Modeling the Dynamics of an
Urban Emergency Medical Services System
Richard Justin Martin N. Gizem Bacaksizlar
The Belk College of Business Department of Software Information Systems
The University of North Carolina at Charlotte The University of North Carolina at Charlotte
9201 University City Blvd, Charlotte, NC 28223 9201 University City Blvd, Charlotte, NC 28223
rjmartin@uncc.edu nbacaksi@uncc.edu
Abstract
Emergency medical services (EMS) are essential to the delivery of on-demand urgent medical
care to patients. The major challenge commonly encountered by EMS agencies is the effective
allocation of resources, specifically ambulances and paramedics, such that coverage is sufficient
and response times are minimized. Compounding the complexity is the growth and shift of
populations which impact EMS demand. In this study, the system dynamics methodology was
applied in order to develop a model, using industry data, that represents an urban EMS system.
Utilizing this model, the relationship between call request demand and resource capacity was
analyzed. A two-scenario analysis was conducted to observe the behavior of the model to a
ch ing number of ambulances and population. A tipping point where continued population
growth causes the system to reach peak capacity was identified. The resulting model will support
EMS managers and dispatchers with demand planning and policy development.
Keywords: emergency medical services, system dynamics, ambulances, healthcare management
I. Introduction
Emergency medical services, commonly referred to as ambulance, paramedic or prehospital
emergency services, are a critical component in the delivery of urgent medical care to
communities. Emergency medical service agencies (EMS) are organizations charged with the
responsibility of providing out- of-hospital acute medical care to the population of a defined
geographic area. EMS agencies also provide transportation to local clinical care facilities, such as
hospitals and emergency departments, for patients who are unable to transport themselves due to
the nature of their condition or circumstances. By their very nature, EMS systems are
extraordinarily complex. The demand for ambulances is dynamic and is known to fluctuate
spatially and temporally based on the time of day and day of the week (Channouf et al., 2007).
EMS managers and dispatchers are faced with the evolving task of deploying ambulances and the
personnel required to provide adequate coverage to their respective service area. Dispatchers have
the option of redeploying their fleet to compensate for spatiotemporal fluctuations, but the scope
of these adjustments is restricted by the pre-determined staffing plan for a given period. Industry
and academic researchers have conducted various studies focused on developing novel deployment
strategies, and associated staffing plans, in an effort to combat call volume variability and
maximize service coverage (Rajagopalan et al., 2011). These deployment models, developed based
on historical data, are ultimately dependent on a comprehensive understanding of demand. Related
EMS researchers have sought to identify more sophisticated approaches to forecasting demand in
order to improve predictive models for demand planning (Channouf et al., 2007) (Chen et al.,
2016) (Setzler et al., 2009) (Aringhieri et al., 2016). EMS managers and dispatchers often describe
deployment planning and redeployment decisions as an art, based on the experiences and intuition
of the individual (Penner et al., 2016). In the context of systems dynamics, these behaviors are
attributed to the mental models of individuals based on their perceptions of demand and the various
decision rules established within the organization (Sterman, 2000).
The primary justification for applying a system dynamics methodology to EMS (ambulance)
systems is to leverage an approach that, based on the current literature, has not been explored in
depth. The current related work in the system dynamics literature has focused primarily on the
development of models addressing broader emergency healthcare care issues. From a policy
perspective, Cooke et al. examined the overcrowding of emergency departments in healthcare
facilities and developed associated models (Cooke et al., 2007). Wang et al. focused on modeling
the coordination and allocation of emergency services at a strategic level under extreme
circumstances such as natural disasters (Wang et al., 2012). Historically, models addressing
common EMS problems such as resource allocation and deployment have been approached using
traditional operations research methodologies and discrete event simulations. By applying a
system dynamics methodology to this problem, the endogenous and exogenous factors that explain
the non-linear interactions between various elements and the feedback processes within the
broader system were highlighted. Specifically, the presented model concentrates on observing the
impact to the supply of ambulances considering fluctuations in call request demand overtime.
While the short-term objective of this study is to advance the demand and capacity planning
capabilities of emergency medical service agencies, the ultimate long-term goal is to improve
patient outcomes and service delivery by understanding system weaknesses and capacity
bottlenecks. This includes testing scenarios such as (1) determining the effect of adjusting the
number of available ambulances in the EMS systems fleet and (2) measuring the impact of
population growth on the local EMS system capacity. Lastly, this project seeks to alter the strongly
held mental models of the managers and dispatchers in the industry. To conduct this study a
collection of multi-year call data has been provided by MEDIC, an emergency medical services
agency serving Mecklenburg County, North Carolina. The scope of the data used includes all 911
emergency medical service calls received over the course of a one year period (2003-2004). Based
on the available data, the time horizon for this study will be focused on a 10-year period spanning
from 2003 — 2013 within the scope of Mecklenburg County. Subsequent models and findings can
be used to conduct related studies of other emergency medical service agencies using comparable
datasets.
II. Model Description
i. Variable Identification
To begin the modeling process, a boundary table (Table 1) was developed to establish scope and
identify which variables are included in, and excluded from, the study. Those variables considered
to be under the influence and control of local EMS agencies and emergency healthcare providers
were considered endogenous, while those variables outside the control of EMS agencies and
emergency healthcare providers were categorized as exogenous. Several variables were
determined to be excluded from this study including the population and healthcare resources
outside of a service area. In the context of this investigation a defined service area is determined
by the geographic area that an individual EMS agency is responsible for providing service
coverage to; such as a county, city, or municipality. Additional external variables were excluded
such as weather conditions, the average income of the population and non-clinical emergency first
responders. After completing the boundary selection, a Causal Loop Diagram (Figure 1) was
developed to illustrate the broader causal relationships among variables.
Table 1: Emergency Medical Services Systems Model Boundary Table
Excluded Variables
Endogenous Variables
Exogenous Variables
Call Response Time
Call Service Time
# of Ambulances
# of Paramedics & EMTs
Distance Between Request
Location & Next Available
Ambulance (Dispatch
Coverage)
Population
Incoming EMS Call Requests
Size of Service Area (Square
Miles)
Populations Access to
Healthcare
% of Population without
Healthcare Insurance
Weather Conditions
Population outside Service
Area
Average Earnings/Income of
Population Service Area
Healthcare Resources outside
of Service Area
Non-Medical/Clinical
Emergency First Responders
ti. Causal Loop Diagram
Many of the variables in the Causal loop diagram directly or indirectly impact two key variables,
the number of EMS call requests received and the call response times. The primary objective of
EMS systems is to reduce individual call response times for high priority calls by as much as
possible. Chen et al. define call response time as the elapsed time from when an operator receives
the EMS call until the arrival of the ambulance at the scene (Chen et al., 2016). Intuitively, the
survival rate of patients with critical conditions is directly impacted by the response time of the
dispatched ambulance. The “# of EMS Call Requests” variable is an accumulator representing the
total number of call requests received for a given period (hour, day, week, etc.). The volume of
calls received impacts the system’s ability to respond to requests, thus increasing the call response
time for individual request instances. The additional variables impacting call response times are
related to logistics, i.e. the number of available resources, current traffic conditions and the
distance between a call request and the responding ambulance. Other variables that impact the
number of call requests in a period include, total population and variables related to the populations
access to healthcare. This includes the percent of the population without health insurance whose
access to healthcare services would be limited based on their circumstance. Ragin et al. conducted
an observational study to identify the primary reasons for patients pursuing care from hospital
emergency departments. They concluded that a patient’s decision to seek care from an emergency
department is “often a choice driven by lack of access to, or dissatisfaction with, other sources of
care” (Ragin et al., 2005). These findings support a prominent hypothesis in healthcare research
that as access to healthcare, and health insurance, increases the need for emergency medical
services decreases.
x
Workforce
valley
4 —~ \
SP aN
\
\\
fal v
{ # of Available he Average Call
| Seamed seats ‘Service Time
\ \ # of Available =
‘\ \ Ambulances \
# of EMS Call / \
Requests in Time \ | |
ae \ / sizeof Service Arca
ON \ . of” / (Square Miles
\ a _+ Call Response \
we Re
Call Request —_ \ a x /
% of Population Rate + ~~ Distance Between Request
without Healthcare " x Location and Next Available
Insurance - ‘ Ambulance Location
_— > Call Request
\ we wae ~~ Current Trafic
Susacd \ Congestion
Healtheare =. ‘
“Sk /
comin, J
Population P Population — Population lation in it
Growth Fraction Growth Rate ie) Sate tires oo
N AR
Figure 1: Emergency Medical Services Systems Causal Loop Diagram
The logic behind this hypothesis is that as more people have access to, and rely on, routine and
preventative medical care, the less they rely on on-demand acute medical care services such as
those provided by EMS agencies and emergency departments. The relationship that exists between
emergency medical services and hospitals is created from emergency calls that require patient
transfer to emergency department facilities. These types of calls account for most of the EMS calls
received and responded to. In a more recent study conducted by MEDIC, the Charlotte
Mecklenburg County EMS Agency, it was found that approximately 70-75% of all calls received
required transport to a local hospital, i.e. emergency departments (Studnek et al., 2013). Reviewing
the causal loop diagram shown in Figure 1, highlights the underlying complexity of EMS systems.
To establish a base model, select variables shown in the broader causal loop diagram such as the
request distance, traffic congestion and the population access to healthcare were excluded. A
simplified causal loop diagram is shown below in Figure 2.
Hourly Call
Request Volume
+
+
Population EMS Call
Requests
pee evs | Ww
Available
Ambulances Ny ) Response Rate
rt Pt
‘Number of Busy
Ambulances
Figure 2: Simplified Emergency Medical Services Systems Causal Loop Diagram
tii. Stock & Flow Diagram
Continuing with the modeling process, a stock and flow diagram (Figure 3) was developed to
depict which variables serve as accumulators, rates of change, and ancillary variables. For the time
being, the following variables were omitted from the stock and flow analysis due to limited data
availability and difficult associated with incorporation; Size of Service Area, Distance Between
Request Location and Next Available Ambulance Location, Percent of Population without
Healthcare Insurance, and Access to Healthcare. Furthermore, the Number of Available
Paramedics/EMTs and the Number of Available Ambulances variables were combined into a stock
variable labeled “Idle Available Ambulances”. The underlying assumption here is that each
available ambulance is staffed with the personnel required to respond to an emergency call request.
Hourly Population
Gro
A \
———, \
Dispatched Buy
ee err | Ambaleces | Ambiboes
Pouidtana >| Senice Aen 8
Growth Rate re 4 Ambulances Per Call ~
———™ Pop Ratio “a
Initial Population in \ ae
Reference PopRatio SO
EAT of Population on
qv
a a
Hourly Call Request fe \ f = x
i 7
ve /
Service Rate Delay
aa
satya , }
Request Dass pee ,
ae,
> Completed Units
a /
\ / / A ff /
} \ / PA Le /
oS Zz es ca zs Active Calls
Incoming Call sereat Call Response Rate Call Service Rate
Figure 3: Emergency Medical Services Systems Stock and Flow Diagram
The stock and flow diagram includes six key stock variables representing the Population in the
Service Area, Number of EMS Call Requests, The Number of Active Calls, Idle Available
Ambulances, Dispatched Ambulances and Busy Ambulances. Typically, ambulance call response
and service times in the industry are reported in minutes (Setzler et al., 2009). However, to ensure
uniformity throughout the entire model, and a reasonable level of granularity for other factors such
as population growth, the models time units were set to hours. At a macro level, the model consists
of three primary flow structures representing; |. Population (people), 2. Calls and, 3. Ambulances.
The flows for calls and ambulances are co-flows with aging, because the flows directly interact
with one-another as calls are received, responded to and completed.
Hourly Population
Growth Fraction
P ion in
Net Service Area
Growth Rate
rr aol Pop Ratio Graph of Pop Effect
Initial Population in
Service Area
‘ Eff of Population on
Reference Pop Ratio Hourly Call Request
Volume
Figure 4: Stock and Flow Diagram — Population Flow Structure
Focusing specifically on the population flow structure (Figure 4), the initial population in service
area variable is set to 755,000, based on 2003 Census population estimates for Mecklenburg
County, NC (Bureau, 2016). Averaging population growth rates over a 10-year period, from 2003-
2013, the annual population growth fraction was calculated to be approximately 2.74%, and then
scaled down to percent/hour serving as the hourly population growth fraction value. As the
population grows overtime, the associated call request volume is expected to increase in the service
area. This relationship is illustrated by the population effect function. Turning now to the call flow
structure (Figure 5), the Hourly Call Request Volume, calculated by multiplying the Hourly Call
Request Data value by the Population Effect Function, serves as the primary input to the flow
structure and determines the value of the Incoming Call Request Rate for each iteration. The
Hourly Call Request Data value is generated based on one of two possible model configurations.
The first configuration uses historical hourly call volumes extracted from the MEDIC dataset for
one randomly selected week, 24 hours for 7 days, providing data sufficient for a 168-iteration
simulation run. The second model configuration allows for considerably longer simulations, where
the value of the Hourly Call Request Data is determined using a function built into Vensim PLE.
The function outputs a normally distributed random integer value given the mean, standard
deviation, maximum and minimum hourly call volume values calculated from the MEDIC dataset.
Random
‘Response Time
\
Response Rate Delay
per Se PSpao ye \™ Random Service Time
‘Hourly Call Request ff \ Cali Time K
Volume / \
; / Va seveaniitnany
/ Requested ints pe Service Rate Delay
Ze a
Hourly Call | Arn <
Request Data_ Hourly Call yf , ww
—~m Request Volume a4 sae units <7
/ Responding Units
‘o /
rs —a /
EMS Call x Active Cals
Incoming Call aa | Call Call Service Rate
Request Rate
Figure 5: Stock and Flow Diagram — Call Flow Structure
Response and service time data values were also aggregated at an hourly level from the original
dataset to calculate statistics and produce normally distributed random values using Vensim.
Incoming calls are collected by the EMS Call Requests stock, and migrate to the Active Calls stock
based on the Call Response Rate. As discussed earlier, response rate is the elapsed time between
when an emergency call is received and when the dispatched ambulance arrives on scene.
Therefore, the variable Response Rate Delay is responsible for moving calls to the active stock
based on the randomly generated response time. A similar delay structure is implemented for Call
Service Rate using randomly generated average service times. To ensure the proper number of
calls are made active for a given period, the number of requested calls are compared against the
number of ambulances currently dispatched. One key assumption of the model is that there is a
one to one relationship between calls and ambulances. This is typically the case in practice,
however, in some cases multiple ambulances are dispatched to the same call. The current model
does not accommodate instances of calls requiring multiple emergency medical first responders.
Available
Ambulances
Di > Busy
> Ambulances Ambulances
——, 4a
Service Dispatch Rate Service Arrival Rate
~ Ambulances Per Call
Service
Completion Rate
Figure 6: Stock and Flow Diagram — Ambulance Flow Structure
Serving as a co-flow structure to calls, ambulances travel through an aging loop, moving forward
from one stock to the other based on status (Figure 6). The initial value of the available ambulances
stock is set to 45, based on the estimated number of ambulances in operation during the beginning
of the data collection period (Penner et al., 2016). Ambulances are moved from the available stock
to the dispatched stock based on incoming call requests. If the number of call requests for a period
is greater than the number of ambulances currently available, only the number of available
ambulances are dispatched, creating a virtual queue in the call flow structure. Ambulances
transition from dispatched to busy is based on the Call Response Rate. Likewise, ambulances
return to the available stock is based on the Service Complete Rate.
III. Base Run & Model Credibility
To evaluate model performance and credibility, the call request volumes produced by the base
model were compared against data used in a 2007 investigation conducted by researchers in
Alberta, Canada. Channouf et al. performed a study concentrated on generating daily and hourly
EMS call volume forecasts (Channouf et al., 2007). The data used for their investigation was
provided by the Calgary EMS System in Alberta, Canada and spanned a period of 50 months from
2000-2004. In preparing the data for analysis, they aggregated call records based on the number
of calls occurring during each hour of the day. They then plotted the hourly call volume counts
over a one-year (Figure 7) and one-week (Figure 8) period to identify any clearly observable trends
and seasonal components present in the data.
number of calls
140 160
L L
120
r 1
1(1/1/2000) 100 200 366(31/12/2000)
days
Figure 7: One-Year Daily Call Volume; Jan-Dec 2000; Alberta, Canada (Channouf et al., 2007)
number of calls
T
1 43 85 127 168
hours (24x7 days)
Figure 8: Hourly Call Volume; One Week Period; Alberta, Canada (Channouf et al., 2007)
From the one-year and one-month perspectives a clear positive trend and seasonal behavior are
visible, with demand reaching peak values during the months of July and December. One would
assume these seasonal peaks are related to increased holiday travel, events, and activities common
during these months. Channouf et al. attributed the positive upward trend as likely being caused
by urban population growth and, as further underlined by McConnel and Wilson, the advancement
of the aging society (McConnel et al., 1998). Visualizing the hourly call volumes at the one-week
perspective uncovered an oscillation demand pattern mode, with demand reaching its highest
values between the hours of 10:00am and 8:00pm Sunday-Thursday and spanning into the late
night/early morning on Friday and Saturday (Channouf et al., 2007). While the data used in
Channouf et al.’s study was collected during a similar period (2000-2004), call volume behavior
is expected to vary slightly in the model due to the differences in the populace between Alberta,
Canada and Mecklenburg County, NC. Figure 9 shows the results for EMS call requests hour by
hour after running the base model for one-week (168-hrs.) while Figure 10 shows the results for
the same variable over a 10-year period with a 2.74% average annual population growth. It can be
observed that as the population increases in the service area, the current number of available
ambulances is sufficient to meet the growing call demand. The impact of adjusting the number of
ambulances in the system are explored during in the scenario analysis.
EMS Call Requests
50
37.5
= 25
8
12.5
0
1 B 85 126 168
Time (Hour)
EMS Call Requests : Current
Figure 9: EMS Call Requests; Base Model; One Week Period; MEDIC Mecklenburg County, NC
EMS Call Requests
calls
1 21908 43816
Time (Hour)
EMS Call Requests : Current
Figure 10: EMS Call Requests; Base Model; 10 Year Period; MEDIC Mecklenburg County, NC
10
Consistent with the data reviewed by Channouf et al., hourly call volume followed an oscillation
demand pattern mode and annual hourly call volume exhibits a subtle positive trend over time. To
further appraise the credibility, the results produced by the ambulance stocks were reviewed
(Figure 11). As expected, the oscillatory behavior of call requests carries over into the behaviors
of ambulances, with available and dispatched ambulances having an inverse relationship. The
delay inherit to the call response and service times can also be seen.
Ambulances (Available vs. Dispatched)
45
33.75
ambulances
N
nN
in
11.25
0
1 43 85 126 168
Time (Hour)
Available Ambul : Current
Dispatched Ambulances : Current
Figure 11: Available vs. Dispatched Ambulances; One-Week Simulation Results
IV. Model Analysis
i. Scenario #1 — Adjusting Fleet Capacity
To assess model durability, two scenarios were crafted to stress test the dynamics of the system,
specifically focusing on the relationship between supply and demand. The model analysis starts
by evaluating the impact of adjusting the initial value of available ambulances, which represents
the number of vehicles in an EMS agencies fleet for a given period. The base model was run with
an initial value of 45 as illustrated in the model credibility section. Scaling this up and down the
influences of having arbitrarily extreme values of 80 and 20 total ambulances were observed.
Viewing the results for Busy Ambulances over a one-week period, given 80 initial available
ambulances (Figure 12), the number of busy ambulances rarely crests over 30. This represents a
significant excess capacity that would equate to higher agency operating costs related to
overstaffing and unnecessary ambulance deployments. Conversely, in the case of only having 20
available ambulances in the fleet (Figure 13), the system is in a constant state of response with
demand exceeding supply. As such, calls go unanswered and backlog as displayed in the EMS
Call Requests stock (Figure 14). Operationally, this would result in ineffective service coverage,
overworked staff, and an increased mortality rate (Erkut et al., 2008).
11
Busy Ambulances
40
30
ambulances
I 43 85 126 168
Time (Hour)
Busy : Current
Figure 12: Busy Ambulances; 80 Initial Available Ambulances; One-Week Simulation Results
Busy Ambulances
20
15
2 10
Ei
5
0
43 85 126 168
Time (Hour)
Busy Ambulances : Current
Figure 13: Busy Ambulances; 20 Initial Available Ambulances; One-Week Simulation Results
EMS Call Requests
600
450
2 300
150
0
1 3 85 126 168
Time (Hour)
EMS Call Requests : Current
Figure 14: EMS Call Requests; 20 Initial Available Ambulances; One-Week Simulation Results
12
ti. Scenario #2 — Impact of Population Growth
Exploring yet another scenario, the impact of call volume demand and ambulance response
capacity given an abnormal increase in the population were measured over time. For the base
model the annual population growth fraction was set to 2.74%, based on the average population
change in Mecklenburg County over a 10-year period (2003-2013) (Bureau, 2016). To mimic an
extreme scenario this value was changed to 10.0% and another simulation ran for 87,360 hour
iterations (10-years). At this extreme growth rate, population grows exponentially to
approximately 2.25 million people (Figure 15). Around the 3.5-year mark, approximately 1.1
million people, the peak system capacity is reached, with 45 ambulances, and the number of EMS
Call Requests starts growing exponentially as calls go unanswered (Figure 16).
Population in Service Area
people
a
z
750,000
1 21908 43816 65723 87630
Time (Hour)
Population in Service Area : Current
Figure 15: Population in Service Area; 10-percent population growth; 87,630-hour Simulation
EMS Call Requests
400,000
300,000
= 200,000
100,000
1 21908 43816 65723 87630
Time (Hour)
EMS Call Requests : Current
Figure 16: EMS Call Requests; 10-percent population growth; 87,630-hour Simulation
13
V. Conclusion & Future Work
In this investigation, the system dynamics methodology was applied to develop a model of an
emergency medical services system in an urban setting. The primary objective was to apply the
system dynamics approach, that have not been applied to the EMS field. Specifically, the impact
of a growing population on the EMS system as well as the effect of adjusting capacity, i.e. the
number of available ambulances, were analyzed. As expected, as the population grows overtime
the associated demand increases and the system becomes more constrained requiring additional
ambulances. Eventually, the system reaches a peak capacity and, without additional ambulance
deployments, calls go unanswered, backlog and therefore service times increase. In the results of
the base run, the initial value of 45 available ambulances was sufficient to meet demand. During
the scenario analysis, the number of ambulances were adjusted to arbitrary values (approximately
+/-50%) to observe the model’s behavior. In its current state, the model can be used by EMS
managers and dispatchers to identify the point of peak capacity, adjust for population growth rate,
and determine the number of ambulances required. Several exogenous variables such as traffic
conditions and the percent of the population without access to health insurance were excluded from
the model. Future work could incorporate these variables, as well as explore additional demand
factors such as the impact of the aging population on demand as discussed by McConnel & Wilson
(McConnel et al., 1998). Furthermore, future models could include flow structures for different
call priorities. For instance, high priority calls requiring shorter response times would take
precedence over lower priority calls that can be delayed for longer periods of time.
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