,which is a binary number (i.e. 0 or 1) indicating whether or not aflight schedule arrives exactly on time.2. ordinal : Ordinal categorical features represent flight schedule fea-tures for which there is a strict adherence to the concept of orderingamong different values of each feature. An example of an ordinal cat-egorical feature in flight schedule data is aircraft type, which effec-tively characterizes the relevance of size and seat capacity for aircraftperformance. 17 igure 3: Feature transformation process of raw data for airline disruption management • Continuous features : These are flight schedule features that representfields in the raw data, which have infinitely many alternatives betweenany two values. Examples of continuous features in raw flight scheduledata include digital timestamps for different time-of-day events (such astakeoff time) during schedule execution.Fig 3 reveals a two-layer data transformation process of raw flight sched-ule data features for airline disruption management. The first layer, knownas feature engineering, enables the creation of additional data features frommathematical functions that characterize rudimentary properties of the airlineoperations control center. Next, these data features are combined with extantlow-level data features in the raw data set and normalized by using fundamen-tal statistical parameters in the second layer through a process called featurescaling.(i)
Feature engineering represents a first-degree transformation of raw flightschedule data that defines the augmentation of properties associated withdaily routines of functional roles in the AOCC by using mathematicalprinciples. Thus, flight schedule features representing geographic locations(i.e. geographical features) such as departure and arrival stations are firsttransformed into spherical directional vectors based upon the longitudeand latitude coordinates of their corresponding airport stations, and sub-sequently transformed into the distance between the departure and arrivalairports on an oblate spheroid Earth via the Vincenty geodesic equation(T. Vincenty, 1975). Ordinal temporal flight schedule features (such asdeparture and arrival times) are transformed into two separate periodic(i.e. sine and/or cosine) vectors of different amplitudes, based upon a184-hr clock period and the percentage of 8-hr work shift completed (atthe time of departure or arrival) by human specialists in the AOCC, re-spectively. The work shift characterization of time-of-day events, via aperiodic vector, is intended to capture and represent daily disruption res-olution proclivities of human specialists, which can be induced by howmuch time the specialists have to address a disruption before their workshift is complete. Cyclic temporal flight schedule features defined by Gre-gorian dates are transformed into four separate periodic vectors, whoseperiods are based upon the season of the year, month of the year, day ofthe week, and day of the year respectively.Lastly, most categorical flight schedule features defined by texts are trans-formed into binary numbers by one-hot encoding (Seger, 2018), whereinall n feature values are represented as a n -dimensional sparse vector withzero entries except for one of the dimensions for which the entry is one.However, categorical flight schedule feature values for aircraft type, whichare defined by aircraft model codes, are transformed into discrete num-bers based upon the total number of available seats in the aircraft. Asecondary objective of feature engineering is to provide a precursor forcontinuous feature representation by ensuring that all data features arein numeric form. As such, feature engineering may not be applicable toflight schedule features that are already in continuous form in a raw dataset.(ii) Feature Scaling represents a second-degree transformation of raw nu-meric data features that include additional features created from featureengineering, such that a uniform statistical grounding basis is used totransform values for all data fields (i.e. flight schedule features) in theraw data set into bounded continuous values that describe a differentiablefunction. We explore three different approaches for enabling feature nor-malization (Pedregosa et al., 2011) namely:
Standard scaling , Range scal-ing , and
Power scaling . 19a)
Standard scaling : Standard scaling or standardization normalizes val-ues for each flight schedule feature in the data set by removing themean of the values and scaling to a unit variance, thus resulting in astandard score for each value. The standard score, z i , of an arbitrarysample (i.e data feature value), x i , in the data set is calculated asfollows: z i = ( x i − u ) s (1)where u and s represent the mean and standard deviation, respec-tively, of all values for each flight schedule feature in the data set. Assuch, standardization provides a platform to ensure that each flightschedule feature in the data set follows a Gaussian distribution withzero mean and a variance of one.(b) Range scaling : Range scaling, otherwise known as min-max normal-ization, transforms each flight schedule feature in the data set byscaling the values of each feature by the difference between the max-imum value and the minimum value (i.e. range). This results inadjusted values of a range (or distance) between zero and one foreach flight schedule feature. The adjusted (range-scaled) value, y i ,of a characteristic flight schedule feature in the data set is calculatedas follows: y i = x i − min( X )max ( X ) − min ( X ) (2)where x i and X represent an original value and set of all originalvalues, respectively, for a flight schedule feature.(c) Power scaling : Power scaling involves adapting a family of paramet-ric and monotonic transformations to convert flight schedule datavalues from any distribution to the closest possible representation ofGaussian distribution, so as to reduce variance and skewness in data.An appropriate power transformation of flight schedule and disrup-tion features is the Yeo-Johnson transform (Weisberg, 2001), because20t can be applied to all forms of numeric data just like standard andrange scaling transforms. The Yeo-Johnson transform is given by: x ( λ ) i = [( x i + 1) λ − /λ if λ (cid:54) = 0 , x i ≥ , ln ( x i + 1) if λ = 0 , x i ≥ , − [( − x i + 1) − λ − / (2 − λ ) if λ (cid:54) = 2 , x i < , − ln ( − x i + 1) if λ = 2 , x i < x i and λ represent an original data value and an arbitrary pa-rameter that is determined through maximum likelihood estimation(Glas, 2017), respectively.Completion of the feature transformation process shown in Fig. 3 results ina refined, continuous data set that can be readily comprehensible by suitablemachine learning estimators. The efficacy of constructing and applying relevant machine learning algo-rithms for identifying and acknowledging high-level properties from data fea-tures (such as flight schedule and disruption data features) is dependent on theform in which the data values are presented. To this end, feature transforma-tion has a strong propensity to increase the number of elements in the flightschedule and disruption feature space that constitutes the problem dimensionsfor airline disruption management. As such, the intrinsic dimensionality of therefined data appropriated for airline disruption management is defined by theleast number of flight schedule and disruption features required to delineateobserved behavioral properties from AOCC routines. Hence, dimensionalityreduction is the process of mitigating the curse of dimensionality (Verleysen& Fran¸cois, 2005) and other unwanted properties of high-dimensional featurespace through classification, visualization, and compression of high dimensionaldata obtained as a result of feature transformation (Van Der Maaten & Hin-ton, 2008). In essence, dimensionality reduction aims to provide a rudimentary21eans to attain and observe the latent feature space of a refined data set forairline disruption management.From a mathematical perspective, we assume that the refined flight scheduleand disruption data set is represented in a n × m matrix X , which consists of n feature vectors x i ( i ∈ { , , ..., n } ) with dimensionality m . Furthermore, weassume that the refined data set has an intrinsic dimensionality d , such that d < m and often d || m . The intrinsic dimensionality property refers to pointsin the refined data set X , which lie near a manifold with dimensionality d thatis embedded in the m -dimensional feature space. To that effect, dimensionalityreduction techniques transmute the refined flight schedule and disruption dataset X with dimensionality m into a new data set Y with dimensionality d ,while maintaining the geometry of the refined data set X as much as possible.Typically, the intrinsic dimensionality d and the geometry of the manifold ofthe new data set Y are unknown, and as such, most dimensionality reductiontechniques require that certain assumptions about the properties (like intrinsicdimensionality) of the refined data set be made a priori. For the remainderof this section, we denote a high dimensional data instance for flight scheduleand disruption (i.e. datapoint) by x i , such that x i is the i th row of the refined m -dimensional data set X . In complement, the low-dimensional equivalent of x i is expressed by y i , where y i is the i th row of the new d -dimensional matrix Y . To demonstrate the usefulness of dimensionality reduction on refined flightschedule and operations data, we investigate two separate techniques that em-ploy linear and nonlinear principles nicknamed PCA and t-SNE , respectively, byutilizing delayed flight schedule and disruption instances for the Weather func-tional domain in SWA-NOC between September 2016 and September 2017. Itis important to note that the flight schedule data for the Weather functional do-main constitutes a subset (with 12,659 delayed flight schedule instances) of thefull refined data set. For validation, we adopt min-max normalization for scal-ing all feature values in the refined data set because both dimensionality reduc-tion techniques strongly depend on Euclidean distances between refined high-22imensional datapoints x i and x j to obtain and simplify the gradient of theirrespective cost functions (Van Der Maaten & Hinton, 2008; Van Der Maatenet al., 2009).1. Principal Component Analysis (PCA) : Principal component analysis or
PCA is a standard non-parametric tool in modern data analysis used forextracting relevant information from large and confusing data sets (Shlens,2014).
PCA is also a full spectral linear technique for dimensionalityreduction that embeds data into a linear subspace of lower dimensionality.In the lower dimension, the refined variables (or data features) in the dataset are transformed into linear combinations of the data features, whichare called principal components. With minimal effort,
PCA provides aschema for reducing a fairly complex data set to a lower dimension inorder to show simplified structures that often define it, by revealing asmuch of the variance in the data as possible. As such, the first and secondprincipal components are the orthogonal linear combinations of the refineddata features that have the largest and second-largest possible variance (orinertia), respectively, in the refined data set. In mathematical terms,
PCA aims to find a linear mapping X that maximizes the variance (or minimizesthe reconstruction error) defined by trace( S T cov( X ) S )), wherein cov( X ) isthe sample covariance matrix of the refined data (Wold et al., 1987). Thus,the linear mapping created by the d principal components (or principaleigenvectors) are solutions to the eigenproblem defined as follows:cov( X ) = λ ( S ) (4)The lower dimensional representation of the refined flight schedule anddisruption feature instances, defined by y i of x i datapoints, are computedby mapping them onto a linear basis Y = XS that solves the eigenproblemfor the d principal eigenvalues defined by λ , via the scikit-learn software(Pedregosa et al., 2011). 23 igure 4: Principal component analysis of indeterminate aleatoric features for Weather domain Fig. 4 presents a visualization of the analysis for the first two principalcomponents describing indeterminate aleatoric features that represent de-lays for the Weather functional domain in SWA-NOC. The first and secondprincipal components represent orthogonal linear combinations of the re-fined flight schedule features that account for 8.1% and 5.6%, respectively,of the variance of indeterminate aleatoric features related to weather de-lays in the data set. Fig. 4 reveals that there are four major types ofweather-related delays (
ATC Hold at Origin , ATC Hold at Destination , Deicing at Gate , and
Hail or Snow Damage ) in the data set.
ATC Holdat Origin and
ATC Hold at Destination represent weather delays dueto gate hold from air traffic control (ATC) at departure and arrival sta-tions respectively.
Deicing at Gate and
Hail or Snow Damage representweather delays due to deicing at the gate, and aircraft swap due to hailor snow damage respectively. Fig. 4 shows that the data set is dividedinto four separate clusters of the same delay type along the axis of thefirst principal component. This reveals that the axis of the first principal24omponent (horizontal) represents linear combinations of flight schedulefeatures that capture the seasonal behavior of weather-related delays, aseach data cluster describes each weather season over the one-year data-collation period. Furthermore, the data set is divided into two polarizing(
ATC Hold at Origin and
ATC Hold at Destination ) and two overlapping(
Deicing at Gate and
Hail and Snow Damage ) clusters along the secondprincipal component (vertical) axis. This shows that the axis of the sec-ond principal component represents linear combinations of flight schedulefeatures that capture the difference in the types of indeterminate aleatoricfeatures for weather-related delays in the refined data set.The patterns and information gleaned from the results and observationsfrom the
PCA method can be appropriated for informing model devel-opment for airline disruption management. For instance, the seasonalrelationship among the four predominant types of weather-related delaysobserved in Fig. 4 can be quantified via a linear combination of flight sched-ule features, which suggests that decision-making by human specialists inthe AOCC is sensitive to weather seasons. In addition, the overlappingeffect observed between
Deicing at Gate and
Hail and Snow Damage inFig. 4 is representative of similarities in the type of disruption resolutionsused for weather-related delays during the winter season, thus bolsteringthe significance of the effect of seasonal properties on decision-making byhuman specialists in the AOCC.2. t-distributed Stochastic Neighborhood Embedding (t-SNE) : t-distributedStochastic neighborhood embedding or t-SNE represents a recent advance-ment in clutering and visualization for dimensionality reduction that pro-vides a nonlinear platform for transforming the Euclidean distances be-tween refined values (i.e. datapoints) of flight schedule and disruptionfeatures into conditional probabilities that define similarities. As such,the similarity of a datapoint x j to another datapoint x i is the conditionalprobability ( p j | i ) that x i will select x j as its neighbor if neighbors are25elected in proportion to their probability density under a Student-t dis-tribution with one degree of freedom (i.e. Cauchy distribution) centeredabout x i (Maaten, 2014; Van Der Maaten & Hinton, 2008). Thus, p j | i remains comparatively high for datapoints in close proximity and insignif-icant for datapoints that are substantially separated. Mathematically, theobjective of t-SNE is to minimize the Kullback-Leibler divergence (Joyce,2011; P´erez-Cruz, 2008) between a joint probability distribution definedby P in the high-dimensional feature space and a joint probability dis-tribution defined by Q in the low-dimensional feature space. Hence, theKullback-Leibler divergence represents the cost function of the followingoptimization problem, which is solved via the scikit-learn software (Pe-dregosa et al., 2011): Figure 5: t-Distributed Stochastic Neighborhood Embedding analysis of indeterminatealeatoric features for Weather domain P || Q ) = (cid:88) i (cid:88) j p ij log p ij q ij s.t. p ij = exp ( −|| x i − x j || / σ ) (cid:80) k (cid:54) = l exp ( −|| x i − x j || / σ ) q ij = (1 + || y i − y j || ) − (cid:80) k (cid:54) = l (1 + || y k − y l || ) − (5)where p ii and q ii are set to zero, and p ij = p ji and q ij = q ji for all i, j .Fig. 5 presents a strictly visual perception of the t-SNE nonlinear pro-jection of the two-dimensional space for flight schedule features, whichdescribes indeterminate aleatoric features that represent delays for theWeather functional domain in SWA-NOC. Similar to observations from PCA , the red and gold clusters in Fig. 5 reveal that weather-related de-lays due to
ATC Hold at Origin and
ATC Hold at Destination are themost prominent and oppositely related, based upon the symmetry ob-served from the small and large blobs of red and gold clusters. As such,the polarizing effect observed between
ATC Hold at Origin and
ATC Holdat Destination in Figs. 4 and 5 can be attributed to the importance of thegeographical location (i.e departure or arrival stations) on how weather-related disruption resolutions are applied in the AOCC. As such, flightschedule features associated with geographical location are relevant forcreating robust models for airline disruption management.
Although dimensionality reduction techniques provide an effective means toreadily (i.e. visually) discern high-level patterns and properties associated witha data set, they are ineffectual in revealing detailed information on the spe-cific importance of flight schedule and disruption features in a data set andtheir corresponding relationships (Koller & Sahami, 1996). To this end, fea-ture selection presents simple fundamental methods for efficiently selecting andinvestigating pertinent associations among data features in a refined data set,which can provide insightful knowledge (or a priori information) for develop-27ng useful data-driven models for robust airline disruption management. Inessence, feature selection methods aim to proactively enhance model predictionperformances by increasing generalization (i.e. minimize data overfitting) anddecreasing model runtimes (Moran & Gordon, 2019). There are three majorcategories of feature selection methods namely: wrapper, filter, and embeddedmethods.Wrapper methods involve algorithms that search the feature space for plau-sible subsets of features by assessing each subset after running a specific model.Typically, the model is validated on a test data set to estimate the model’serror rate, before a score is registered for each feature subset and the featuresubset with the best score is ultimately selected. Unlike computationally inten-sive wrapper methods, filter methods do not consider a model when searchingthe feature space for relevant subsets of the feature space, and rely on generalstatistical measures such as Pearson correlation coefficient (Benesty et al., 2009)and mutual information (Jiang et al., 2010). In this manner, filter methods aresomewhat analogous to dimensionality reduction techniques, such that they arenot customized to a particular type of predictive model and consume signifi-cantly less computational resources than wrapper methods. Embedded meth-ods involve feature selection methods that are entrenched in a specific learningalgorithm that performs classification (or regression) and feature selection con-currently. As such, embedded methods deliver the advantages of both wrapperand filter methods with medium computational expense.To demonstrate the relevance of feature selection on refined flight schedulingand operations data, we apply two specific types of feature selection that be-long to the filter and embedded categories, respectively, to identify flight sched-ule features that are pertinent for disruption management during turnaround.Turnaround is an airline process (or time period) primarily representative ofloading, unloading and occasional servicing of aircraft, and is crucial for mini-mizing overall flight schedule delays. In addition to reducing overall flight delay,most airlines typically aim to expedite the turnaround process as much as pos-sible in order to avoid causing discomfort to passengers, stemming from long28aits in the aircraft on the ground, thus invariably minimizing loss of passengergoodwill.In that regard, the filter method that we apply is defined by mutual in-formation and the embedded method is defined by a Gaussian process, suchthat actual turnaround duration is set as the target flight schedule feature. Wedo not consider wrapper methods in our discussion because of the significantcomputational expense required as compared to filter and embedded methods.Similar to the dimensionality reduction analysis discussed in Section 3.3, weutilize delayed flight schedule and disruption instances for the Weather func-tional domain in SWA-NOC between September 2016 and September 2017 forour analysis. For validation, we adopt standardization for the second-degree transformation (i.e. scaling) of all feature (i.e label and target) values in therefined data set, because the algorithms for both filter and embedded methodsperform best with a zero-mean Gaussian distribution as prior instantiation foreach feature space in the refined data set (C. E. Rasmussen & Williams, 2006;Jiang et al., 2010; Ross, 2014).1.
Mutual Information Regression (MIR) : Mutual information is a non-negativemeasure from information theory that provides an excellent statistic forquantifying the degree of relatedness among flight schedule and disruptionfeatures in a refined data set. In that regard, mutual information is closelyrelated to the entropy of a flight schedule feature based upon observinganother flight schedule feature in a refined data set (Kraskov et al., 2004).In addition to the ability to readily identify relationships amongst datafeatures, mutual information provides a fundamental metric for straight-forward interpretation of the relationships among data features as sharedinformation (i.e. shannons or bits) between data features. To that effect,mutual information is insensitive to the number of instances in a data set(Ross, 2014). 29 igure 6: Mutual information of flight schedule data features for Weather Domain with respectto actual turnaround duration
Mathematically, mutual information, I , is expressed as: I ( X ; Y ) = (cid:90) X (cid:90) Y p ( x, y ) log p ( x, y ) p ( x ) p ( y ) dxdy (6)where p ( x, y ) is the joint probability density function of X and Y , and p ( x ) and p ( y ) are the marginal probability density functions of X and Y respectively. Thus, for feature selection, the objective of MIR is tomaximize the mutual information between a subset of flight schedule fea-tures defined by X s and a target flight schedule feature defined by y asrepresented by the following optimization problem: s ∗ = arg max s I ( X s ; y ) s.t. | s | = k (7)where k is the number of features that are to be selected. A non-parametric30egression algorithm based upon entropy estimation from k-nearest neigh-bor distances is used to solve the NP-hard optimization problem via thescikit-learn software (Pedregosa et al., 2011), for a set of possible com-binations of data features that increases exponentially (Gao et al., 2015;Kraskov et al., 2004).Fig. 6 shows the mutual dependence, in decreasing order, of flight sched-ule features (i.e. determinate aleatoric and epistemic features) on actualturnaround period for instances of flight delay from the Weather func-tional domain. Fig. 6 reveals that turnaround duration adjusted duringschedule execution has the highest mutual information of over 3, thus im-plying that it has the strongest mutual dependency on the decison-makingfor estimating actual turnaround duration during disruption management.In addition, turnaround period estimated prior to schedule execution anda flights capacity to be a route originator (i.e. first departure flight of theday) have the second and third highest mutual information of 0.4 and 0.3respectively, thereby revealing a weak mutual dependency on the estima-tion of actual turnaround schedule for managing weather-related delay offlight schedule. Month of the year (moy) can not be selected as a signifi-cant predictor for estimating actual turnaround duration because of zeromutual dependency as shown in Fig. 6.2. Gaussian Process Regression (GPR) : A Gaussian process is a stochasticprocess (i.e. random variables indexed by time or space) where a finitecollection of random variables have a multivariate normal distribution (C.E. Rasmussen & Williams, 2006). As such, Gaussian Process Regressionor
GPR is the inference of continuous feature values with a Gaussianprocess (or distribution) prior, such that the marginal likelihood of thedata is maximized (C. E. Rasmussen & Williams, 2006). Converse to
MIR ,which is a model-free method for dimensionality reduction and featureselection,
GPR is an embedded method that offers nonlinear and non-parametric regression properties that enable the natural decomposition of31ight schedule features in an airline data set for simultaneously attaininghigh fidelity dimensionality reduction and feature selection.
GPR providesan appropriate medium to obtain the sensitivity and importance of flightschedule and disruption features necessary for informing the developmentof appropriate models for airline disruption management.Following the nomenclature in C. E. Rasmussen & Williams (2006), con-sider a training data set defined by D with n observations, such that D = { ( x i , y i ) | i = 1 , ..., n } , where x represents an input vector of flightschedule features of dimension D and y is a scalar target or output fea-ture. As such, the column input vector of flight schedule features for all n instances are collected in a matrix X of size D × n , and scalar outcomesof the target feature are collected in the vector y to yield D = ( X , y ). GPR assumes that outcomes of a target feature defined by y are noisy ob-servations of an unknown function of the input flight schedule features x such that y = f ( x )+ (cid:15) , where (cid:15) represents independent and identically dis-tributed zero mean Gaussian random variables with unknown variance σ n .Thus, a Gaussian process prior is placed over all values of f ( x ) before y isobserved, such that f ( x ) | θ ∼ GP ( m ( x ; θ ) , K ( x , x ; θ )) and m ( x ), K ( x , x )and θ represent a mean function, a covariance function, and all hyperpa-rameters that influence the mean and covariance functions, respectively.A combination of Bayes’ rule and Gaussian identities (C. E. Rasmussen &Williams, 2006) provides a method to retrieve the posterior distributionof the values of f ( x ) after observing y , such that σ n ∈ θ albeit the meanand covariance functions are independent of θ (Lee et al., 2020). As such,the posterior distribution is defined by the analytical solution for f : f | y , X ∼ N ( µ + KK − n ( y − µ ) , K − KK − n K ) , (8)where µ is the prior mean of f , K represents the prior covariance functionevaluated at X , and K − n = ( K + σ n I ) − . In order to obtain predictionsof target outcomes for new test cases represented by a collection of input32ight schedule features X ∗ , f ∗ is defined as: f ∗ | y , X , X ∗ ∼ N ( µ ∗ + K ( X ∗ , X ) K − n ( y − µ ) ,K ( X ∗ ) − K ( X ∗ , X ) K − n K ( X , X ∗ )) , (9)where µ ∗ is the prior mean function evaluated at X ∗ .Computationally, GPR estimates the maximum marginal log likelihood ofthe distribution for the target flight schedule feature in a training data set,such that hyperparameters (or lengthscales) associated with all input flightschedule features that define different drivers of disruption managementby the AOCC are optimized with respect to a certain kernel (covariance)function.
Figure 7: Probability densities of test turnaround duration and mean predictions ofturnaround duration for delayed flight schedule instances in Weather domain
As previously mentioned, a subset of the data set defined only by flightschedules delayed by weather incidents is used for the
GPR demonstration.This subset of data is split into two separate sets of training and test (new)data respectively, such that the training data (70% of the data subsetrandomly selected) is used to fit the
GPR model for actual turnaroundduration and the test data (i.e. remaining 30% of the data subset thatis unseen) is used to validate the model by verifying that the test data isconsistent with mean predictions from the model. Plotting the probabilitydensity function of the test data, revealed a lognormal distribution of33 igure 8: Mean predicted turnaround duration data vs. test turnaround duration data the actual turnaround duration in the data set, as evidenced by Fig. 7.Hence, the Matern32 kernel function, which is a combination of Gammaand Bessel functions correlated by an hyperparameter of 3/2, is selectedto fit the
GPR model by means of a Gaussian process software namedGPy (SheffieldML, 2014).Fig. 8 shows the plot of the mean predictions of the actual turnaround du-ration from the
GPR model versus the actual turnaround duration fromthe test data, for which the turnaround duration values in both axes arescaled to a unit variance from the mean of the data values. The red di-agonal line in Fig. 8 represents the 45-degree line, while each blue starrepresents a coordinate of the mean
GPR prediction and test data de-scribing actual turnaround duration for each datapoint (i.e. instance ofweather-delayed flight schedule). Fig. 8 shows that the coordinates forthe datapoints follow the trend of red diagonal line almost perfectly (rootmean square error of 9%), which indicates that the
GPR model is able34 able 2: Lengthscales of refined data features for predicting actual turnaround durationthrough Gaussian process regression
GPR.Mat32.lengthscale Feature Class Feature Name sin date cos date orig x dir orig y dir orig z dir
ONBD CT
SCHED TURN MINS
ADJST TURN MINS schd acft type actl acft type
SWAP FLT FLAG
ATC Hold at Origin
ATC Hold at Destination
Deicing at Gate
Ice on Wings
Lightning Strike
Turbulence
Hail or Snow Damage igure 9: Quantile-Quantile plot of standard mean error between predicted and test data foractual turnaround duration to effectively predict “unknown” actual turnaround duration. Each co-ordinate that falls on the red line implies an exact prediction of the testdata by the GPR model, and as such, Fig. 8 shows that the
GPR modelperfectly predicts actual turnaround periods that lie over six standarddeviations away from the mean.Table 2 shows the values of the optimized hyperparameters (i.e. length-scales) of refined flight schedule and disruption features for estimatingactual turnaround time. Lower values in Table 2 indicate higher impor-tance of features for predicting actual turnaround period. Similar to theresult from
MIR , turnaround duration adjusted during schedule execution(i.e.
ADJST TURN MINS ) is the most significant epistemic flight sched-ule feature for predicting actual turnaround duration, as indicated by itslow lengthscale value of approximately 45. Of all the aleatoric features(determinate and indeterminate), disruption features representing deic-36ng at the gate, lightning strike, turbulence, and hail and snow damage(all with lengthscale values of 1) are the most significant for accuratelyestimating actual turnaround period during schedule execution.Fig. 9 shows the quantile-quantile (QQ) plot of the standard mean er-ror (SME) between the mean predictions from the
GPR model and thetest data for actual turnaround duration. The straight red line in Fig. 9represents the trend line for a standard normal distribution, and as such,the bilinear trend for standard mean error (portrayed by the blue dots)in Fig. 9 confirms that the distribution of actual turnaround period forweather-delayed flight schedules is lognormal. Categorically, the overlap-ping trend between the 45-degree red line and the spread of the coordi-nates in Fig. 8, coupled with the lognormal distribution trend noted fromthe QQ plot in Fig. 9, validates that the turnaround process for weather-delayed flight schedules is indeed a Gaussian process. To that effect, therelationship between the data features (shown in Table 2) and the actualturnaround duration during schedule execution (i.e. target feature) canbe described by a Matern32 covariance function.
4. Conclusion and Future Work
This paper provided macroscopic and microscopic analysis of the histori-cal airline scheduling and operations data necessary for addressing disruptionmanagement in a major airline in the United States. Through macroscopicanalysis, we identified that over 94% of the irregular operations over a one-yearperiod occurred due to different forms of flight schedule delays. To that end, weinvestigated crucial drivers and properties for effectively managing flight sched-ule delays through microscopic analysis of weather-delayed flight schedule data,which also demonstrated a toolbox for applying appropriate machine learningtechniques to enable data-driven schedule recovery during airline disruptionmanagement. In a sequel to this paper, we extensively discuss the processesand routines used to obtain high fidelity data-driven models for simultaneously-37ntegrated recovery in airline disruption management.
Acknowledgement
The authors would like to thank Blair Reeves, Chien Yu Chen, Kevin Wiecek,Jeff Agold, Dave Harrington, Rick Dalton, and Phil Beck, at Southwest AirlinesNetwork Operations Control (SWA-NOC), for their expert inputs in abstractingthe data used for this work.
Conflict of Interest
All authors have no conflict of interest to report.
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