Tridib Mukherjee and Sandeep K. S. Gupta
Impact Lab, Department of Computer Science and Engineering
School of Computing & Informatics
Arizona State University, Tempe, AZ 85287
Abstract—Crises management for smart-infrastructure – infused
with sensors, actuators, and intelligent agent technologies for
monitoring, access control, and crisis response – requires objective
and quantitative evaluation to learn for future. The concept of
criticality – characterizing the effect of crises on the inhabitants of
smart-infrastructure – is used in this regard. This paper establishes
a Criticality Response Modeling (CRM) framework to perform
quantitative evaluation of criticality response. The framework can
further be incorporated in any criticality-aware middleware for
smart-infrastructure. An established stochastic model for criticality
response is used from our previous work. The effectiveness of
criticality response is measured in terms of the Manageability met-
ric, characterized by the Q-value or Qualifiedness of the response
actions. The CRM is applied to fire emergencies in an envisioned
smart Oil & Gas Production Platforms (OGPP). A simulation based
evaluation, using CRM over OGPP, show that high manageability
is achieved with – i) fast criticality detection, ii) fast response
actuation, and iii) non-obliviousness to any subsequent criticality
during response actuation – verifying the applicability of Q-value
as the manageability metric.
Index Terms—Crisis Response, Criticality, Stochastic Model,
Crises management is a challenging problem for homeland
security. Typically, crises management encompasses four phases
of operation : 1) immediate response to the crisis for pro-
tecting lives and property, 2) recovery efforts in the aftermath
of the crisis, 3) mitigation to lessen the impact of the crises,
and 4) preparedness to learn from the outcome for future crises.
Figure 1 depicts a simple scenario in which a fire breaks out
(crisis) in a building and demonstrates how crisis management
should enable adaptive response and recovery involving possible
human activities (e.g. fire-fighters and inhabitants). Lessons
learned from the 9/11 terrorist attacks and the natural disasters
such as Katrina, call for better preparedness for such crises
to effectively handle them . It is essential to learn from
the outcome of previous crises response to improve the pre-
paredness . Evaluating the effectiveness of crises response
processes is therefore of utmost interest in this regard to
verify the outcome (Figure 1). Attempts to develop standard
evaluation criteria for crisis management have generally resulted
in cumbersome documents such as reports/recommendations,
personnel training, and so on .
These qualitative measures, although important for the analy-
sis of the crises and their aftermath, are inadequate for a smart-
infrastructure – infrastructure infused with sensors, actuators,
and intelligent agent technologies  – which require quan-
titative measures and procedures for their evaluation. Further,
the existence of the automated agents can overlap the actions
for mitigation (termed as the mitigative actions) with the
crises response – requiring different evaluation framework for
crises management in the smart-infrastructure. The rest of the
paper interchangeably uses the terms “response action” and
“mitigative action”. The effect of crises to the inhabitants of a
smart-infrastructure has been characterized as criticality in our
previous work . Although criticalities are unpredictable, they
are not unexpected , and depend on the occurrences of
the causing critical events (Figure 1). A state-based stochastic
model has been established to capture the probable criticali-
ties and the corresponding response actions’ effectiveness .
The theoretical foundation presented in  characterizes the
effectiveness as Manageability, measured in terms of Q-value
or Qualifiedness of the response actions. However, a cohesive
framework binding the response processes to the theoretical
model to evaluate real-life emergency response processes is
The goal of this paper is to develop a generic modeling
framework, which uses the established stochastic model to
evaluate the effectiveness of crises response. In this regard, there
are three major contributions of the paper:
1) Development of Criticality Response Modeling (CRM)
framework to evaluate criticality response effectiveness.
2) Application of the CRM framework on fire emergencies
in the Oil & Gas Production Platforms (OGPP).
3) Simulation based verification by evaluating the fire emer-
gency response process using CRM over OGPP.
The CRM framework can be incorporated in any context-aware
middleware  for handling criticalities in smart-infrastructure.
Results show that manageability is inversely affected by – i)
the criticality detection delay, and ii) the response actuation
delay. This verifies the applicability of Q-value as the man-
ageability metric. CRM further allows comparison between
Fig. 1. Criticality management under fire break-out in a smart building
different criticality response action selection policies – enabling
automated learning and crises preparedness. In this regard, two
different action selection policies – i) Greedy, which selects the
response actions based on the actions’ success probabilities; and
ii) Mitigative Action based Criticality Management (MACM),
which selects the actions to maximize the Q-value  – are
compared for fire emergencies in OGPP. It is verified that
actions, oblivious to any subsequent criticality, lead to lower
manageability – further validating the use of Q-value as the
II. RELATED WORK
A large number of research has been geared towards the
design, development and evaluation of computing systems for
crises response. Examples include – i) a multi-modal data gath-
ering and dissemination platform being investigatedby the RES-
CUE project ; ii) a provisioning tool for resource allocation
and decision making for the Emergency Managers envisioned
by the Secure-CITI project ; and iii) a resource management
system for multi-crisis handling in urban settings .
Performance evaluation of such systems is essential to en-
sure service availability during crises. Evaluation of large-
scale reliable distributed computing systems for any “sense-
and-respond” applications including crises management  has
been performed in terms of timeliness and appropriateness of
response actions . The advent of safety-critical systems
(e.g. heart pacemaker and computer networks in modern cars)
enabled in-depth research  to evaluate these systems in
terms of operational reliability avoiding failures during crises
As opposed to these approaches, this paper focuses on de-
veloping an evaluation framework for the entire crises response
process in smart-infrastructure encompassing – i) physical, ii)
human, and iii) computational components. To this effect, the
Criticality Response Modeling (CRM) framework is proposed
based on – i) the concept of criticality, characterizing crises in
smart-infrastructure  ; and ii) an established stochastic
model for criticality response .
Fig. 2. Critical State Transition Diagram
III. CRITICALITY RESPONSE MODELING (CRM)
This section proposes the Criticality Response Modeling
(CRM) framework for evaluating criticality response effective-
ness. We begin with a brief overview on criticality and the state
based stochastic model  followed by the CRM framework.
A. Criticality: Concepts and Characteristics
The changes in the smart-infrastructure and its environment,
which lead the system into a disaster (such as loss of lives
and/or property) are called critical events . Criticalities are
the effects of the critical events on the smart-infrastructure. It
should be noted that by definition, criticalities lead to disasters
if proper and timely response actions are not performed. The
timing requirement associated with a criticality is referred to as
the window-of-opportunity for the criticality  . Detection
of criticalities and actuation of the response actions have to
abide by the corresponding window-of-opportunities of the
criticalities in the smart-infrastructure.
To this effect, a verifiable property of criticality manage-
ment called Responsiveness is identified and analyzed in .
Responsiveness characterizes the speed with which the smart-
infrastructure initiates the critical event detection. A control-
lability condition is established based on the temporal prop-
erties of criticalities. This condition encompasses the level of
responsiveness to give an upper bound on the time taken for
detecting and responding to the critical events. The higher the
responsiveness the more time there is to take the response
The effectiveness of criticality response is further character-
ized in terms of Manageability, which depends on the control-
lability condition and the uncertainties involved in performing
the response actions due to possible human involvement.
B. Stochastic model for criticality response
A state-based stochastic model to characterize criticality
response is established in . Smart-infrastructure under one or
more criticalities is in the critical state, otherwise it is in normal
state. Figure 2 depicts a hierarchical organization of the critical
states. A critical event takes the system down the hierarchy
through the downward links – also termed as the Criticality
Links (CLs) (Figure 2). Response actions, on the other hand,
take the system up the hierarchy toward the normal state through
Fig. 3.Modeling Framework for Criticality Management
the upward links – also termed as the Mitigative Links (MLs)
(Figure 2). CLs and MLs further associate with a probability
. The probabilities associated with the CLs signify the
probabilities of the corresponding criticalities’ occurrences. The
probabilities associated with the MLs signify the probabilities
of the corresponding response actions’ success.
The manageability of a criticality response process is mea-
sured in terms of Q-value (determining the Qualifiedness of the
response actions) achieved by the selected actions from a critical
state . The Q-value is defined as the probability of reaching
the normal state based on: 1) the individual link probabilities
of the selected response actions (i.e. the probabilities associated
with the corresponding MLs), 2) probabilities of additional
criticalities while taking the actions (i.e. probabilities associated
with the CLs originating from the intermediate states), and 3)
conformation to the controllability condition .
C. Framework for evaluating criticality response
Given the definition of criticality, and the foundation for
determining the manageability of criticality response, we now
present the CRM framework, which binds the real-life crises
response processes to the stochastic model. The framework
enables: i) evaluation of the effect of detection and response
actuation delays on the manageability; and ii) comparison of the
outcome of different response action selection policies. Figure
3 elaborates “Evaluate Effectiveness of Response Process” of
Figure 1, using the CRM framework to apply the stochastic
model to evaluate the effectiveness of criticality response pro-
cesses. As depicted in Figure 3, the proposed CRM framework
consists of five principal components:
1. Identification of the Criticalities: First and foremost, the
criticalities are identified based on the possible outcomes of
the causing critical events.
2. Determination of the Window-of-opportunities: Secondly, the
window-of-opportunity associated with the identified criticali-
ties are determined. This is achieved through experimental study
and statistical analysis from previous occurrences of similar
critical events. Further, the window-of-opportunity can be situ-
ation dependent, and therefore can depend on the existence of
simultaneous criticalities as well as the response actions selected
for those criticalities.
3. Determination of critical states: The critical states are deter-
mined based on the identified criticalities and the possibilities
of their concurrent occurrences.
4. Determination of critical state transition probabilities: The
probabilities associated with the CLs are derived from the possi-
ble human error probabilities that lead to additional criticalities.
The probabilities associated with the MLs are derived from the
successful completion probability of the actions. Similar to the
window-of-opportunitydetermination, this process also depends
on the statistical analysis and human behavior modeling under
the crises situation.
5. Application of the stochastic model: Once the critical states
are identified and their transition probabilities are determined,
the stochastic model can be used to calculate the Q-value for
any selected set of response actions for any set of criticalities.
The CRM framework can be used in any criticality-aware
middleware for the smart-infrastructure. The entire criticality
response process is evaluated based on how much time is taken
to perform the selected set of response actions and the transition
probabilities associated with the corresponding MLs. The Q-
value of the selected set of actions determine the manageability
in the range [0,1]. Such evaluation enables quantitative analysis
of the outcome of the criticality response process based on
the effect of the actuation delay of the selected actions and
the criticality detection delay. Additionally, two different set of
action selection policies can be compared for a better learning
process improving the preparedness of crises management.
The following section uses the CRM framework on a real
crisis situation – fire emergencies in offshore Oil & Gas Pro-
duction Platforms (OGPP) – based on which the aforementioned
claims are verified in Section V.
IV. FIRE EMERGENCY IN OIL & GAS PRODUCTION
We commence by briefly describing the emergency response
process. Figure 4 depicts a sample flow of events and actions
during fire emergencymanagement in the OGPP. An alarm is set
off in the OGPP under fire and explosion. In case an imminent
danger is ascertained (i.e. the alarm is not a false alarm), the
workplace is made safe by taking all the equipments to the safe
state. In this way, any possible spread of fire and explosion due
to chemical elements used in the equipments are avoided.
Apart from this, the personnel (if any) are egressed (evacu-
ated) based on an evaluation of the possible evacuation paths.
The evacuation paths are later assessed to affirm the tenability.
If in certain situations (such as spread of fire) the quality of
the evacuation path deteriorates an alternate route is chosen for
evacuation. The evacuation process further involves i) collection
of personal survival suits, and ii) assisting other personnel if
needed (or as directed). At the end of the evacuation, the
evacuees are registered at a temporary refuge. It is obvious that
once this stage is reached, the danger to the evacuees’ lives
is averted. This recovery process further includes the action
of making the equipment safe and giving feedback for proper
learning and preparedness to the future fire emergencies.
However, such feedback is subjective and therefore is inad-
equate for smart-infrastructures, envisioned for OGPP in this
paper. Embedded devices (sensors, handhelds, home automation
systems etc.) and automated agent technologies can be deployed
to enable evaluation and facilitation of the emergency response.
This paper applies the CRM framework for an objective evalu-
ation of the fire emergency response. This will enable better
learning capabilities of the automated agents based on the
quantitatively measured outcome of the response actions.
Fire & Explosion?
Return process equipment?
to safe state?
Make workplace safe?
Evaluate potential evacuation?
paths and choose route (or?
Move along evacuation?
Listen & follow PA?
Register at temporary?
Response to? c1?
Response to? c2?
Response to? c3?
Response to? c4?
State? i? (only? ci? active)?
State? ij ? (?ci? &? cj?active)?
State? ij k ?
criticality response process to MACM framework.
Flow of actions for fire emergencies in OGPP and the mapping of the
A. Applying the CRM Framework
1) Identify the Criticalities: The ’yes’ branches going out of
the decision boxes (shaded diamonds) in Figure 4 are mapped
to different criticalities. Accordingly, the set of criticalities in
case of a fire emergency in OGPP is summarized below:
• Criticality 1 (c1): Alarm for fire and explosion.
• Criticality 2 (c2): Imminent danger (such as health hazards
to the building inhabitants) under fire and explosion.
• Criticality 3 (c3): Persons getting trapped due to spreading
of fire and explosion.
• Criticality 4 (c4): Evacuation path is not tenable.
2) Window-of-opportunity for the criticalities: The average
time for survival of people under asphyxiation (which happens
due to fire and explosion) is 12 minutes. Criticalities c1, c2,
and c3 therefore have window-of-opportunities of 12 minutes
each. The window-of-opportunity of c4 also depends on the
time taken to find out the tenability of the evacuation route.
The time taken to determine the tenability of the evacuation
route is same as the time to perform evacuation through the
route (i.e. the response action time for c2) .
3) Critical States: The last three criticalities (c2, c3, and
c4) can occur only as a consequence of the first criticality (c1).
Figure 5 shows the critical states reached due to the occurrences
of the criticalities. State n is the normal state. Any other state of
the form i, ij, and ijk denotes the situation where ciis active,
ci& cjare active, and ci& cj&ckare active respectively. Note
here that the flow-chart in Figure 4 shows a sequential view
of the criticalities and their handling. In reality, there can be
different sequences in the occurrences of criticalities as captured
in the state transition diagram in Figure 5. For example, it might
be possible that after the fire alarm is set off (i.e. criticality c1
occurs) it is evaluated that the evacuation paths are not tenable
(i.e. criticality c4 occurs), leading to the possibility of state 14.
4) Critical State Transition Probabilities: Each ML in Figure
5 associates with a label which maps the actions in Figure 4. The
response actions for c1 includes returning process equipments
to safe state and making the workplace safe. The response
action for c2 is the evacuation of people through chosen routes.
Upon occurrence of c3, additional people are assisted in their
scenario of fire and explosion in OGPP.
State transition diagram for the criticalities and response actions in the
evacuation. Criticality c4 requires response such as evacuation
through different route to avoid any disaster.
The precise human error probabilities, which determine the
probabilities of successfully completing the mitigative actions
and the probabilities of any subsequent criticalities, have been
estimated in . These estimations are used to determine the
probabilities associated with the MLs and CLs. The calculation
of probabilities for CLs is performed by taking a product
of the error probabilities that lead to the criticalities. The
probabilities for MLs are calculated by taking a product of
success probabilities (subtracting the error probabilities from
1) of all the actions associated to the corresponding responses.
In case of the states with multiple simultaneous criticalities the
probabilities of all the outgoing links are further normalized
such that they all add up to 1. As expected, this leads to
reduced success probabilities for the same set of actions under
the influence of multiple simultaneous criticalities. In the state
transition diagram (Figure 5), it should be noted that if there
is a combination of two criticalities (c1 and c3, or, c1 and
c4) or three criticalities (c1, c3, and c4), it may be possible
to take response actions such that all the intermediate states
are bypassed. However, this direct transition to the normal
state excludes the actions pertaining to c1 and focuses only
on evacuation of people to temporary refuge.
V. EVALUATION OF THE CRISIS RESPONSE PROCESS FOR
FIRE EMERGENCIES IN OGPP
This section presents a simulation based analysis evaluating
the performance of the criticality response using CRM model.
We simulated the scenario of fire emergency musters on OGPP
as described in the previous section. Two different response
action selection approaches have been evaluated:
1) Greedy approach – selects response actions correspond-
ing to ML with maximum probability (oblivious to the
possibility of any subsequent criticalities)
2) Mitigative Action based Criticality Management (MACM)
approach – selects response actions corresponding to ML
with maximum Q-value .
For example, the greedy approach selects RC3 at state 143 in
Figure 5 to transit to state 14, whereas the MACM approach
selects RC3, and RA from state 143 to transit directly to n.
This way any intermediate criticalities due to human errors are
avoided. The goal of the simulation based evaluation is – i) to
verify the applicability of Q-value as the manageability metric;
and ii) to compare the manageability of the fire emergency in
OGPP for both greedy and MACM approaches.
A. Simulation Model
The simulator was developed in C++ where the criticalities
were implemented as timer events. We implemented the state
transition hierarchy in Figure 5 as an adjacency matrix with
the values representing the probabilities of state transition.
Different experiments, varying the time to perform response
actions and to detect criticalities, were performed on the same
adjacency matrix for consistency. The probabilities associated
with CLs therefore determine the timer triggers that result in
the lower-level criticality. The response actions (weights for
the MLs) are implemented as timer waits for performing the
actions. The criticality detection was performed in a periodic
manner. The criticality detection period and the time for the
criticality response actions (which depend on the structure and
architecture of the OGPP) are varied to observe the response
actions’ manageability, measured in terms of the Q-value. These
experiments were further performed for differing number of
B. Simulation Results
Figure 6 compares the manageability achieved by the Greedy
approach and the MACM approach. The comparison is per-
formed for – i) varying criticality detection delay, ii) different
time to perform response action (the results are taken for
varying the response action time for criticality c4 only to
avoid repetition), and iii) different number of simultaneous
criticalities. Results show that the greedy approach may lead
to lower manageability. The MACM approach, on the other
hand, achieves better manageability. It can be concluded that
response actions, oblivious to the subsequent criticalities (as in
Greedy approach), result in less manageability even with high
immediate success probability. This validates the applicability
of the Q-value as the manageability metric.
Increasing the time for criticality response actions has similar
effect as increasing the period of detection as both may lead
to violation of the controllability condition. The set of results
in Figure 7 shows these variations using the MACM approach
for different number of simultaneous criticalities. As expected,
we find that as period of detection and criticality response
actuation time increase, the manageability either remains the
same or decreases, drastically in some cases due to control-
lability condition violation (Figure 7). Further, as expected,
the manageability decreases with any increase in number of
simultaneous criticalities (Figures 6 and 7). These results further
validate the Q-value as the manageability metric.
The actuation delay of response to c4 has higher impact on
the manageability (Figures 7(c) and (d)) when compared to the
actuation delay of response to c1 (Figures 7(a) and (b)). This
is because the response to c4 contributes to more MLs – MLs
from states 14, 143, and 134 (Figure 5) – than the response to
c1 (ML from state 1). Informally, this means that evaluation of
and movement along the evacuation paths should be fast enough
to minimize life losses (again validating the applicability of the
Q-value as the metric for the manageability of the criticalities).
Criticality Response Modeling (CRM) framework was de-
veloped enabling objective evaluation of crises response pro-
cesses. The evaluation determines the effectiveness of crises
response in terms of manageability (measured as the Q-values
of the response actions for the criticalities occurred). CRM
was applied for fire emergencies in OGPP. As expected, the
criticality detection delay and the response actuation delay
inversely affects the manageability validating the applicability
The CRM framework can be further used to perform com-
parative study on the outcome of different response actions. In
this regard, CRM was used to compare the manageability of
two different response action selection criteria in OGPP. Re-
sults showed that response actions, oblivious to the subsequent
criticalities, result in less manageability – further validating the
applicability of Q-value as the manageability metric.
Also, such comparison and evaluation, enabled by the CRM
framework, can incur significantly steeper learning curve for
the smart-infrastructure resulting in better crises preparedness –
one of the most difficult challenges in homeland security.
The authors are thankful to Krishna Venkatasubramanian for
his contributions in developing the simulaton model; and to
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(a) c4 action time = 1 minute(b) c4 action time = 4 minutes Download full-text
Fig. 6.Variation of manageability for response actions selected by Greedy and MACM approach (w.r.t. detection delay and actuation delay in response to c4).
(a) 2 simultaneous criticalities(b) 3 simultaneous criticalities
(c) 2 simultaneous criticalities (d) 3 simultaneous criticalities
Fig. 7. Variation of manageability using MACM approach w.r.t. detection delay and action time for responding to c1 and c4.