Table of Contents
Achieving what cannot be done: C oping with the time constants in
a dynamic decision task
Berndt Brehmer
Department of War Studies
Swedish National Defence College
P.O. Box 27805
SE-115 93 Stockholm, Sweden
Tel. +46 8 788 8495
berndt.brehmer@ fhs.mil.se
Staffan Nahlinder
Command and Control Systems
Swedish Defence Research A gency
P.O. Box 1165
SE-581 11 Linképing, Sweden
Tel. +46 13 37 8163
staffan.nahlinder@ foi.se
Abstract
This study examines how people handle time constants in dynamic tasks, using
a microworld called NEWFIRE, which simulates forest fire fighting. The
participants did not discriminate between fires requiring different number of
units if they were not allowed to move any units before the fire started. If they
were allowed to do so, performance improved. This suggests that the
participants do not learn the time constants, and that they used the heuristic to
preposition the units to avoid having to do so. Using such heuristics may well
be how people handle dynamic tasks also in other circumstances. More effort
should therefore be put into studying what people actually do in dynamic tasks,
not only into whether or not they perform optimally.
KEY WORDS: DYNAMIC DECISION MAKING, TIME CONSTANTS, HEURISTICS,
MICROWORLDS
There is mounting evidence that people encounter problems when trying to control dynamic
systems, even when these systems are simple (e.g., Booth-Sweeney & Sterman, 2000; Jensen
& Brehmer, 2003). Y et, the world is full of such systems so people must have found ways of
coping with them, even if what they do may deviate from what would be required on the basis
of normative theory, such as control theory or system dynamics. This would hardly be
surprising. Control theory and system dynamics are recent inventions, and hardly part of
people’s natural intuitions. In another class of tasks that also requires the use of recent
normative theory for optimal performance, i.e. decision theory, people do not make decisions
according to normative theory either, but use different forms of heuristics (see Hastie &
Dawes, 2002, for a recent overview of this research). Perhaps we would find people using
various heuristics also in dynamic tasks, if we looked for them?
This paper presents two experiments concerned with this problem. Specifically, the
experiments concem how people cope with one of the three forms of feedback delays in a
dynamic task: the time constants.
The task studied is that of forest fire fighting, using NEWFIRE, a microworld designed by
Lovborg and Brehmer (1991), which has found widespread use in studies of dynamic decision
making. In experiments with this microworld, the participants are asked to assume the role of
a fire chief located in his command post. He or she receives information about fires from a
spotter plane, and on the basis of this information, he or she sends out orders where to go to
the fire fighting units (FFU). These units then report back about their activities and locations,
and so it goes until the fire or fires have been extinguished. The concept is shown in Figure 1.
Figure 1. The NEWFIRE concept.
This task has all the characteristics of a dynamic decision task as defined by Brehmer and
Allard (1991):
e It requires a series of decisions
e These decisions are not independent
e The state of the task changes, both autonomously, e.g., due to changes in the direction
and strength of the prevailing wind, and as a consequence of the decision maker’s
actions, i.e., how he or she uses the FFUs
e Decisions must be made in real time
To cope with this task, the participant must be able to understand how fire spreads and how
the FFUs can be used to fight the fire. Specifically, the task requires the participant to place
the FFUs on the fire, or in the fire’s way, depending on the extent to which the fire has spread
and the distance that the FFUs would have to travel to reach the fire. When the fire and the
FFU meet, the extinction process starts automatically.
As in all dynamic tasks, the participant must understand and cope with the various forms of
feedback delays in the task. One form of delay that can never be avoided is the time constant,
i.e., the fact that the FFUs require time to reach the fire, and that the fire extinction process
requires time. The problem that the participant faces here is that while the FFUs are on their
way, the fire spreads even further. As a consequence, the participant must send the
appropriate number of fire fighting units to the fire. If there is a significant distance to that
fire, he or she cannot send only the number that seems to be required at the point in time when
the command is issued, for when the units reach the fire, it will have spread, and more units
will be needed than were required when the units were sent out. Of course, the converse may
also be true. If the fire is very far away, it may well have extinguished itself before the FFUs
reach it.
In earlier studies, NEWFIRE has been used to investigate how people cope with the time
constants, as well as with other forms of delays such as dead time and delayed reports from
the FFUs (see Brehmer, 1995). The results have shown that while the participants are able to
cope with the time constants, quickly learning to respond rapidly and massively to a fire, they
have considerable problems with dead time and delayed reports (Brehmer, 1989). A possible
explanation for this finding is that while the time constants can be seen to happen, dead time
and delayed reports require inferences from the participants. However, even though the results
show that people are able to cope with the time constants by means of sending out many FFUs
to a fire so as to be sure to have enough FFUs on site, we do not know whether this reflects a
more or less well calibrated strategy for handling the time constants, or whether it just
represents a very general rule of responding rapidly and massively. To investigate this
problem is the purpose of the present study.
The first question for the study concemed the precision with which the participants respond to
a fire. Is this a well-calibrated response, tuned to the actual need of FFUs when they arrive at
the fire, or is it just a very general response where the participant sends what he or she has as
quickly as possible? To answer this question, we compared the response to fires requiring
different numbers of FFUs in Experiment I. The results were surprising, at least when we first
received them, albeit, perhaps not in hindsight, and led us to investigate the heuristics our
participants used in the second experiment.
Experiment I
The purpose of Experiment I was to assess the precision in the participants’ response to a fire
by comparing the number of FFUs they sent out to a fire requiring only one unit and a fire
requiring four units in NEWFIRE.
Participants
Ten undergraduate students were paid to take part in the experiment.
The simulation: NEWFIRE
NEWFIRE (Levborg & Brehmer, 1991) is a general program for studying dynamic decision
making in spatio-temporal decision problems such as forest fires. It is written in
SMALLTALK and runs on a standard PC.
The general concept has been illustrated above (Fig. 1). Figure 2 shows what the participant
sees. The figure shows that the participants face a computer generated map with 18 x 18
(=324) squares. This represents forest. In these experiments, the forest was homogenous, as
indicated by all squares having the same shade of green. (It is possible to vary the terrain in
the program.) In the forest, there is a base where the FFUs are located. To the left, there is a
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Figure 2. The NEWFIRE interface. Forest is represented by green squares, fires by the green
aquares tuming red (e.g., L5), FFUs by blue squares and the base, if there is one, by a brown
square.
message box which gives messages from the FFUs, a box displaying the commands that have
been given to the various FFUs and a weather report which gives the strength and direction of
the wind.
In the middle of the map there was a base (a brown square marked with B) where eight FFUs
were located at the start of a trial. After some period of time (in these experiments 40 sec. in
Experiment I and 20 sec. in Experiment II), a fire starts, and this is indicated by a square on
the map turning red. As the fire spreads, more and more squares tum red, and as fire is
extinguished, the squares tun black. The participant sends out a FFU by first clicking on it
and then on the location to which he or she wishes it to go. A message appears in the message
window to the left saying that the unit is on the move. As the unit reaches its destination, it
first mobilises (which takes one time unit) (and it sends the message “Mobilizing”) and then
starts to fight fire (and it sends the message “Fighting fire”), if there is a fire in its location.
After the fire has been extinguished, the FFUs demobilize for one time unit (sending the
message “Demobilizing”). The time required for extinguishing a fire is a variable that can be
set by the experimenter, as is the speed with which the FFUs travel to the fire. The participant
can send as many units as he or she wished to a fire (out of a total of eight units) but putting
more than one unit in the same location does not result in faster extinction. The number of
fires is also a variable in the program. In the experiments reported here, there are two kinds of
scenarios: one-fire scenarios and two-fire scenarios. A trial lasts until the fire has been
extinguished or until all of the forest has been lost, or until the base has been lost. The fire
spreads in the direction of the prevailing wind and its shape and the speed with which it
spreads depends on the strength of the wind according to a fire model based on results from
actual studies of forest fires.
The FFUs moved at the rate of 1 square/time unit.
NEWFIRE is a clock driven simulation. The picture is updated once every twenty seconds. (in
Experiment I, in Experiment II the screen was updated every 10 sec.) An update interval is
called a “time unit”.
Design
The design was a within-subjects design with distance between fire and the base as the factor.
The factor had two levels: close fires, which required only one FFU, ie., they could be
extinguished simply by sending one unit directly to the location of the fire, and distant fires,
which required four units, i.e., the participant had to predict which four squares would be on
fire when the FFUs reached them, and position the FFUs accordingly. There were eight fires
of each kind. In addition, there were 12 “filler items”, as described below. They were
introduced to control the participants’ expectations. In all, the participants extinguished 28
different fires.
The time constant in this task is a function of the speed at which the FFUs move, the size of
the fire, and the distance between the FFUs and the fire. The latter aspects vary as the scenario
develops, and so do, of course, the requisite numbers of FFUs needed for a given fire. The
definition of the independent variable in terms of close and distant fires holds only for the
moment in time when the fire starts, given that the FFUs have not been moved from their
initial positions. As we shall see, there is an important an important consideration in these
experiments.
Fire scenarios. In all scenarios, the base was located in one of the middle four squares in the
map, 19, 110, J9 or J10, se Figure 1. The FFUs were placed in the surrounding eight squares.
All test scenarios involved a fire starting on the diagonal, with close fires starting at a distance
1 or 2 squares from the closest FFU and distant fires starting at a distance of 5 or 6 squares
from the closest FFU (if the units were in the starting positions around the base). This yielded
eight different starting positions for close fires and eight different starting positions for distant
fires. In additions to these 16 test scenarios, there were 12 filler scenarios. Seven of these had
two fires rather than one and five had a single fire starting in a position between the close and
the distant fires. These scenarios were included to control for the participants’ expectations
and make it impossible for them to position their FFUs in appropriate locations in advance.
The two-fire scenarios also served the function to make the participants conserve their
resources, and not send all their FFUs to the first fire they saw.
The first fire ignited 40 seconds (2 time units) after the start of the scenario in all scenarios. In
the two-fire scenarios, the second fire ignited 70-100 seconds after the ignition of the first fire.
Instructions. The participants received standard instructions (see Lovborg & Brehmer, 1991,
for details). They were told that their task was to act as fire chiefs and that they would receive
reports about fire on the screen from a spotter plane that reported the position of a fire
accurately and without delay. The screen and the mechanics of giving commands and the way
in which the FFUs would respond were explained. They were further told that their task was
to preserve the base and as much forest as possible. Thus, they had two goals: To protect the
base and to extinguish the fire(s) as quickly as possible. These goals were sometimes in
conflict, but the participants’ handling of these conflicts was not examined in this experiment.
Procedure. After receiving the instructions, the participants were given an opportunity to
practice, using the mouse, and to familiarize themselves with the experimental setting for
about 20 minutes. They then went through the 28 scenarios. They experiment required about
1% hr. to complete.
Results
To assess possible learning effects, the scenarios were divided into four blocks, with 7 (in the
analyses involving all 28 fires) or 4 (in the analyses involving only the test scenarios)
scenarios in each block.
Number of units sent to different fires. When the number of commands issued after the start of
a fire was examined for the two kinds of test scenarios, the results showed that the participants
quickly leamed to discriminate between scenarios requiring 1 unit and scenarios requiring 4
units. There was no significant change over blocks, but the number of commands issued for
the distant fires exceeded that for the close fires (8.35 vs. 6.36, F 1/143 = 16.23, p < .0001).
Remembering that two commands are required to reposition a FFU, this means that the
participants used slightly more than the required number of 4 (The mean number was 4.2) for
the distant fires and considerably more than the required number of 1 (The mean number of
units sent out was 3.2) for the close fires.
Overall performance. The primary dependent variable to assess performance in NEWFIRE is
the number of cells lost to fire. An analysis of all 28 scenarios showed that there was a
learning effect (F 3/238 = 4.52, p <.004). Performance was worse in the first block than in the
remaining three blocks, which did not differ significantly according to a Scheffe post hoc
analysis. Only two of the 280 (10 participants x 28 scenarios), or 0.7% of the scenarios ended
with a loss of base. These two scenarios were excluded from the analyses.
Next, the results for close and distant fires were examined. These results could not be
subjected to an analysis of variance because of extreme differences in within-cells variances
between the two conditions. However, the results, are clear enough also without statistical
analysis. Thus, for close fires, the number of cells lost to fire was 1 over blocks and for distant
fires, it was 5.7 with no systematic trend over blocks for either kind of fire.
If the participants had left the FFUs in their initial positions and then issued the correct
commands to their FFUs after the fire had started, we would have expected that they would
have lost 1 square to fire for the close fires and 4 squares for the distant fires. The results
showed that although the participants lost the expected number of one square for the close
fires, they lost an average of 5.7 squares for the distant fires, ie, more than the expected
number.
The participants repositioned their FFUs in the interval between the scenario started and the
time when the fire started as shown by the fact that they issued an average of 15.03
commands during this interval. Since it takes two commands to move a FFU, this means that
they managed to move almost all FFUs during the interval. Despite this, their performance
was worse than expected for the distant fires. This shows that they were not very efficient in
repositioning their units, or that they were unable to translate the new positions into effective
fire fighting commands. The fact that the participants send out four FFUs to the distant fires
required, but nevertheless lose more than the expected number of cells for these fires supports
the second of these hypotheses.
Discussion
The purpose of this experiment was to investigate whether the participants would learn the
time constants for the firefighting task. Evidence for such leaming would be that the
participants would have used the appropriate number of FFUs for different fires. The results
indicated that they were able to distinguish between the two kinds of fire at last to some
extent, and that the difference in response for the two fires was in the appropriate direction.
Their response was not very precise, however, with close to the optimal number for the distant
fires and considerable overreaction to the close fires to which 3 units, rather than 1, were sent
out. As a consequence, the participants actually reached the optimal number of one square lost
to fire for the close fires although at considerable cost. For the distant fires, the participants
performed worse than expected, despite their repositioning of the FFUs in the interval
between the scenario started and the fire ignited. They sent out slightly more than four units
that would have been required had they left the units at the base, rather than repositioning
them. This suggests that the repositioning of the units was not as efficient as it could have
been, or that the participants were notable to translate the new positions into effective fire
fighting commands. Both close and distant fires start on one of the diagonals, the distant fires
starting farther out than the close ones. (If the participants sent one FFU out along each
dianoal (NNW, NNE, SSW and SSE) as far as possible before the fire ignited, they would
have been able to reach both kinds of fires with that FFU.) As noted above, the fact that they
loose more fire than expected despite sending out the appropriate number of units supports the
second of these hypotheses. This suggests that the participants do not only have problems
with the temporal aspect of the task (i.e., finding the appropriate number of units to send out
at the correct point in time) but also with the spatial aspects, that is, to which locations that
they should send the units. This is in agreement with other results obtained with the fire
fighting simulation (Brehmer, 1998), which show that participants in these kinds of
experiments have problems predicting how the fire will spread.
These results, then, give little evidence of any precise learning of the time constants of the
task. The attempts to move the units into a better position before the fire may actually be seen
as an attempt to avoid learning these time constants, and to reduce all fires to fires of the same
kind, that is, fires to which the participants could send out the maximum number of FFUs
available to them as quickly as possible. This is, of course, an effective strategy in that
achieves the goal of extinguishing the fire. But it is not efficient in terms of cost. Specifically,
it is too costly for the fires requiring only one FFU, and in view of the fact that the
participants have moved the units before the fire has started, it is also costly for the fires
requiring 4 units. For the latter fires, the participants do not seem to be able to profit from
their repositioning of the FFUs and reduce the number of FFUs sent to these fires. One
possible explanation is, of course, that the high number of FFUs sent to these fires reflects the
same tendency to send many FFUs to a fire as the high number of FFUs sent to the fires that
would have required only one FFU.
The fact, that the participants repositioned the FFUs in the interval between the start of the
scenario and the ignition of the fire, makes it hard to assess the extent to which they learned
the precise time constants of the task. In Experiment II, therefore, we examine how the
participants handle the time constants under conditions when they are not allowed to
reposition their FFUs in the interval between the start of the scenario and the ignition of the
fire.
Experiment II
Participants
Forty undergraduate students were paid to participate in the experiment.
Simulation
This experiment used NEWFIRE, the same simulation as that used in Experiment I. However,
compared to the version used in Experiment I, that used in Experiment II also showed the
accumulated cost in a trial at the top of the map display, Cost was displayed in terms of
money units, and the cost of the various activities were as follows: A unit being inactive cost
nothing, when it moved that cost 2 money units per time unit, mobilizing, fighting fire,
demobilizing cost 4 money units/time unit and watching (= when a unit had been sent out to a
location where there was no fire (yet)) cost 1 money unit/time unit. The cost factors were the
same in the two conditions of the experiment (see below).
The update rate was set to 10 seconds rather than 20 seconds as in the first experiment simply
so that that the participants would not have to be inactive for so long before the first fire.
While considerably faster than the update rate in the first experiment, experience with
NEWFIRE shows that a 10 second update rate in no way makes excessive demands on the
participants, and it is not likely that the difference in update rates is the explanation for the
differences in results between Experiments I and II.
Design
There were two experimental conditions. In the first, the Variant condition, the strength and
direction of the wind was determined randomly for each scenario. In addition, the initial
positions of the FFUs varied randomly. Four of the scenarios in this condition involved two
fires, the remaining 16 one fire. In the two-fire scenarios, the second fire ignited in some
location of the forest 70-100 seconds after the first had ignited. The second condition was
called the Constant condition, and in this condition, the direction and strength of the wind was
the same in all scenarios. The FFUs were always located in the eight squares surrounding the
base as they were in Experiment I. Ten of the 20 scenarios were two-fire scenarios of the
same kind as those in the Variant condition.
In each condition, the participants received a total of 20 scenarios. Half of the single fire
scenarios in each condition, i.e., 8 out of 16 in the Variant condition and 5 out of 10 in the
Constant condition were one-FFU test scenarios of the same kind as those used in Experiment
I while the remaining were four-FFU-scenarios, as in Experiment I.
Procedure
The participants received the standard instructions for NEWFIRE used in Experiment I, but
the instructions also included the information about the cost of different activities described
above, and the instructions emphasized that the participants’ goals were to put out the fire as
quickly and with as little cost as possible. The need to protect the base was emphasized, and
the participants were informed that if the fire reached the base, the trial was over. The
participants were also told that they were not allowed to move the FFUs until a fire had
started. As in Experiment I, participants were allowed about 20 minutes to familiarize
themselves with the simulation. After that they received the 20 trials in their condition in a
random order unique for each participant. After 45 minutes those who wanted were allowed a
break. The experiment took between 2 and 4hr to complete.
Results
To determine if there were learning effects, the data from the experiment were analyzed
combining scenarios into four blocks of five scenarios each.
All trials in which the participants violated the rule forbidding them to issue commands before
a fire had started were excluded from the analyses. This happened in four out of the total of 40
participants x 20 scenarios (= 800 scenarios) data set. These scenarios were treated as missing
data.
The base was lost to fire in 84 of the total of 800 scenarios (11%). For trials in which the base
was lost, the total loss of forest was set to 324 cells. The logic here was that when the base
was lost, the participant could no longer control the FFUs and, consequently, all forest would
be lost. As in Experiment I, there was significant improvement over blocks of scenarios (F
3/117 = 10.77, p < .000005). Performance was better in the Variant condition than in the
Constant condition (F 1/19 = 4.42, p < .005), probably because there were more two-fire
scenarios in that condition, but, more important there was no interaction between conditions
and blocks suggesting that leaning proceeded in the same way in both conditions.
The final level of performance in the fourth block was an average of 38 cells lost to fire,
compared to an average of 2 cells lost to fire in Experiment I. Thus, both the results with
respect to cells lost and bases lost show that performance in Experiment II was worse than
that in Experiment I.
Close and distant fires
There was no difference between the number of FFUs sent out in one-FFU and four-FFU
scenarios to the fire during the first time period after the ignition in either condition, and no
difference between the conditions. That is, the participants did not discriminate between the
two kinds of scenarios. They learned to respond rapidly and massively, increasing the number
of units sent out to the fire during the first time period from 1.6 units in the first block to 2.5
units in the fourth block (F 3/117 = 25.97, p < 000001), with no main effect of conditions and
no conditions by blocks interaction. The final value of 2.5 is what should be expected if the
participants had sent 1 FFU to the one-FFU fires and 4 FFUs to the four FFU-fires.
Individual analyses
The participants were divided into “Good” and “Bad” participants according to their
performance over the 20 scenarios in their condition, the “Good” participants were those
loosing the least forest in each condition, and the “Bad” participants being those who lost
most forest. An analysis of variance showed that the “Good” participants sent out
significantly more FFUs to the fire in the first time unit than the bad participants (F 1/19 =
64.48, p < 0005). This was true both for close and distant fires, there was no participants by
fires interaction. Thus, the “Good” participants had not learned the time constants better than
the “Bad” participants.
Discussion
The results from Experiment II show that the participants did not learn to discriminate
between the two fires. This suggests that they do not leam the time constants of the fire-
fighting task under conditions when they are required to do so, but not allowed to rely on the
heuristic of repositioning the FFUs before the fire breaks out. This, in turn, suggests that the
adaptation to the time constants, seen in this and earlier experiments with NEWFIRE,
expresses a general strategy of massive and rapid responding rather than an adaptation to the
specific time constants of the task. It is interesting to note that this is true also on the
individual level: successful participants differ from less successful participants only in that
they employ the strategy of responding rapidly and massively to a greater extent than less
successful participants. The successful participants did not learn to discriminate between the
two finds of fire better than the less successful participants, so there is no evidence that they
leamed the precise time constants better.
Whether people are actually unable to adapt to the specific time constants, we do not know, of
course. We can only note that they did not do so in this experiment. The fact that they use the
heuristic of repositioning their FFUs when allowed to do so, suggests that they may be aware
of the difficulties that they have with the precise time constants and seek alternatives.
Specifically, the alternative chosen would be to adopt a strategy that makes it unnecessary to
learn the time constants by repositioning the FFUs so that all fires become similar and require
the same response. Although this strategy is costly in that it requires them to send out their
FFUs from their rest state at the base, it nevertheless gets the job done much better than if
they had not employed this strategy. Evidence for this is the much better overall performance
in Experiment I than in Experiment II (0,7% base losses compared to 11% base losses, and an
average of 2 cells lost to fire compared to 34 cells lost to fire in the last block, dramatic
differences both), despite that there were more of the more difficult two-fire scenarios in
Experiment I (43% vs. 35%). The strategy employed by the participants is, of course, neither
new nor unknown; many city ordinances require fire stations to be located so that any fire in
the city can be reached within a specified period of time.
The participants in NEWFIRE thus discover a way of achieving their goal, without
performing the task in an optimal way (hence the somewhat extravagant title of this paper).
Of course, we do not know if this is because they cannot learn the time constants, or because
they are satisfied with what they can achieve without learning these constants. The main
effect of ignoring these time constants is, after all, only that it makes the fighting of the fires
more expensive, not that it prevents them from actually extinguishing the fire. That is, it may
be that the participants decide to achieve one of the goals: extinguishing fire, at the expense of
the other goal: that of extinguishing the fire(s) at the lowest possible cost. Whatever the
explanation, the participants find a way of performing the task that does not require them to
cope with the exact time constants of the task. It is clear that they understand the general
implications of the time constants, viz., that they must respond rapidly and massively, and the
better they follow this simple rule, the better their performance. That is, it seems that they
employ a simple qualitative heuristic rule, and avoid coping with the quantitative details. This
suggests that it may be the quantitative aspects of the task, rather than its general dynamic
nature, that gives problems. This may well be exacerbated in this task by the fact that these
quantitative aspects have to be estimated by the participants from what they experience in the
task; they are not displayed in numerical form. Perhaps this is the case also for other dynamic
tasks. That is, it may well be that participants fail in such tasks, not because they do not
understand the dynamics, but because they cannot handle the quantitative details required to
demonstrate their understanding. This suggests that it may be important to distinguish
between these aspects of performance, and that it is necessary to obtain separate indicators for
the understanding of the general nature of the task, and for the ability to handle the
quantitative details.
It may also be, that people rely on heuristic rules, such as the prepositioning of the FFUs in
NEWFIRE (and of fire stations in cities) shown here, to handle other dynamic tasks as well.
To find these heuristics, we need to study how people actually behave in dynamic tasks, not
only whether they live up to what normative systems require.
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fighting experiments. Riso National Laboratory, Denmark, Riso-M-2953.
Author note
The authors are indebted to Leif Lovborg and Anders Winman for their help with Experiment
I and to Eva Jensen for her comments on earlier versions of the paper. The research reported
here was support by grants from the Swedish Social Research Council and the Swedish
Armed Forces (“The ROLF project).
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