CONFLICT RESOLUTION FOR FREE FLIGHT CONSIDERING

DEGREE OF DANGER AND CONCESSION

Mustafa Suphi Erden, Kemal Leblebicioğlu

Department of Electrical & Electronics Engineering, Computer Vision and Intelligent Systems Research Laboratory,

Middle East Technical University, 06531 Ankara, Turkey

Keywords: Air traffic management, free flight, conflict resolution, fuzzy reasoning.

Abstract: In this study a conflict resolution technique based on danger

and concession considerations is presented for

free flight paradigm. A danger function which assigns a danger value for the conflict situation, and a

concession function which assigns a concession value for the path followed by the aircraft are constructed.

The danger and concession values are input to a fuzzy decision module. This module outputs the amount of

deviation from the optimal path and the conflict is solved following these deviations. The method presented

here is the third method we have been studying regarding to the conflict resolution problem. Its results are

presented with a comparison to our other two studies.

1 INTRODUCTION

The air traffic load whole around the world is

estimated to double in the year 2025 (Perry, 1997).

The increasing demand of airspace due to the

increase in air traffic forces current Air Traffic

Management Systems (ATMS), which are mainly

relying on human, to be replaced with safer and

more efficient intelligent control systems. It is stated

that “Due to the increasing traffic, the workload of

human air traffic controllers will soon be too heavy

to handle and the current centralized ATMS will be

more and more unsafe (estimated one major accident

per week by the year 2015) and also inefficient (5.5

billion dollars lost annually)”, (Sekhavat and Sastry,

1998). In today’s ATMS, the air-traffic controllers

(ATC) take the whole load in both arranging the

paths and solving the conflicts between aircraft

paths. However the increase in the number of flights

makes the system so complicated that it is

impossible for a centralized controller to manage the

control in an efficient way. More seriously, a

collapse in the centralized controller would lead to

the collapse of the whole system. The increasing

technology, such as Center-TRACON (Terminal

Radar Approach Control) Automation System for

trajectory calculations and Automatic Dependent

Surveillance (ADS) making use of Global

Positioning System (GPS) for navigation

information, lead to a new system in air traffic

control, namely the ‘free flight’. The idea of free

flight is based on more autonomous aircraft

capabilities that are only possible with the currently

developed communication, navigation, guidance and

intelligence technologies. One of the major problems

to be solved in free flight is the conflict resolution

that will avoid the crashing of aircrafts.

This paper deals with the problem of conflict

resol

ution as a sub-problem of air traffic

management based on free flight. In our previous

works we had studied on the same problem with

“potential field” (Erden et al., 2001) and

“negotiation” (Erden et al., 2002) based conflict

resolution techniques. Potential field based conflict

resolution is widely studied in the literature (Bosg,

1997; Eby et al., 1999; Tomlin at al., 1998; Pappas

et al., 1997; Tomlin et al., 2000). This approach is

attractive because it is simple to be applied. It is

based on simple calculations and it necessitates no

communication between aircrafts. However, lacking

of communication brings about the disadvantage of

lacking of cooperation between the aircrafts.

Negotiation based conflict resolution on the other

hand is a technique which solves the conflict by

negotiation between the aircrafts. This negotiation

system necessitates quite complicated reasoning

algorithms and a lot of communication between the

aircrafts. These two techniques represent the trade-

off between cooperation and simplicity in conflict

resolution algorithms. The “danger-concession”

based algorithm developed here might be considered

185

Erden M. and Leblebicio

glu K. (2004).

CONFLICT RESOLUTION FOR FREE FLIGHT CONSIDERING DEGREE OF DANGER AND CONCESSION.

In Proceedings of the First International Conference on Informatics in Control, Automation and Robotics, pages 185-192

DOI: 10.5220/0001133501850192

 SciTePress

as a middle range algorithm between these two.

Namely, the algorithm here lets some cooperation

with simpler communication between aircrafts. This

technique makes use of the idea of a compromise

between danger and concession. At any instant, the

aircrafts determine the amount of the danger they

face and the amount of the concession they have

made till that time. The functions determining these

amounts might be different for any aircraft. After the

amount of danger and concession are determined the

fuzzy rule based system determines the amount of

deviation for each aircraft.

2 CONFLICT AND CONFLICT

RESOLUTION

Aircrafts follow their optimised paths while flying.

The optimisation is made according to the goals of

each aircraft, in a global manner. The optimization

criteria can be based on fuel consumption,

atmosphere conditions, maneuverability of the

aircraft, timing considerations, passenger comfort,

etc. The structure of the plane, the pilot preferences,

the task to be accomplished, or any other thing may

affect the weight of cited criteria while constructing

the cost function of the optimization. As a result,

each aircraft has a different optimization function for

path construction, and these cost criteria may change

in time according to different situations. Although

the aircraft paths in certain areas may be constructed

by optimization, it is impossible to foresee all the

air-traffic around an aircraft’s flight path. Hence,

there is always the possibility that any two flight-

paths may cross each other at a point at same time.

When this occurs aircrafts come closer than a

minimum distance and a conflict occurs. The result

of such conflict may be so tragic that they may even

have a crash.

The accepted formal definition of the conflict is

given in terms of the accepted minimum separation

criteria between aircrafts. This criterion is 1000 feet

vertically and 3 miles horizontally around airport, 5

miles horizontally elsewhere in the en route

environment. Since the conflicts are mostly in the en

route the concern for the free flight conflict

resolution techniques is the 5 miles limit. In fact, this

5 miles standard comes from the technical limits of

the radar, which completes a scan every 12 seconds

(Perry, 1997). When the satellite-based ADS

technology is implemented on a large scale, this 5-

miles separation standard can be significantly

reduced, and hopefully the free flight system will

have much less separation standards. Currently this

standard is in order and the applications here will be

based on this 5-miles separation. In (Tomlin at al.,

1998), the detection zone defined by the radius of

aircraft’s sensing capability is suggested to be 100

miles. This range could be of concern for the

conflict resolution algorithms to operate in general

applications.

As mentioned before, general conflict situation

formalizations and resolution techniques are mainly

concerned with the en route flight. The en route

flights of aircrafts are generally constant speed,

linear, constant level cruise flights. The preferable

solutions for conflicts are maneuvers that change the

direction of the flight, in the same level, with

constant speed. This is what pilots prefer for flight

quality and passenger comfort. The conflict

formulation and the proposed resolution technique in

this research are in accord with this preference: the

conflict resolution technique here is based on

constant speed, constant level maneuvers.

In current air-traffic control systems, conflict

resolution is performed centrally by ATC. The

technique is totally centralized, and air traffic

controllers have the highly stressful task of manually

guiding and sequencing many aircrafts through their

sectors of airspace. In order to simplify the system,

ATC avoids the problem of multi aircraft conflict by

placing the aircrafts in holding patterns (Tomlin et

al., 1998). This simplification of the system results

in inefficient solutions. Furthermore, the current

system is unreliable since any failure in the central

ATC will affect all the aircrafts relying on that

center.

In free flight control scheme aircrafts will be

capable of solving conflicts between themselves.

The stressful task of ATC will be distributed among

the aircrafts; they will take action according to real

time situations, rather than predefined routes or

plans. Although the decentralization of the conflict

resolution will be achieved relying on the intelligent

systems, it still seems to be too early to leave out the

ATC. Even in a completely free flight system ATC

will exist to foresee some of the conflicts and inform

aircrafts about these when they are far away from

their detection zone. This will probably be more safe

and efficient since it will be possible to take effect in

advance. In this research such a contribution of ATC

to conflict resolution is not of concern. Only

autonomous conflict resolution applicable to the

conflicts in detection zone is studied.

When two conflicting aircrafts are taken into

account, they both have their pre-planned, probably

linearly directed, routes that cross each other at the

same time. In order to solve the conflict, at least one

ICINCO 2004 - INTELLIGENT CONTROL SYSTEMS AND OPTIMIZATION

186

of them should change its route in near region of the

conflict. But it will be fairer if both of them deviate

from their routes. Of course, each one will want to

deviate less from its path. (Then the conflict

resolution problem can be considered and modelled

as a zero-sum game (Mestertob-Gibbson, 1992),

being competed on the amount of deviation.) The

conflict resolution should avoid the conflict with

minimum deviation from the optimised paths. From

point of view of an aircraft there is a trade-off

between eliminating the danger and following the

optimal path. In the technique here the trade-off

between the danger and concession of an aircraft is

considered to represent the trade-off between the

sacrifices of the two aircrafts. It is assumed here that

when the two aircrafts determine their deviations

depending on the amount of danger of the conflict

and the concession each has made, the resultant

solution between the two aircrafts will be a fair one.

3 CONFLICT RESOLUTION

CONSIDERING DEGREE OF

DANGER AND CONCESSION

WITH A FUZZY RULE BASED

REASONING

Structure of the Model

In this conflict resolution model the degree of

danger and concessions made by the aircrafts are

taken into account. A fuzzy-rule based reasoning is

used to relate danger and concession values to the

deviation of aircraft from its optimum path. The

deviations are performed by turning in the clockwise

direction from the optimum paths. Clockwise

direction is considered here as the “‘rule of the road’

which specifies the direction of the avoidance for

conflict maneuvers” (Pappas, 1997). There is no

negotiation in this scheme, but some cooperation in

the sense to transmit the position, velocity, and

destination information. Considering the

communication between aircrafts, this technique is

not as complicated as the negotiation model (Erden

et al., 2002), but a little more complicated than the

potential field model (Erden et al., 2001). The

danger and concession values are determined by the

danger and concession functions of the aircrafts. It

is necessary to make appropriate danger and

concession definitions according to the structure of

the plane and formulate it to give a value in the

range [0,1]. These functions would be expected to be

different for each aircraft due to different

considerations in conflict resolution, but they are

taken as the same in the simulations here. From the

view of a plane the data it needs related to the other

plane is the other plane’s instant position, velocity

and destination. The solution generated by this

method will be a fair one according to the danger

and concession definitions. In the simulations in this

research, similar aircraft and similar pilot

considerations (minimum deviation) are assumed;

hence the results obtained are expected to be fair in

the sense of equal deviation from the paths. The

block diagram of this model is given in Fig. 1.

After the degree of deviation is determined

(Fig.1), it is multiplied by π/2, and this gives the

deviation angle of the plane. The deviation is (u

/2) degrees clock-wise turning according to the

direction pointing to the destination from the instant

position of the aircraft. Determination of this

deviation has nothing to do with the heading of the

aircraft; hence the aircraft may turn in counter

clockwise direction, if its direction of heading is

more than the required clockwise turning.

Figure 1: Block diagram for the reasoning of degree of

deviation.

Concession Function

Concession function assigns a degree of concession

value to the aircraft according to the conflict

situation. This calculation considers the path

followed by the plane up to that instant, and the path

it would have followed if no conflict had occurred.

Consider the situation in Fig. 2. In this figure the

conflict resolution process starts when the plane is at

point A, and B is the point that the plane wants to

reach after solving the conflict. S denotes the

optimum (in general shortest) path from A to B that

the aircraft would have followed if there had been no

conflict. P shows the instantaneous position of the

aircraft. The aircraft has followed the path

designated by L

up to that instant from the

beginning of conflict resolution, and at best it can go

through L

from that point on. The concession the

aircraft has made till now is a matter of the

difference between the optimum path without

conflict and the best path it can have followed from

that time on. Let’s define L as the sum of L

and L

CONFLICT RESOLUTION FOR FREE FLIGHT CONSIDERING DEGREE OF DANGER AND CONCESSION

187

L =L

(1)

Then a normalized concession can be defined as

follows,

Concession=(L–S)/L , [0, 1] (2)

When L is too large, it means that very much

deviation from the optimum path has occurred, and

concession approaches to 1. Concession is zero if L

and S are the same, namely if there is no difference

between the optimum path and the best path that has

being followed till that instant.

Figure 2: Variables used in calculation of concession.

Danger Function

Danger function assigns a danger value to the

conflict situation according to the degree of danger.

Each aircraft is assigned the same value of danger

because they are both subject to the same conflict.

The function considers the minimum distance that

would occur between the aircrafts if they flew on the

direct paths from their instant positions to their

destinations. This distance is compared with the

minimum safe distance allowed between the

aircrafts.

Consider the conflict situation in Fig. 3. Aircraft

1 is initially at (x

) at t=0, with velocity v

, its

destination being (x

). Aircraft 2 is at (u

), with

velocity v

, and its destination is at (u

).The

distance between is d

at that instant. Their distances

to the intersection of their direct paths (x

), are l

and l

respectively. Minimum distance is assumed to

occur when the aircrafts are at the square points at

time t

. This assumption is valid for all situations of

minimum distance occurrence; even in the case one

plane has passed the intersection point. A careful

inspection will reveal that in different cases the signs

of parameters will change but the results found will

be the same. Hence, it is valid to perform the

calculation for this particular case and apply it to any

conflict situation.

Using simple geometry, coordinates of the

intersection point of direct paths are found as in Eq.3

and Eq.4.

Figure 3: Calculation of the minimum distance in a

conflict situation.

−

⋅+

−

⋅−−

(3)

)

−

⋅−+=

(4)

Then the remaining calculation is to find the

distance between the aircrafts at any time, and

minimizing it with respect to time. The distance

between the aircrafts at time t is given by Eq.5 (by

the cosine theorem).

(5)

cos)t

l)(t

l(2

l()t(d −−−−+−=

When we take the derivative of d(t) and equate it

to zero, we find the minimum distance time as,

(6)

The minimum distance (d

min

) occurs at time t

The danger function is defined as in Eq.7.

v)cos(2

)

v(cos

⋅⋅−+

+⋅−+

⎪

⎩

⎪

⎨

⎧

≥

〈

−

⋅

min

dif,0

min

dif,

min

danger

(7)

Danger is calculated when the minimum distance

is less than the danger distance, r

min

, namely if a

conflict situation exists. Considering the first line of

the equation, the right part stands for the degree of

danger; it is 0 if d

min

is equal to r

min

(no conflict), and

1 if d

min

is equal to zero (the aircrafts will crush if the

conflict is not solved). The left part, r

min

, makes

the distance between the aircrafts effective in

determining the degree of danger. If they are far

away from each other there is not much to worry

ICINCO 2004 - INTELLIGENT CONTROL SYSTEMS AND OPTIMIZATION

188

since they will have time to make maneuvers; then

this ratio is almost zero. On the other hand it

approaches to 1 if the aircrafts get close to each

other. With this function a value in the range [0, 1] is

assigned to the situation, as the degree of danger.

Fuzzy Reasoning

The fuzzy reasoning block assigns a degree of

deviation angle to each danger-concession pair. The

logic is simple, that the deviation should be

increased with increasing danger, and be decreased

with increasing concession. Since avoiding danger is

more important than making less concession the

predominance is given to the danger consideration.

(This can be observed on the last columns of the rule

table. If there is a big danger, the deviation is

determined to be very big – as F, G, I – even if the

concession is zero.) The input and output

membership functions and the rule table are shown

in Fig. 4. Input and output variables are in the range

[0, 1] as mentioned before.

Figure 4: Membership functions and the rule table of

fuzzy reasoning using the degree of danger and

concession.

Simulation Results

Fig. 5 shows four simulation results for different

conflict situations. The parameters and velocities of

the aircrafts are depicted on the figures. In these

simulation results there are two noteworthy things.

One of them is the smoothness of the paths. The

other is that the maneuvers have been made

immediately after the planes go in the alert zone, far

before they get too close to each other. For the figure

at the right-bottom, the alert zone is doubled (40nm)

compared to other figures, to see the early effect of

resolution. The planes have put themselves in non-

conflicting routes at about 20 nm away from each

other. The right-up figure is also important to see the

early effect and smooth path features of this

technique. (A comparison of this figure with the

similar ones in the negotiation case (Erden et al.,

2001) would reveal that, in this technique the paths

are smoother and the planes approach each other

only once as near as the minimum distance.)

Figure 5: Simulation results for danger-concession-fuzzy

resolution model.

Danger-Concession-Fuzzy Reasoning Based

Conflict Resolution for More Than Two Aircraft

Conflicts

Being suitable to be generalized for more than two

aircraft conflicts is another important feature of

conflict resolution algorithms. (Potential field

technique is very easy to be generalized for more

than two aircrafts (Erden et al., 2001), but

negotiation based conflict resolution is not. In our

study negotiation was generalized only to three

aircraft conflicts. (Erden et al., 2002). The technique

here is similar to potential field technique in the

sense of easiness to be generalized to more than two

aircrafts.

In danger-concession-fuzzy reasoning based

algorithm above each aircraft is assigned a degree of

danger value according to the conflict situation with

the other aircraft, and a concession value

considering how much deviation the aircraft has

made from its optimal path. These danger and

concession values are used in a fuzzy reasoning

module to determine the degree of deviation from

the direct path pointing to the destination. With this

degree of deviation the vector to be commanded to

the aircraft is determined. In order to generalize this

method to more than two aircraft conflicts, the same

algorithm is used for each aircraft in the conflict.

Each aircraft in the conflict is assigned a direction to

CONFLICT RESOLUTION FOR FREE FLIGHT CONSIDERING DEGREE OF DANGER AND CONCESSION

189

be followed by every other aircraft in the conflict.

The vectors pointing in these directions are summed,

and this gives the resultant direction to be followed

by the aircraft. In this way an average of the

deviations commanded by all aircrafts is obtained as

the resultant deviation. In Fig. 6, the results obtained

for three, four, and five aircraft conflicts are

depicted. The parameters used are indicated on the

figures.

Figure 6. Danger-Concession-Fuzzy Reasoning based

conflict resolution for more than two aircrafts.

In these figures one can observe two positive

features of the algorithm. First one is that aircrafts

make maneuvers in advance before approaching to

each other. In this way the conflict is solved much

before they come close. (This problem was faced

with the negotiation based conflict resolution (Erden

et al., 2002).) Second, the maneuver is distributed to

a wide range of route, hence sharp turns are avoided.

(This is a general problem of potential field based

conflict resolution, where unflyable paths occur

(Erden et al., 2001)). The alert zone in these

simulations is taken to be 40 km. Some of the

aircrafts are already in the alert zone of others when

the simulation starts.

A drawback of this method is that: the aircrafts

are directed according to the determined directions,

but the safety of these directions is not tested at each

iteration. (That was the case in negotiation based

conflict resolution). In the case of the method

described here, there may be situations that two

aircrafts approach too much to each other when the

traffic is too crowded. This is the case in Fig. 7. In

this figure the parameters related to danger and alert

zones are different from the above figures. The

situation is a five aircraft conflict. Aircrafts 4 and 5

come too close to each other at the point indicated

by the arrow. At these points the distance between

them is less than the minimum separation distance

depicted on the figure. This kind of a problem is

probable to occur with any kind of conflict

resolution technique when the number of aircrafts in

the conflict situation is heavily increased. This result

points to the fact that heavier air traffic conditions

necessitate more safe-guaranteed conflict resolution

techniques. It should be necessary to equip the

conflict resolution algorithms with testing modules

and modify the generated paths if the requirements

are not met. It would also be possible to avoid such

problems by tuning the parameters of the algorithm.

For example increasing the coefficient in danger

calculation might result in paths more far from each

other. However, such an approach would provide a

partial solution rather than a general one. This is

because there would occur again such problems if

the conflict situation is changed and more and more

aircrafts are included.

Figure 7: A five aircraft conflict resolution in which

aircrafts 4 and 5 come too close to each other.

4 CONCLUSION

The increase in air traffic, force the air traffic

management systems to be evolved towards more

decentralized control systems. With the improved

technologies in the fields of radio wave

communication, navigation, and intelligence, it

seems the current air traffic management systems

will soon be replaced with multi agent based

decentralized management systems compatible with

‘free flight’. Free flight is a recently developed air

traffic control structure in which much of the

workload of the central controller is distributed

among the aircraft agents and aircrafts are capable of

planning their paths and solving much of the

conflicts cooperating with each other. One of the

major problems to be solved in a free flight system

is “conflict resolution”. The paths of two aircrafts

are said to be conflicting if the aircrafts come closer

than a predefined distance at some point of these

paths. Conflict resolution algorithms are to solve

these conflicts by modifying the pre-planned paths

ICINCO 2004 - INTELLIGENT CONTROL SYSTEMS AND OPTIMIZATION

190

of aircrafts in a proper manner. The matter here is

that conflict resolution algorithms should be

compatible with the free flight understanding, in the

sense that they should be feasible to be applied to

different optimisation strategies of aircrafts. It is not

supposed to force the aircrafts in predefined

structured paths, rather to consider different criteria

such as size, maneuverability, pilot considerations,

passenger comfort, etc and command an appropriate

maneuver in real time. The paths generated should

be near optimal with respect to these aircraft specific

criteria. Therefore the matter is to develop conflict

resolution algorithms capable of handling different

optimization strategies.

The conflict resolution algorithm developed here

is based on considering the degree of danger in the

conflict, and the degree of concession the aircraft

has made by deviating from its optimal path till that

instant. Degree of danger and degree of concession

are fed to a rule based fuzzy reasoning module to

determine the degree of deviation. In determining

the degree of danger the minimum distance that

would occur from the optimal path is utilized. For

this the information of actual position, destination,

and velocity of the other aircraft is needed.

(Therefore a communication channel, less

complicated than in the case of negotiation is needed

for transmission of some data. (Erden et al., 2002))

This scheme is also suitable for the consideration of

different criteria for aircrafts. The definitions of

danger and concession may change with respect to

different criteria. (It seems that this technique lies

between the potential field (Erden et al., 2001) and

negotiation (Erden et al., 2002) approaches

considering the simplicity in the sense of algorithmic

and technological applicability. The algorithm is

simpler than negotiation but not as simple as

potential fields, and it needs some communication

but not as much as in the case of negotiation.)

The technique presented here can be compared

with the ones we had studied before also on the basis

of the paths generated. In potential field case,

although the technique is simple to apply and easy to

manipulate, the paths generated tend to be stuck in

some situations and sometimes result in unflyable

paths. This is a result of the fact that the forces

defined may cancel out the effects of each other in a

way the aircraft cannot jump out of the situation it is

stuck in. And in some instants the effect of one of

the forces immediately becomes so significant that a

very sharp, unflyable path occurs. These two

problems are faced with in many different

applications of potential fields with different force

definitions during the studies. The negotiation

technique overcomes this problem, since the

maneuvers are determined by negotiation rather than

the guidance of forces. However, this technique still

suffers from the sharp turnings although they are

flyable. Since the negotiation cannot take place in

far distances, the maneuvers can only be made when

the aircrafts come close enough to be able to

negotiate. Starting the maneuvers in close regions

results in sharp turnings. The danger-concession

technique does not need a complicated

communication like negotiation. It is possible that

the position and velocity information of aircrafts can

be transferred to considerably far distances.

Therefore, danger-concession technique enables the

aircrafts to make maneuvers in advance before

coming close to each other. Consequently the

resulting paths are smooth and almost equally

distributed to all flight paths. However, it should be

noted that the paths generated by the danger-

concession technique are not tested in each

maneuver, as it is case in the negotiation technique.

A way of equipping the danger-concession

technique with a testing mechanism might be to

incorporate it with negotiation. This incorporation

might be in a way that aircrafts follow the paths

generated by the danger-concession technique, and

start negotiation in the case they are close to each

other.

Another comparison of the three conflict

resolution techniques may be based on how much

cooperation of the other parties in conflict is needed

for the techniques to work properly. This point is

important especially when a breakdown in the

system of any aircraft is considered. The most robust

technique considering a breakdown is the potential

field based conflict resolution, since the only thing

necessary is the position information of the other

aircrafts, which can easily be gathered with onboard

radars. Hence, it does not need any communication

between aircrafts. The danger-concession based

technique, presented here, necessitates the final

position and velocity information of the other

aircraft. Therefore it needs some communication.

However, velocity and final position information can

be estimated with some simple onboard algorithms.

In case of any communication breakdown these

estimation algorithms may take effect and in this

way the algorithm may not necessitate any

communication between aircrafts. In the negotiation

case communication between the aircrafts is a must.

Therefore negotiation based conflict resolution could

not be used if any of the aircrafts is unable to

negotiate.

It should be noted that the ‘free flight’ based air

traffic management is yet in the level of an idea to

be applied in future. Therefore the flight and conflict

CONFLICT RESOLUTION FOR FREE FLIGHT CONSIDERING DEGREE OF DANGER AND CONCESSION

191

resolution specifications of this kind of a flight

system are not yet well defined. Besides, there is not

a widespread established technology compatible

with this scheme. This research should be

considered as a study that may give ideas for

constructing future conflict resolution schemes for

free flight. The technology used, the design

structure, and the capability of high-tech aircrafts

will determine the concrete specifications of the

conflict resolution algorithms to be used in free

flight. One more thing to be noted is that this

research is a simulation based study; hence the

algorithms developed here lack mathematical

verifications. Therefore in any application of these

kinds of conflict resolution techniques, some

assurance mechanisms may be necessary to test the

resulting paths (such an assurance exists in

negotiation based conflict resolution (Erden et al.,

2001)).

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