Application of human factors data to estimating air traffic control conflicts

Trxu~sprtRPS. Vol. 8. pp. 20>217.

Pergamon Press 1974.

Printed in Great Britain

APPLICATION OF HUMAN FACTORS DATA TO ESTIMATING AIR TRAFFIC CONTROL CONFLICTSJWILLIAM J. DUNLAY JR.$ and ROBERT HORONJEFF Institute of Transportation

and Traffic Engineering, University of California, Berkeley. U.S.A. (Receiued 25 July 1973)

Abstract-This paper seeks to define and estimate the frequency of aircraft interactions (called conflicts) which entail controller intervention. The task of conflict detection is viewed as a stimulusresponse process in which the strength of stimulation is a particular closest-approach separation between aircraft, and the corresponding probability of response is the fraction of times controllers judge that separation to be a potential violation of the 5 nautical mile minimum separation standard. Data from human factors studies of air traffic control are used to estimate response probabilities for a wide range of closest-approach separations. Two types of response probability are defined. The first type (normative) predicts when controllers should intervene based on an analysis of human and equipment errors in the air tratfic control process. The second type (descriptive) predicts when controllers actually intervene based on data from real-time simulations of conflict detection. These response probabilities are incorporated into an empirical model for estimating the expected number of conflicts in a specified time using data from ATC flight-progress strips.

Further discussion of controller workload models is beyond the scope of this paper. The point here is that for this application the expected number of conflicts should be defined as the number of times a controller perceives a potential violation and intervenes rather than the actual number of potential violations.$ Two basic types of conflicts are possible: (1) overtake conflicts due to fast aircraft overtaking slower aircraft flying on the same airway and at the same altitude, and (2) crossing conflicts between aircraft whose paths intersect. These two types of conflicts are considered independently in this research. The problem of estimating the number of conflicts can be divided into two parts. The first, referred to as the “stimulus-response problem”, is to determine what separations actually cause the controller to intervene. The second part is to estimate the frequency of such conflict-causing separations in a given air traffic pattern. It is the first part that is discussed in detail in this paper. Research into the second part is still in progress and is therefore not discussed. However, an empirical model for estimating the mean and variance of the number of conflicts in a specified time period is derived.

INTRODUCTION The objective of this paper is to develop a probabilistic definition of a conflict based upon human factors considerations and a procedure for estimating the expected number of conflicts that will occur in a given pattern of air traffic. A conflict is defined as the occurrence of a separation so small as to cause an air traffic controller to intervene and issue a control instruction that will prevent the violation of minimum separation rules. This definition stems from the application of the expected number of conflicts to the problem of computing controller workload (Amin and Mayfield, 1967: Ratner clr ul. 1972; Faison ef al. 1970; Arad et al. 1963). In such applications the expected number of conflicts in a specified time period is multiplied by the workload time required to resolve each conflict to obtain the total conflict-related workload time. This quantity is then added to the workload time required for routine ATC (air traffic control) tasks. Workload capacity is defined as the number of operations at which the total workload time reaches some specified upper limit, e.g. so many minutes in one hour. t This research was supported by the FAA under contract No. DOT-FA72-WA-2827. f Current address: Department of Civil Engineering, University of Texas, Austin, Texas, U.S.A. §A potential violation is a violation that would occur if the controller did not take corrective action.

Description qf system To facilitate the control of air traffic, airspace divided into small units called sectors. A sector 205

is is

WILLIAMJ. DUNLAYJR. and ROBERTHORONJEFF

206

Fliqht LWd

Fliqhi Direction

I.

Typical high-altitude,

enroute

air traffic control

sector. the volume of airspace assigned to one radar control1er.t There are basically four types of air traffic control sectors: (1) terminal area, (2) oceanic, (3) lowaltitude enroute, and (4) high-altitude enroute. Because aircraft speeds and traffic patterns differ in these four types of sectors, each type must be analyzed separately. This paper is restricted to high-altitude enroute sectors. A typical high-altitude enroute sector is shown in Fig. 1. Each sector contains a three-dimensional network of one-way airways defined primarily by ground-based radio navigation aids called fixes or VORTACs. e.g. t A radar controller may have one or more assistants helping him with certain routine tasks, but the tasks of monitoring the scope and resolving potential violations are assumed to be his responsibility alone. $ A flight level number is the altitude m feet above mean sea level divided by 100. $ By 1975 all sectors within the conterminous United States will have digitized radar displays on which radar targets will take the form of small rectangular boxes. Flight number Aircraft type True air speed Ground speed

Previous fix

GMT at current fix

GMTat

Current fix

pr%o”s

[ I

Flight level

BDF in Fig. 1. A high-altitude sector includes flight levels 240 through 410.1 Airspace between flight levels 180 and 600 over the continental United States is designated as positive control airspace. All aircraft desiring to fly in this area must file an IFR flight plan with FAA air traffic control. A flight plan provides ATC with essential information on each aircraft which is printed on flight-progress strips and distributed to all sectors through which the aircraft will pass. A sample flight strip is shown in Fig. 2. The flight strip of Fig. 2 is for TWA flight 38 which is a Boeing 707 with transponder type A flying at a true air speed of 460 knots or 475 knots ground speed at flight level 410. The flight originated at Los Angeles International Airport (LAX) and is destined for Philadelphia International Airport (PHL). Flight strips are the source of data to be used later for exploring stochastic characteristics of aircraft separations. On existing enroute radar displays, aircraft targets (called blips) for which the controller is responsible appear as double slashes called radar-beacon or secondary radar targets as shown in Fig. 3(a).$ The actual aircraft position is about in the middle of the slash closest to the radar antenna. The second slash is just to distinguish targets which are under control. The control of enroute air traffic involves many different tasks. Some are routine procedural tasks required for every flight that passes through a sector, e.g. handoffs from and to adjacent sectors and processing flight-progress strips for each flight. However, this paper is concerned with only one task of the air traffic controller: monitoring a radar display of air traffic in his sector for the purpose of ensuring safe separations between aircraft. Enroute radar control procedures as outlined in the FAA Enroute Air Traffic Control Handbook (1973) require that the controller separate aircraft targets at the same flight level by at least 5 nautical miles (nmi). When the controller judges that two aircraft will come closer than 5 nmi he must intervene and issue a

Next fix

Routing

Application

of human

factors

207

data

Radar antenna

Radar beacon slashes

-Airways

(b)

(a) Fig. 3. Radar display and targets,

control instruction. The usual control instruction for enroute air traffic is a radar vector, i.e. an instruction for one aircraft to temporarily change heading. A radar vector is preferred to an altitude change because the corrective change in horizontal separation desired from a vector can be verified visually on the radar scope. An altitude change must be verified by voice communication with the pilot.7 In addition, an altitude change results in a greater fuel penalty. Previous research A conflict has been defined in previous research as the potential violation of a specified minimum distance separation, say S,. In terms of the stimulus-response conflict definition used in this paper, the implied assumption has been that SC is the one and only separation that causes the controller to intervene..$ That is to say, the expected number of conflicts has been defined simply as the number of separations less than or equal to SC. The value of S, used most often has been 5 nmi (Amin and Mayfield, 1967; Arad et a/., 1963; Ratner et al., 1972. Under this definition the estimated number of conflicts represents the number of actual violations of the 5-nmi separation standard that would occur if the controller did not intervene. The first and only explicit attempt to define a conflict in terms of a controller intervention rather than an actual violation was by Faison et al. (1970). They assumed an S, of t Digitized radar displays will have the capability of providing continua1 altitude information for each aircraft. $ This assumption has never been made explicit because conflict detection has not previously been treated as a stimulus-response situation.

7 nmi because they felt that controller allows for error by adding a safety margin to the 5 nmi minimum. From this discussion it is clear that very little explicit account has been taken of human factors aspects of conflict detection in previous conflict definitions. STIMULUS-RESPONSE

DEFINITION

OF CONFLICT

The number of events controllers perceive as potential violations and the actual number of potential violations may differ because of uncertainties in the controller’s perception. One source of uncertainty is the error in the radar display. Another is the controller’s limited ability to judge separations between radar targets. A third and very important source of error is the fact that controllers must act well in advance as soon as they suspect a potential violation. This means they must extrapolate separations a short time into the future. For these reasons controllers tend to act conservatively. Therefore, the number of controller interventions is almost certainly greater than the number of actual violations. This fact has been acknowledged in previous research. For example, in their conflict definition Faison et al. (1970) wrote “Seven miles is used because it is felt that due to the difficulty in predicting the future position of aircraft on intersecting paths, controllers will generally add some separation to insure that the 3 or 5-mile minimum is not violated”. Researchers at Stanford Research Institute report that “. . . controllers tend to maintain or increase separations whenever it appears to them that separations may decrease below lo-20 miles if they take no action.. .” (Ratner et al. 1972).

208

Wn I IAM J. DI:YI.AY JR. and ROWRT HOROMWP

-

Track

Intersection

Seporotion

Fig. 4. David’s crossing

In this paper the process of detecting conflicts is assumed to be a stimulussresponse process. The stimulus is the closest-approach separation between a pair of aircraft which would occur if no corrective action were taken by the controller. The response is whether or not the controller perceives that separation as a potential violation. This process is considered in two ways: (1) based on laboratory simulations of conflict detection. what separations actuallj~ cause the controller to intervene, and (2) based upon an analysis of the human and equipment errors in the air traffic control process, what separations should cause the controller to intervene so that a specified level of performance is attained. The first of these approaches will be referred to as the “descriptive approach,” and the second the “normative approach”. In the text which follows reference is made to human-factors data collected during various laboratory experiments involving air traffic controllers. It must be pointed out at the outset that none of these data were collected explicitly for the applications proposed in this paper. Such data are cited for demonstration purposes only and because they are the only available data relevant to this application. It is hoped that once the value of applying such data to estimating conflicts has been demonstrated, human-factors researchers will be encouraged to collect more appropriate data. ln fact, one important objective of this research is to demonstrate the need for such data and to suggest the type of data required. Drscriptiw

approach

The descriptive approach seeks to estimate the probability that particular aircraft separations actually t Now at Eurocontrol Experimental Center, France. 1 Track-intersection separation is the distance separation between a pair of aircraft when the first aircraft is at the intcrscction measured along the path of the second Grcraft.

6)

situation.

cause the controller to intervene without explicit consideration of how well he performs and without regard to whether or not the intervention is really necessary. Only one set of data, collected by David (1967)t while at the University of Loughborough, England, is known to be pertinent to this approach. David’s research was a laboratory study of controller ability to detect conflicts and advise conflict-avoidance maneuvers under a variety of aircraft crossing situations. The basic crossing situation studied is shown in Fig. 4. The subjects in David’s experiments were 13 air traffic controllers. They were asked to monitor two radar targets converging toward each other at the same altitude and to issue a control instruction; i.e. an avoidance maneuver, when they judged that the separation between the two targets would become less than the minimum allowable separation of 5 nmi if they did not intervene. Sixty-four different simulations, in which a number of factors such as approach angle, speeds. and track-intersection separationf were varied. were presented to each subject. However, only the closest-approach separation associated with each simulation was considered in defining the stimulusresponse relationship in this research. The percent of individuals who called each simulation a conflict was computed. This percentage is assumed to represent an estimate of the probability of response associated with the particular closestapproach separation involved in the simulation. Thus, the data from David (1967) available to estimate a stimulus-response relationship consists of the 64 data points: (.sir Pr(CIsij), i = I. . . 64. where si is the closest-approach separation in simulation i, and Pr(C/s,) is the corresponding fraction of individuals who advised a maneuver. These data are shown graphically in Fig. 5. It was decided to throw out as

Application

of human factors data

209

0 = Experimental Data Points Cumulative-normal approximation

0

4

2

16 Closes+~*pprooS~

Fig. 5. Percent of situations called conflict vs closest-approach

outliers the four lowest data points shown near the abscissa in Fig. 5. This left 60 data points for the analysis described below. It has been found in a variety of applications that the probability of a response as a function of the strength of stimulation can be approximated satisfactorily by a cumulative normal distribution, i.e.

, cs-!Na P{ConflictsJS

= s} = 1 - Q&

1 _-oo e-“!* dt

where p is the track-intersection separation for which the probability of conflict is one-half. In terms of the 60 data points described above, the cumulative normal formulation is P{Conflict [S = si} = 1 - ~

1

J2n

[(4-fiy*,*

dt;

.--UI i = 1,

,60.

The Berkson Normit Method? was used to obtain estimates of p and G. These estimates have excellent small-sample properties, e.g. smallest mean square error, etc. Normit Chi-square goodness-of-fit tests were then applied. The results of this analysis are presented in Table 1 and shown graphically by the curve in Fig. 5. David’s (1967) data were not collected for the purpose of defining a stimulus-response relationship and, therefore, have several deficiencies for this application. One major deficiency is that a very small range of values for closest-approach separation (namely, &8 nmi) was tested. A second deficiency is that subjects viewed only one pair of crossing aircraft at a time, 7 Described in New Statistical Tables XXIV (Biometrika 44, 1957). pp. 41 l-430.

I6

SepbOration 1’s ln mi’,

whereas in actual crossing conflicts The effect of this perceive conflicts collection efforts.

separation.

ATC practice a number of potential must be monitored simultaneously. second deficiency on how controllers should be investigated in future data

Normative approach In the normative approach the question is asked: “What perceived separations should cause the controller to intervene such that some specified measure of performance is satisfied?” A number of measures ofperformance could be proposed. The one used in this paper is the percent of real violations a controller can detect given the limitations in his ability to judge and extrapolate separations and the errors in the radar display. Denote by “E” the total error due to controller judgment and radar system errors. Then, if the actual closest approach separation is s, the controller perceives that separation as s + E, which means that the probability of a conflict is P{Conflict IS = si = P{(s + E) 5 S,) where S, is the normative decision rule. That is to say, the controller would be instructed to intervene when he thinks that the separation between a pair of aircraft will become as small as S, To assume S, to be the 5 nmi minimum separation standard would almost certainly result in an unacceptable level of performance, i.e. an unacceptable value for the probability that the controller will detect separations less than 5 nmi. Therefore, it is desirable to define S,, in terms of some LI priori value for level of performance, e.g. 95 per cent.

210

WILLIAM J. D~JNLAY JR. and R~RERT HORONJE~F Table 1. Results of Berkson fJ

642

4.56

Normit

Normit

analysis

x2

51.8

of stimulus-response

df

Pf

58

0.70

* Significance nrobabilitv in the test of the hypothesis cumulative-normal distribution.

It may seem that it is proposed to replace the 5-mile rule within an S,-mile rule, but this is not the case. There are a number of reasons for not violating the Smile rule, the most compelling of which is that, in studies of radar resolution,S it has been found that a /. 556-mile target separation was necessary to attain target resolution 95 per cent of the time” (Chapman, 1971). If two targets are not radar-resolved, the controller has to take drastic action, e.g. tell one of the aircraft to dive, to ensure safe separation. Therefore, it is desirable to ensure that the controller will prevent the violation of the Smile rule by defining the decision rule, S,, such that the probability of controller invention for an actual violation is arbitrarily high. In this research three measurable components of the total error E have been identified: (1) errors in the controller’s absolute judgment of separations on the radar scope,1 (2) errors in the controller’s extrapolation of future separations between aircraft, and (3) errors in the radar display of aircraft positions.

Controller absolute,judgment

errors

Absolute judgment errors have been measured in a laboratory study conducted by Connolly and McCosker (1970). In this experiment controllers were shown a simulated radar display of two moving radar beacon targets. The task of the controller was to monitor the scope and to verbally express his judgment of separation when cued by the appearance of a small white dot on the scope. Two types of flight paths were presented to the controller: (1) “in-trail” situations in which two aircraft followed each other at the same heading, and (2) converging situations where the two aircraft flew different headings. Data on the error in controller judgments collected in the above experiment are plotted on probability paper in Fig. 6. From this plot and from goodnessof-fit tests it is concluded that the data for each 7 Radar resolution refers to the ability of a radar system to distinguish two aircraft in close proximity. Failure to resolve means that the signals overlap and appear garbled or as one target on the display. $ Absolute judgment of separation refers to estimating the distance between two targets at a specific instant.

data in Fig. 5 Conclusion Do not reject

that the data

follow a

situation are approximately normally distributed with the means and standard deviations shown on Fig. 6. In addition, it was found through appropriate statistical tests that both the means and the variances are significantly different for the in-trail and converging situations. In general, controllers were better able to judge in-trail separations. This finding is not surprising and presents no problems in this research since overtake and crossing situations are treated independently. What is surprising is that errors in judgment were found to be insensitive to the magnitude of the separations displayed. There are a number of deficiencies in the above judgment data for the application proposed here. First of all, controllers viewed only one aircraft separation at a time. Furthermore, judgment of separation was the only task of the subjects in this experiment. The Connolly and McCosker (1970) experiments employed a terminal area radar display rather than an enroute display. The maximum range of the display used in the experiments was about 60 nmi whereas enroute radar can have a range of up to 200 nmi. In addition, the concentric rings on terminal radar displays, which are intended to serve as a reference scale to aid the controller’s eye in judging distances, are 5 nmi apart as opposed to a 12 nmi spacing on enroute radar displays. What effect these differences in range and in range-ring spacing have on the accuracy of controller judgments is not known but should be investigated. Errors in controller extrapolations Very little quantitative data exists on the ability of controllers to extrapolate separations. In David’s (1969) laboratory experiments, subjects were asked to say at the same time they made their conflict decision how near they thought the two crossing aircraft would be at their closest point. This is probably the most relevant data that exist on this subject. However. these data have not been analyzed. There is one other study by Mangelsdorf (1955) that gives some quantitative evidence of how accurately controllers can extrapolate future positions of aircraft. This experiment was designed to study the variability of collision judgments. A simulated radar display of

Application of human factors data I

I

I

I

211

I

I

0.98 -

/-

,

/

/‘P

0.95 /

a’

0.90CI80%. .c.: 0.60: ci: a400 .-z $ 0.205 v

P’

0.107

Stondard

Sample

0.05 Converging

Separwns A -0.5nmi

I.1 nmi

48

0.12

1

:. do not reject hypothesis

I

0.00

-2.0

-1.5

* Significance pmbobility in a chi-square, goodness-of-fit test against the normal distribution I I I I I

-1.0

-0.5

Error in Judgement

0

0.5

of Separation

1.0 1.5 - nmi

2.0

Fig. 6. Controller absolute judgement errors.

two targets on converging courses was presented to various subjects. The targets were not moving but the speeds and headings of the targets were apparent from the blip trails which represent blip positions at previous sweeps of the radar antenna. The task of the subjects was to adjust the position of one target such that the targets would be on a collision course. This was done by moving one target forward or backward along its course. This adjustment procedure, called the psychophysical method of adjustment, has been employed in

a number

of human factors studies of the air traffic controller (MC&ire. 1957: Mangelsdorf, 1955). Whether or not one can infer information about the controller’s ability to judge future separations from such experiments is a subject of debate among human factors researchers. A number of different traffic situations (i.e. different angles of convergence, speeds, extrapolations distances, etc.) were shown to four subjects. These factors are illustrated in Fig. 7.

Pbint of intersection (not shown to subject) Adjuetoble target

Fig. 7. Traffic factors in Mangelsdorfs experiments.

WILLIAM J. DLINLAY JR. and ROBERT HORONJEFF

212 A SL ‘Z 2 .;;

Stondord deviation d exhoPolated ]udgment (SDE) / ~*-___--__-.--

ZE _cc,E L 0) __/* G,” Vertical intercept (SDA) 53 G.5 0, 0 Extropolotion Oistonce

//Ob;~~ex~ro@o~ion 5 - nmi

Fig. 8. Effect of extrapolation distance on judgement error. The S.D. of the errors in the collision judgments was computed for the different experimental conditions. The magnitude of this S.D. is of no interest in this research, since the experiment was not sufficiently comparable to ATC conflict detection. What is hoped can be learned from these experiments is how the error in judgment varied with extrapolation distance. A plot of the S.D. in judgment against extrapolation distance turned out to be a linearly increasing function as shown in Fig. 8. In Mangelsdorfs (195.5) experiment the slope of the line in Fig. 8 was about 0.06. In another study by McGuire (1957) using the same adjustment procedure but with the point of intersection shown on the display, the slope of the linear relation between S.D. of judgment error and extrapolation distance was only 4 per cent. It should be emphasized that both Mangelsdorf (1955) and McGuire (1957) found the increase in S.D. with extrapolation distance to be very nearly linear over the range of extrapolation distances tested. To demonstrate the normative approach, it is assumed that the vertical intercept of Fig. 8 corresponds to the S.D. of absolute judgment errors (SD,) from Fig. 6. It is further assumed that the slope of this linear relationship represents approximately how errors in separation judgment vary with extrapolation distance. To be conservative the 6 per cent slope is employed. Thus, to estimate the S.D. of errors in extrapolated judgments, one enters Fig. 8 with an observed extrapolation distance as shown by the dashed arrows. In David’s (1967, 1969) laboratory experiments an approximate extrapolation time was measured. Although David’s extrapolation time varied with approach angle and relative velocity. 95 per cent Table

2. Distribution

In-trail separations Crossing separations

of errors due to absolute and extrapolation N( -0.2 N( -0.5

of all extrapolation times measured were less than 200 sec. Since high altitude enroute aircraft are traveling at about 480 knots, this translates to an extrapolation distance of 200 x 480 x l/3600 = 27 nmi. The corresponding S.D. of the error in extrapolated judgments for crossing separations obtained as in Fig. 8 is SD, = SD <+ 0.06(27) but SD 4 = 1.1 (from Fig. 6) so SD, = I.1 + 1.6 = 2.7 nmi. The effect of extrapolation distance on the mean of the judgment error distribution was not studied and therefore cannot be considered. I 0.9999

I

I

I

1

.

DOto lpnored

0.999 -

.

0.99 . 0.95 -

f

0.90

I

B 2 Q60 Q 2 0.40 :: 0.60 i

judgment

nmi, 0.6 nmi)t nmi, 2.7 nmi) a normal

I

.

I

0.01

I

-2r)

I

I

0 Enroute

t The notation N(a,b) indicates with mean (a) and SD. (b).

I

-

-0.5

0

Display

I

0.5 Errors -

1

1.0

I

20

nmi

distribution Fig. 9. Enroute

radar

separation

errors

(Ref. 7).

Application of human factors data In overtake situations it is felt that extrapolation has little or no effect on absolute judgment errors because the relative velocities among in-trail aircraft are small and generally known by the controller from flight strip information. Therefore, the effect of extrapolation on in-trail judgment errors is assumed negligible. It should be pointed out that the ability of controllers to extrapolate separation between in-trail aircraft has not been investigated. Based on the above assumptions the total distribution of error due to absolute judgment and extrapolation is summarized in Table 2. Radar system error Radar system error refers to the difference between an actual airspace separation and the corresponding radar separation displayed on the scope to scale, i.e. in terms of nmi. In a study of enroute radar system error performed by Chapman (1971), airspace separations were measured between two aircraft equipped with onboard distance measuring equipment. In addition, time correlated measurements of the corresponding displayed separations were made. Separations measured in the airspace by on-board equipment were assumed to be known without error. The resultant errors, defined as the differences between airspace separations and displayed separations, are plotted on probability paper in Fig. 9. It has been hypothesized in a number of radarerror studies that there are two types of variability in displayed separations: (1) a small constant intrinsic variability and (2) intermittent large disturbances which occur at random (Chapman, 1971; Holliday, 1970). The large intermittent disturbances are due to false targets and electronic distortions and, therefore, it is assumed that such disturbances do not affect controller judgments. In Fig. 9 the solid circles represent data points in the tail of the radar error distribution which were assumed to be intermittent errors and are therefore ignored. The data in the center portion of the distribution have been fitted by eye with a straight line which is assumed to represent the intrinsic variability in displayed separations. Thus, intrinsic radar system error is assumed to have a normal distribution with a mean of 0.1 nmi and a S.D. of 0.4 nmi.

polated judgment

213 error and (2) radar system error, i.e. E = E, + c2

where JN( -0.2 nmi, 0.6 nmi) for overtakes1 El - 1N( -0.5 nmi, 2.7 nmi) for crossings 1

Ed- N{O.l nmi, 0.4 nmi}. Hence

1N( -0.1,0.7)

for overtakes1

e - 1N( -0.4, 2.7) for crossings 1’ As stated previously, the probability given the actual separation S is

of a conflict

P{Conflict 1S = sj = P{s + E) I SD}. From the distribution

of E, the distribution

of (s + a) is

(s + E) _ ) N(s - O.IO.7) for overtakes\

1N(s - 0.4, 2.7) for crossings 1’ The value of the decision rule, S,, for which the a priori level of performance (which is that the controller be able to detect real violations of the 5 nmi rule 95 per cent of the time) is satisfied can be expressed as PiConflict

IS = 5j = Pj(5 + a) 5 S,} = 0.95.

From the distribution overtakes:

of s + E this becomes

S, - (5 - 0.1) P(5 + E) I S,} = @ ~ o~7-- ~- = 0.95

2”;

= 1.645 (from tables) S, = 6.05 nmi - say 6 nmi

crossings:

S, - (5 - 0.4) @ -m-.--2-

= 0.95

S, - 4.6 __-.~ = 1.645 2.7 S, = 9.04 nmi - say 9 nmi. Using the above values of S,, the conditional conflict probabilities for the normative case are Overtakes:

P(Conflict IS = s} = P((s + a) I 6)

=@

y-04 0.7

Total perception error Total perception error, denoted by E, refers difference from all sources between a separation airspace and the controller’s perception of that tion. The total error E is assumed to be the two independent random variables: (1) total

Crossings: to the in the separasum of extra-

PIConflict 1S = s} = P((s + a) 5 9) = ~ 9 - (s - 0.4) 2.7

These two conditional conflict probabilities plotted as a function of s in Fig. 10.

’ are

WILLIAM

‘14

J.

D~INLAY

JR. and RWKRT HOROXJW~

__

Performonce (0.95

015

maosure nmi)

0.2 -

I 0

2

4

5 6 S=Actual

Fig. 10. Conditional

EMPIRICAL

MODEL

FOR

ESTIMATING

8 Separation

conflict

CONFLICTS

The objective of this research is to estimate the expected number of conflicts in a specified period of time, e.g. the busy hour of a day, in both existing and future (nonobservable) air traffic patterns. Estimating future conflicts requires the development of a mathematical model of aircraft separations in terms of some predictable random phenomenon such as aircraft flow rate. However, existing conflicts can be estimated from empirical analysis of aircraft separations. A description of an empirical model from which one can estimate a mean and variance for the number of conflicts using data on observed aircraft separations is given below. The model is derived in terms of crossing conflicts. In addition, this experiment is applicable to both the descriptive and normative definitions of conflict. It is assumed that the relationship between conflict probability and separation can be approximated satisfactorily by a step function consisting of N steps as shown in Fig. 11. The number and widths of the steps depend on the accuracy with which one wishes to approximate the relationship.

IO - nmi

probabilities

12

14

16

I8

case.

for normative

Erprritnrnt Imagine an experiment in which data on closestapproach separations are collected during the same specified time period on each of J days. Separations for each day are sorted into various size categories corresponding to the finite size intervals shown along the abscissa in Fig. 11. Each separation that occurs in [si, si+ r] is assumed to be a Bernoulli trial with a constant probability that it is called a conflict equal to Pi from Fig. 11. Let NY) represent the number of separations in the specified time period that lie in the interval [si, .ti+ r] Where:

Pi=Pr

{Conflict)

Sc[Si.Si+,]}

0.99 P,

0 .66=

P2

~

Data

The data for the following experiment are closestapproach crossing separations computed as in Dunlay (1972) from flight-strip fix times and velocities and approach angles measured on a scale map of a sector. It has been found that control instructions are not reflected in flight-strip fix times. Therefore. it is assumed that the data represent approximately what would have happened if no corrective action were taken by the controller.

0.22=

----A--5

I

‘?

52 53 s4 S= Closest Approach

Fig.

I I. Discrete

P4

I I5 55 Separation

2?

25

$6 - n mi

approximation to conditional probability function.

conflict

215

Application of human factors data on day j. It is assumed that the NY), j = 1, 2, . . ., J, are independent observations on the same random variable Ni. That is to say, the same time periods on the J different days are assumed to be independent and identical conditions for observing the random variable Ni (the number of separations in [sir si+,] during that time period). Let- Ci be the number of separations in [si, si+ i] that are conflicts. Then, conditionally on N, the random variable Ci has a binomial distribution by the above Bernoulli trial assumption. Therefore, the ex-

petted

value of Ci is E{CiJ = E,,[E{Ci

INJI= E,,[Ni PiI

E{C,j = Pi E{N,}

(1)

and the variance of Ci is Var{C,} = E,]Var{ Ci 1Ni}] + VarNf[E{ CL1Ni}] = E,]NiPi(

1 - pi)] + Var,]Pi

Var(Ci} = P,(l - P,)E{N,}

Nil

+ Pf Var{N,}.

Table 3. Data table for empirical crossing conflict model Crossing separation size categories (nmi)

Day

o-5

5-8

8-10

10-14

1420

j

NY’

NY’

NY’

NY’

NY

3 1 1 2 2 2 2 0 2 0 1 0 1 1 2 5 2 3 3 4 3 5 1 0 1 0

1 2 3 4 5 6 I 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

0 0 0

0 0 0 0 0 0

0 0 0 0 0

1 2 0

0 0 0

1

1 0 0 1 0 0 0 0 1

0 0

1

0 1

i

1

2

3

4

Total W’iJ Var{Ni}

46 1.77 2.18 0.99 1.75 2.12

47 1.81 2.08 0.86 1.56 1.76

33 1.27 1.63 0.56 0.71 0.82

3 0.12 0.11 0.22 0.03 0.03

E{C} = 5 E{C,} = 4.13 conflicts i= 1

Var{C} = i Var{C,} + 2cCov{C,, i=1 k.I kCI

C,} = 4.81 + 2(-0.02) = 4.77

1 0 2 1 4 2 2 4 2 1 1 1 1 2 4 2 2 1 4 6 1

55 2.12 2.19 0.04 0.08

.

(2)

216

WILLIAM J. DUNLAY

The mean and variance of the total number

JR. and R~H~RT HoKoNJt by

of con-

flicts in a specified time period, C = 2 Ci, are i=l Y

E(C;

=

1

E(C,)

,=I

Var{C) = C Var{Ci) + 2 C Cov{C,, C,). i=l

k., !.'I

What remains to determine is the covariance C, and C,. By definition this covariance may expressed Cov(C,,

of be

controller’s ability to detect potential encouraged.

conflicts will be

Ackno~~lerlyrmrnts~The authors are grateful to G. F. Newell and C. E. Antoniak of the University of California. Berkeley, for their helpful comments, and to Hugh David of Eurocontrol Experimental Center for copies of his reports. This research was supported by the U. S. Federal Aviation Administration under contract DOT-FA72-WA2827. The judgments and opinions expressed in this paper are those of the authors and not necessarily those of the sponsoring agency.

C,) = E{C,C,} - E{C,JE{C,) REFERENCES

which reduces to CovjCk.C,j

=

P,P,Cov{N,,N,j

(3)

where Cov{N,, N,} is the sample covariance of N, and N,. It is clear from equations (l), (2), and (3) that the stochastic properties of the Cts in the above experiment are determined completely by the joint probability distribution of the NTs along with the exogeneous P,‘s. Exc~mplr: Table 3 is a tabulation of the number of closest-approach crossing separations that fall into each of five size categories during the same 2-5 hr period on 26 days. At the bottom of the table is a summary of the calculations for the mean and variance of the total number of crossing conflicts. A simplifying assumption implicit in the above experiment is that all closest approach separations of a particular size are treated identically and independently by the controller. i.e. there is one set of P;s. Another point to note about this empirical model is that all closest-approach crossing separations in a sector can be analyzed together without regard to which flight level or crossing point they are from. CONCLUSION

The feasibility of applying data from human-factors experiments involving air traffic controllers to estimating the expected number of conflicts in a given pattern of air traffic is demonstrated in this paper. Past experiments on human controllers were not conducted for estimating conflicts and, therefore. have certain deficiencies for this application. However, since these experiments represent the only existing sources of pertinent data, they are used for demonstration purposes with the hope that further research into the

Amin A. and Mayfield C. E. (1967) ilr~trl,~i.\ of (‘o!~oY>/ and TrQic in thr Operutionul NAS En~~iror~nw~t. Fran hl~n Institute Research Laboratories for U.S. Federal Aviation Administration. Report No. FAA-RD-67-25. Arad Bar-Atid (1963) Control Load. Control Capacity ad Optimal Sector Design. Interim Report on Project No. 102-l lR, RD-64-16, U.S. Federal Aviation Agency. Bradbury P. U. and Busch A. C. (1972) Measurenlent and Amlvsis of ASR-4 S~stenz Error. U.S. Federal Aviation Administration. National Aviation Facilities Experimental Center. Report No. FAA-RD-73-62. Chapman C. (1971) MC~I.YIII.~III(IIII mtl ilrztrl~%.\ qf En Route ,47C Digitul Rtrdar S~strm Errors. U.S. Federal Aviation Administration. National Aviation Facilities Experimental Center, Report No. FAA-RD-7 l-63. Connolly, D. W. and McCoskcr W. R. (1970) Hwnut7 Fucro,t in U,w of Twt~~iml Rtrrlur (Amloyue) Disp1a.1 S?stems. U.S. Federal Aviation Administration, National Aviation Facilities Experimental Center. Report No. FAA-RD-70-66. David H. (1969) Human factors in air trafic control. ,4 Study cd’ the Ability of rlw Huwu~ Opwaror IO Pdict Dangerousl~~ Clo.w Appronchr.\ Simulated Radur Displu~x Ph.D.

University of Technology. David H. (1967) Muneuwrs Control1er.s Estimared

Brtwrrrl

Thesis. Loughborough.

Airc,rtr/i

on

Loughborough England.

R~c~ornnwdrd hr Air Trtrffic, Oh.wruiny Elrctronic Simflutrons urd Their Cansequence.s. Loughborough Universiiy of

Technology. Department of Ergonomics and Cybernetics. Dunlay W. J. (1972) A Stochmric Model of’ Controlled Airrvu!, Tmffic. U.S. Federal Aviation Administration. Report No. FAA-AV-7 t-6. Faison W. E.. Meisner M. B.. Percrson P. H. and Given J. J. (1970) ,4m~l~ricu/ Studj~ of .4/r Trtrtfic’ CupuciIj~ it7 the New York Metropolirm Arru. U.S. Federal Aviation Administration, Report No. FAA-RD-70-7. Holliday R. H. (1970) Enyimeri+l Surw.v unrl 4nc1lj,si.\ qf En Routr A TC Ruriur.lDivplu~ S~strnl Error\. U.S. Federal Aviation Administration. National Aviation Facilities Experimental Center. Report No. FAA-RD70-46. Mangelsdorf J. E. (1955) Vuriahlus Affrrrirx/ rhr Acrwwr of- Collision Judymrr~‘ts ou Radar-T \,pe bisplays. Ohio State University, Laboratory of A;iation Psychology. Wright Air Development Center, Report No. WADCTR-55-462.

Application

of human

McGuire J. C. (1957) Effect of TrafJic Conjigurations on the Accuracy of Radar Air Traffic Controller Judgments. Ohio State University, Laboratory of Aviation Psychology, Wright Air Development Center, Report No. WADC-TR-56-73. Ratner R. S., Williams J. O., Glaser M. B., Stuntz S. E. and Couluris G. J. (1972) The Air Trafic Controller’s Contribution to ATC System Capacity in Manual and Automated EnGronmenrs. Vols. I and II. Stanford Research Institute for U.S. Federal Aviation Administration, Report No. FAA-RD-72-63.

factors

data

217

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Rhmek-Ce communiquC s’efforce de dCfinir et d’tvaluer la frtquence des interactions des appareils (ce que l’on entend par “conflits”) qui ntcessitent l’intervention du contrhleur. La &he de dCtection des conflits est considtrCe comme un processus de stimulus-r&action od l’intensitb de stimulation correspond & une separation particulikre de couloirs d’atterrissage/de dtcollage trop rapprochts entre les appareils tandis que la probabiliti: correspondante de reaction est la fraction du nombre de fois oi les contrijleurs jugent que cette stparation risque d’entrainer une violation de la norme de stparation minimale qui est de cinq milles marins. On utilise les donnees rCsultat des etudes entreprises sur les facteurs humains associts au contrBle de trafic abien pour &valuer les probabilitts de rCaction pour une gamme ttendue de situations de sbparation des trajectoires d’atterrissage trop rapprochtes. On d&nit deux types de probabilite de &action. Le premier type (normatif) prtdit a quel moment les contrbleurs doivent intervenir en se basant sur une analyse des erreurs humaines et des anomalies de fonctionnement de l’dquipement au tours du processus de contrBle du trafic aerien. Le second type (descriptif) prCdit le moment oh les contrBleurs interviennent en fait en se basant sur les don&es obtenues par la simulation en temps rtel de la dCtection des conflits. Ces probabilitCs de r&action sont incorporCes B un modkle empirique permettant d’bvaluer le nombre p&u de conflits au tours d’une ptriode de temps spCcifibe en se basant sur les don&es obtenues B partir des bandes de trajectoires de vols dont disposent les contr6leurs de trafic abrien.

Zusammenfassung-Gegenstand der Untersuchungen war, solche Konfliktsituationen zu definieren und in ihrer Hlufigkeit abzuschitzen, die das Eingreifen von Fluglotsen erforderlich machen. Die Aufgabe, Konfliktsituationen zu erkennen, wird als ein Reiz-Eingriff-ProzeB angesehen. Dabei ist die Stirke des Reizes ein bestimmter Minimalanflugabstand zwischen Flugzeugen. Die entsprechende Eingriffswahrscheinlichkeit ergibt sich aus dem Zeitanteil, in dem Fluglotsen diesen Abstand als eine potentielle Unterschreitung der Abstandsstaffelung von 5 Seemeilen beurteilen. Ergebnissc von Untersuchungen, die sich mit Humanfaktoren in der Flugsicherung befaRten, wurden dazu verwendef die Eingriffwahrscheinlichkeiten fir eine groRe Spannweite von Minimalanflugabstinden zu ermitteln. Dabei konnten zwei Arten von Eingriffswahrscheinlichkeiten definiert werden. Die erste (normative) gibt, ausgehend von Untcrsuchungen iiber menschliches Fehlverhalten und von Gerltefehlern bei der Flugsicherung, Auskunft dariiber, wann Fluglotsen eingreifen sollten. Die zweite Art-deskriptiv-sagt aus, wann sie tat&chlich eingreifen, wobei hierftir Datenmaterial aus Real-time-Simulationen der Konflikterkennung verwendet wurde. Die so ermittclten Eingriffswahrscheinlichkeiten sind Bestandteil eines empirischen Modells, mit dem sich auf der Grundlage von Flugdatenstreifen die voraussichtliche Anzahl von Konfliktsituationen innerhalb eines bestimmten Zeitraumes vorausschgtzen 1iBt.