Modeling Short-term Fatigue Decrements in the
Successive/Simultaneous Discrimination Task
Taylor Curley (firstname.lastname@example.org)
Beavercreek, OH 45324 USA
Megan B. Morris (email@example.com)
Air Force Research Laboratory
WPAFB, OH 45433 USA
Previous research using goal-directed computational models
has demonstrated that microlapses, or brief disruptions in ef-
fortful cognitive processing, are related to decreases in vigi-
lance as a function of time-on-task in the psychomotor vig-
ilance test (PVT) (Veksler and Gunzelmann, 2018). We ex-
tended these computational accounts of fatigue to model per-
formance in two vigilance tasks that differ with respect to de-
mands on working memory, i.e., successive vs. simultane-
ous discrimination (Davies and Parasuraman, 1982). While
task performance was not affected by working memory de-
mands, simulations show that fatigue moderators successfully
capture decreases in vigilance over time. Additionally, partic-
ipants showed greater individual differences in model parame-
ters related to task performance, but not in the effects of fatigue
across time. These results highlight the importance of fatigue
moderators in computational accounts of vigilance tasks.
Keywords: ACT-R; fatigue; vigilance; microlapse
The ability to direct and sustain attention over prolonged pe-
riods of time is essential to normal functioning in adults.
Speciﬁcally, the ability to sustain conscious processing of a
particular set of stimuli for periods longer than 10 s, or “vig-
ilant attention” (VA; Robertson and Garavan, 2004; Robert-
son and O’Connell, 2010; Langner and Eickhoff, 2013), is
directly linked to performance on continuous detection tasks
such as the psychomotor vigilance test (PVT), where partic-
ipants are asked to respond immediately upon presentation
of a stimulus (Dinges and Powell, 1985). The PVT has tradi-
tionally been used to demonstrate decreases in VA under con-
ditions of fatigue, where increases in degree of sleep loss are
positively associated with response errors and latency (Doran
et al., 2001; Dorrian and Dinges, 2004; Gunzelmann et al.,
2009b). While most studies examine changes in PVT per-
formance over the course of multiple days (typically coupled
with sleep deprivation), researchers have also detected and
modeled vigilance decrements over the course of single ex-
periment sessions (e.g., 30-min tasks; Veksler and Gunzel-
mann, 2018). These methods successfully simulate the ef-
fects of fatigue on a few brief vigilance tasks, such as the PVT
and the Mackworth Clock Task (Mackworth, 1948); however,
it is unclear whether these methods can account for vigilance
decrements in other related tasks.
In this paper, we describe a computational account of per-
formance on two vigilance tasks in which participants are
asked to view stimuli comprised of pairs of vertical lines
and respond when the stimuli meet certain criteria. Our pri-
mary goals were to a) examine differences in processing and
performance between successive and simultaneous discrim-
ination tasks, b) determine whether computational accounts
of fatigue provide a better ﬁt to observed data compared to
baseline models, and c) examine differences in parameter es-
timates across tasks and individuals.
Accounts of Vigilance Decrements
Theoretical accounts of VA share the idea that attention mod-
ulates performance on vigilance tasks, but differ on the exact
mechanism. Underload accounts argue that vigilance decre-
ments stem from “drifts” of attention away from the task, mo-
tivated by the monotony of the task (e.g., Robertson et al.,
1997; Smallwood and Schooler, 2006). Overload accounts,
however, argue the opposite: The taxing nature of vigilance
tasks induces fatigue, resulting in “lapses” of attention that
negatively affect performance as a function of time-on-task
(c.f. Warm and Dember, 1998). Most computational accounts
of fatigue are inspired by overload hypotheses of VA and treat
alertness as a resource that is exhausted with fatigue and re-
plenished with rest (Gunzelmann et al., 2009a). Speciﬁcally,
performance on simple vigilance tasks, such as the PVT, has
been conceptualized as a balance between fatigue and com-
pensation, where individuals offset decrements by changing
response behavior, such as lowering the requirements needed
to initiate a response. This performance is additionally af-
fected by small lapses in attention, termed microlapses, which
are positively related to fatigue and time-on-task (Gunzel-
mann et al., 2009b; Veksler and Gunzelmann, 2018).
Simultaneous vs. Successive Discrimination
An important topic in vigilance research is understanding
how fatigue affects the different cognitive processes that sup-
port task performance. This is especially true for the role of
working memory (WM) capacity, which has been shown to
be strongly correlated to lapses in vigilance (Unsworth et al.,
2010) and, more speciﬁcally, to PVT performance (Unsworth
et al., 2021). One method for understanding the link between
WM and vigilance is by contrasting performance on simul-
taneous versus successive discrimination tasks (Davies and
Parasuraman, 1982; Caggiano and Parasuraman, 2004). In si-
multaneous discrimination tasks, all of the information that
is needed to correctly classify a target item is included in the
Figure 1: Examples of target trials during the lines task. In
the Simultaneous condition, targets were either pairs of lines
with different (A) or identical (B) lengths. In the Successive
condition, targets were either pairs of lines that were both
short (C) or both long (D).
trial. During successive discrimination tasks, however, the re-
sponse requirements are such that the stimuli presented dur-
ing a trial must be compared to a template of the target item
held in WM. The WM requirements of successive discrimi-
nation tasks make them particularly sensitive to the effects of
fatigue, where task performance declines more rapidly across
trials compared to performance in a comparable simultane-
ous discrimination task (See et al., 1995; although also see
Gartenberg et al., 2018).
The Current Study
We manipulated simultaneous vs. successive discrimination
in the current study using a task in which participants are
asked to view pairs of lines that are centrally-located on a
computer screen (Figure 1). During each trial, participants
were shown pairs of black vertical lines for 150 ms following
a variable interstimulus interval (between 1.3 and 1.7 sec).
The lengths of the two lines (either 14.6 or 18 mm) were ran-
domly chosen during each trial. In the Simultaneous condi-
tion, participants were asked to respond only when both lines
were the same length or different lengths. In the Successive
condition, participants were asked to respond only if both
lines matched and were of a particular size (short or long).
Here, template-matching is not needed in the Simultaneous
condition, as observers need only to determine differences be-
tween lines in order to provide a response. In the Successive
condition, however, a template of either two “short” or two
“long” lines is needed for a comparison. We modeled perfor-
mance in both of these tasks to better understand differences
in performance due to WM capacity and fatigue.
The models were based on data collected from 24 young adult
volunteers (Mage =21.17, SDage =2.23) recruited through
the University of Dayton Research Institute and surrounding
area. Participants were asked to complete two experiment
Description Bounds BM? Fixed?
υInitial utility value [0.0, ∞] Yes No
τInitial utility threshold [0.0, ∞] Yes No
λMicrolapse penalty [0.98] No Yes
ρUtility ToT penalty [-1.0, 0.0] No No
κThreshold ToT penalty [-1.0, 0.0] No No
γConﬂict resolution time [0.05] Yes Yes
Table 1: Parameters of the ACT-R lines models with indi-
cations as to whether they are a) included in the baseline
model (BM) and b) if they are ﬁxed values or freely estimated.
“ToT” = “time-on-task”.
sessions lasting 2 hr each, where part of the study was to com-
plete the successive or simultaneous discrimination tasks on
separate days. We counterbalanced the order in which partic-
ipants completed these tasks to mitigate the inﬂuence of one
discrimination task over the other. The discrimination tasks
each consisted of 100 practice trials (which are excluded from
the statistical analyses reported in this paper) and 1,600 test
trials, and took approximately 45 min to complete. All par-
ticipants gave written informed consent in accordance with
the Declaration of Helsinki and were compensated for their
We developed the model using the Adaptive Control of
Thought-Rational, or ACT-R (Anderson et al., 2004), cogni-
tive architecture, with inspiration from previous models of the
PVT (Gunzelmann et al., 2009b; Walsh et al., 2017; Veksler
and Gunzelmann, 2018). ACT-R models behavior as emerg-
ing from a series of if/then rules that govern which actions (or
“productions”) are selected in a given situation, which itself is
governed by a central cognitive system. The productions that
are selected are a function of a) the amount of activation and
noise for any given production (i.e., utility values) and b) the
minimum activation required for a production to be selected
(i.e., utility threshold). The strength of any given production
can change as a function of baseline activation, the number of
times a production is selected, and the match between the out-
side environment and production speciﬁcations. Here, utility
values and thresholds will be determined by parameters re-
lated to fatigue. Table 1 brieﬂy lists the critical parameters
we use in our models, descriptions of the parameters, and the
speciﬁc simulations that they are included in.
For the tasks in the current study, the production rules can
be divided into four stages for any given trial:
•Pre-attentive: Prior to stimulus onset (i.e., lines appearing
on the screen), participants must withhold a response as
they anticipate a signal. Here, the model selects the Wait
production to ﬁre continuously until another production is
selected, such as when lines appear on the screen. Under
conditions of fatigue, however, the model may select and
ﬁre the Respond production, even in the absence of a valid
stimulus. This simulates false start responses when no lines
are presented on the screen.
•Attentive: Immediately upon detecting a visual stimulus,
the model will ﬁre the Attend production, which represents
the relatively automatic process of attending to and har-
vesting information about a visual cue. Similar to the pre-
attentive stage, the model can erroneously choose the Re-
spond production immediately after the Attend production,
which simulates false start responses that are quicker than
•Decision: After moving attention to a visual cue, partici-
pants must decide whether the stimulus meets the response
criteria (Match production) or not (Mismatch production).
For the simultaneous discrimination task, the model is able
to make this determination using only the stimuli presented
on the screen. For the successive discrimination task, how-
ever, the model is required to compare test stimuli to a tem-
plate held in WM, which requires more time and effort, i.e.,
about 50 ms extra. In either case, if the Match production
is selected, then participants prepare to give a keyboard re-
sponse; otherwise, the model will select the Wait produc-
tion in anticipation of the next trial. Incorrect responses,
which increase under conditions of fatigue, occur when a)
the Mismatch production is selected given a target stimu-
lus (“Miss”) and b) when the Match production is selected
given a non-target stimulus (“False Alarm”).
•Response: When the model has decided to respond, it ﬁres
the Respond production, which simulates the physical act
of pressing the “j” key on a keyboard. Consistent with
Fitt’s Law (Fitts, 1954), the model takes approximately
300 ms to execute the movement at the beginning of the
experiment and becomes quicker as a function of practice
throughout the task.
Additionally, the model can ﬁre the Microlapse production,
which is a brief interruption in model processing (50 ms).
Microlapses occur when there are no productions with acti-
vations that exceed the production selection threshold and in-
crease as a function of fatigue, simulating lapses in VA during
continuous response tasks (Gunzelmann et al., 2009b).
In our full model, fatigue penalizes both the utility values
(U) of these target productions and the threshold of the selec-
tion mechanism that controls which production is executed
(UT ). Speciﬁcally, utility values at a given time tare a func-
tion of both time-on-task and occurrence of microlapses, such
U(t) = υ×[λNml ×(1+t)ρ],(1)
where υis the initial utility value, λis a penalty for micro-
lapses, Nml is the number of microlapses that have occurred
in a given cycle, ρis a time-on-task penalty speciﬁc to utility
values, and tis the amount of time (in minutes) spent in the
Model Cond υ τ ρ κ -2LL
Baseline Sim. 1.17 0.56 - - 1546.88
Succ. 1.90 0.35 - - 2016.71
Fatigue Sim. 1.43 0.81 -0.18 -0.21 1374.88
Succ. 2.03 1.02 -0.24 -0.20 1497.86
Table 2: Best-ﬁtting parameters and associated ﬁt for models
ﬁt to all data.
The production selection threshold is affected much in the
same way; however, only time-on-task, and not the occur-
rence of microlapses, has a direct effect on τ:
U T (t) = τ×(1+t)κ,(2)
where τis the initial utility threshold value, κis the time-
on-task penalty speciﬁc to the utility threshold and, tis the
amount of time spent on the task (scaled to minutes).
We ﬁt the observed experiment data from both tasks to two
models: One without fatigue moderators (“Baseline Model”)
and one with fatigue moderators (“Fatigue Model”). In both
models, we freely estimated the starting utility values (υ) and
utility thresholds (τ). In the Fatigue Model, we additionally
estimated the time-on-task penalties for utility values (ρ) and
the utility threshold (κ). We ﬁxed the conﬂict resolution time
(γ) and microlapse penalty (λ) parameters to 50 ms and 0.98,
respectively1, although only γis present in both Baseline and
Fatigue models. The models were ﬁt using maximum likeli-
hood estimation and approximate Bayesian computation with
differential evolution (Turner and Sederberg, 2012) against
the joint log-likelihoods of the observed vs. simulated reac-
tion times (RTs) (log-normal distribution), hit rates (Binomial
distribution), and false alarm rates (Binomial distribution).
All models were developed using the Julia language (Bezan-
son et al., 2017) and ﬁt using the Optim.jl (Mogensen and
Riseth, 2018) and DifferentialEvolutionMCMC.jl (2022)
Here, we present only a few analyses regarding the behav-
ioral data before discussing model ﬁt indices. The results of
the experiment are described in more detail elsewhere (c.f.
Morris et al., 2022).
We conducted a 2 (Condition: Simultaneous [Sim] vs. Suc-
cessive [Succ]) x 4 (Block: 4 blocks of 400 trials) within-
subjects ANOVA, with Greenhouse-Geisser corrections on
degrees of freedom where assumptions of sphericity were
violated. For RTs, there was only a main effect of Block,
F(1.56,31.13) = 6.95, p<0.05, reﬂecting a signiﬁcant in-
crease between Block 1, M= 0.58, SE = 0.02, and Block 2,
1We did not freely estimate these values because these values
have strong precedence in the extant literature (c.f. Veksler and Gun-
zelmann, 2018) and because early simulations indicated that model
ﬁt was not affected by these parameters.
Cond. υ τ ρ κ -2LL
Sim. 3.63 1.74 -0.21 -0.20 1525.61
(0.40) (0.31) (0.02) (0.02) (95.81)
Succ. 3.62 1.53 -0.23 -0.20 1580.08
(0.38) (0.39) (0.02) (0.01) (103.00)
Table 3: Means and standard errors of the mean (in parenthe-
ses) of the best-ﬁtting parameters and associated ﬁt for indi-
M= 0.63, SE = 0.02, p<0.05. RTs in Block 3, M= 0.64,
SE = 0.02, and 4, M= 0.63, SE = 0.02, did not signiﬁcantly
differ from each other, ps <0.05. A similar pattern emerged
for accuracy, where there was also a main effect of Block,
F(1.59,31.73) = 3.83, p=0.02. A partial interaction contrast
indicates that accuracy was signiﬁcantly higher for Block 1,
M= 0.91, SE = 0.01, compared to all other blocks, Ms = 0.89,
SEs = 0.01, χ2(1)= 6473.10. p<0.05. There were no signif-
icant main effects of Condition, nor were there any signiﬁcant
interactions between Condition and Block, ps >0.05.
We ﬁrst ﬁt the aggregated experiment data to the separate
Baseline and Fatigue models. For both experiment con-
ditions, the models with fatigue penalties (Sim: -2LL =
1374.88, BIC = 1417.27; Succ: -2LL = 1497.86, BIC =
1540.25) ﬁt the observed data better than the Baseline mod-
els (Sim: -2LL = 1546.88, BIC = 1568.07; Succ: -2LL =
2016.71, BIC = 2037.90). Table 2 lists the separate parame-
ters that were recovered from this process.
Given the better ﬁt, we also estimated model parameters
separately for each participant, but only using the Fatigue
model of task performance (Table 3). For both the Simultane-
ous and Successive conditions (Figure 3), the estimated initial
utility values varied greatly across participants (Msim = 3.63,
SEsim = 0.40, Msucc = 3.62, SEsucc = 0.38), while the cor-
responding initial utility thresholds were lower and were less
varied (Msim = 1.74, SEsim = 0.31, Msucc = 1.53, SEsucc =
0.39). Interestingly, estimates for both the utility value (Msim
= -0.21, SEsim = 0.02, Msucc = -0.23, SEsucc = 0.02) and
utility threshold (Msim = -0.20, SEsim = 0.02, Msucc = -
0.20, SEsucc = 0.01) time-on-task penalty parameters were
similar and exhibited little variation. These estimates did not
differ signiﬁcantly between the two experiment conditions,
As expected, the initial utility value and threshold esti-
mates were correlated, r= 0.77, t(43) = 8.01, p<0.05,
reﬂecting the need for productions to exceed the selection
threshold. Initial utility values were signiﬁcantly correlated
with utility time-on-task, r= -0.42, t(43) = -3.03, p<0.05,
and threshold time-on-task, r= 0.40, t(43) = 2.84, p<0.05,
parameter estimates. Similarly, the initial threshold values
were also signiﬁcantly correlated with utility time-on-task, r
= -0.70, t(43) = -6.34, p<0.05, and threshold time-on-task,
r= 0.32, t(43) = 2.19, p<0.05, parameter estimates. The
Est. Utility Value
Est. Utility Threshold
−1.00 −0.75 −0.50 −0.25 0.00
−0.4 −0.3 −0.2 −0.1 0.0
Est. Utility TOT Penalty
Est. Threshold TOT Penalty
Figure 2: Parameter estimates across participants for the
initial utility and threshold values (a) as well as the utility
and threshold time-on-task penalties (b) for the Simultaneous
Est. Utility Value
Est. Utility Threshold
−1.00 −0.75 −0.50 −0.25 0.00
−0.4 −0.3 −0.2 −0.1 0.0
Est. Utility TOT Penalty
Est. Threshold TOT Penalty
Figure 3: Parameter estimates across participants for the ini-
tial utility and threshold values (a) as well as the utility and
threshold time-on-task penalties (b) for the Successive condi-
two time-on-task parameters were not signiﬁcantly related to
each other, r= 0.02, t(43) = 0.10, p= 0.92.
These simulations support previous computational accounts
of fatigue mechanisms (e.g., Gunzelmann et al., 2009b, 2015)
and suggest that accounting for the effects of fatigue in a brief
vigilance task provides a better ﬁt to observed experiment
data compared to models that do not account for fatigue, re-
gardless of the WM requirements in the experiment task, i.e.,
Simultaneous vs. Successive conditions. They also suggest
that penalties to both production utility values and produc-
tion selection thresholds as a function of duration (Veksler
and Gunzelmann, 2018) provide an accurate account of the
decreases in response accuracy and increases in RTs in ACT-
R models of the discrimination vigilance tasks. The param-
eters recovered from model-ﬁtting indicate that while there
are individual differences in factors related to general model
performance, i.e., initial production utility values and produc-
tion selection thresholds, this is not the case for parameters
that describe decrements as a function of time-on-task, where
all estimates for both the utility value and threshold penalty
parameters showed little variation from -0.2.
The lack of differences between the two conditions in both
behavioral and computational analyses contradict a resource-
depletion hypothesis of vigilance decrements (Caggiano and
Parasuraman, 2004), where the additional WM requirements
of the Successive lines task were expected to result in greater
decreases in performance. The results are consistent, how-
ever, with a general resource-control theory of vigilance
(Thomson et al., 2015), where greater decreases in vigilance
are expected for tasks that are more difﬁcult, but not for those
that increase task engagement. In this particular task, re-
quiring participants to hold a template of the target stimuli
conﬁgured in WM might not have been sufﬁciently taxing
in order to replicate the results of previous simultaneous/suc-
cessive research (Parasuraman and Mouloua, 1987; Caggiano
and Parasuraman, 2004). Alternatively, the Successive condi-
tion might have been sufﬁciently taxing, but also engaging
enough to offset average differences in performance. An-
other possibility is that the stimuli used in the task (based on
Parasuraman and Mouloua, 1987) were more taxing than pre-
vious speeded discrimination tasks, resulting in similar per-
formance outcomes in both tasks. Regardless, the improve-
ment in ﬁt between the Baseline and Fatigue models impli-
cates a performance decrement due to time-on-task, consis-
tent with both theoretical and computational accounts of vig-
ilance. Overall, these models extend previous accounts of
fatigue and highlight the importance of accounting for decre-
ments in brief vigilance tasks.
The opinions expressed herein are solely those of the authors
and do not necessarily represent the opinions of the United
States Government, the U.S. Department of Defense, the U.S.
Air Force, or any of their subsidiaries, or employees. Distri-
bution A. Approved for public release. Case number AFRL-
2022-1772. The authors thank Bella Veksler and Chris Fisher
for their help with model development and comments on the
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