Management of a local help-line set up to help families find temporary shelter is seeking help understanding the impact and importance of resource levels. For planning purposes, this report examines the number of community resources (usually church rooms) that might be needed at any given time to keep families off the street. Further, this model provides evidence that – en lieu of these partnerships – the need for emergency hotel shelter would rise significantly.

1.
Ensuring Adequate Temporary Shelter in Hampton Roads A Model
of Supply and Demand
George Arbogust
©2016

2. Executive Summary
Management of a local help-line set up to help families find temporary shelter is seeking
help understanding the impact and importance of resource levels. In response, a model
was built and used to test changes that could not otherwise have been conducted on the
real system. Specifically, the model tested the impact of changing resources on the
number of families who left the system without getting help. For planning purposes, this
report examines the number of community resources (usually church rooms) that might
be needed at any given time to keep families off the street. Further, this model provides
evidence that – en lieu of these partnerships – the need for emergency hotel shelter would
rise significantly.
Project Background
As part of their goal of breaking the cycle of homelessness in the Hampton Roads area, a
local charity has established a 24 Hour Homeless Emergency Response Hotline. Staff
are available by phone 24/7 to help homeless families assess resources and meet
emergency needs.
This represents only a portion of demand for shelter in the region and this group focuses
on serving families. As such, the model and reports should not be construed to define the
entire range of need in the area. Instead, this model is intended to demonstrate how this
group uses the resources available to it (which are often shared with other similar
organizations) to help the families who call their help-line.
Alternatives Investigated
The tested range of scenarios were driven by changes in resources and consisted of the
following:
• Scenario 1: Baseline – 30 shelter rooms; 30 hotel rooms; 10 church rooms
• Scenario Range 2: Changes in availability of church shelter rooms
• Scenario Range 3: Changes in availability of hotel rooms; zero church rooms
available
Projects Metrics & Goals
The key metric considered in this study is the number of families that leave the system
without receiving any assistance finding shelter. The level of resources available to the
help-line has an effect on the number of families who don’t get help. The primary goal of
the study is to determine the number of church shelter rooms that are needed to ensure
that everyone is served and that no family seeking assistance is left without shelter. A
!2

3. secondary goal is to demonstrate that hotel rooms can not replace the church shelters on a
1:1 basis; this phenomena can be contributed to the likely length of stay at each type of
facility as those who get into hotel rooms are likely to stay longer than the might have
otherwise.
Modeling Approach
A modeled simulation of the demand and supply of temporary homeless shelter in
Hampton Roads was employed to evaluate the impact of changes in the quantity of
several types of shelters on the ability to meet demand and not turn families away.
The help-line had previously recorded the incoming calls for a year and this data was
analyzed and used in the building of a simulation model of the system; specifically this
data was used to represent a true pattern of demand in the region for temporary homeless
assistance. Supplementing the data collected by the call center were interviews with
management, which also provided data used in the model. (See Appendix A & B for
additional information)
Project Results and Recommendations
As stated, the study was conducted to conclude the sufficient level of community back-up
shelter needed (such as church rooms) in order to meet the demand of all families seeking
temporary shelter. Analysis of the data indicates that 7 church shelter rooms are needed
in order to meet the demand and ensure that no families are left out on the street. We
also conclude that if the community resource was lost, the number of hotel rooms needed
at peak times would increase by nearly a third. (See Appendix D for more information).
In order to test changes to the level of resources in the model, a feature of the modeling
software called Process Analyzer (PAN) was used. This tool assists in the evaluation of
alternatives presented by the execution of different simulation model scenarios. This is
useful to decision-makers who can use it to focus in on the solution the simulation model
is addressing. At the stage when the PAN is utilized, the simulation model is assumed to
be complete, validated, and configured appropriately for use by the Process Analyzer. The
role of the Process Analyzer then is to allow for comparison of the outputs from validated
models based on different model inputs. The results of our analysis are listed below with
a description of important PAN terms.
!3

4. Definition of Terms
Controls—Inputs that are considered to affect the operation of the model in a manner that
can be monitored/viewed in the output of the model.
Responses—Outputs that represent measures of how the model performed during the run.
Scenario—A collection of controls and responses as applied to a given simulation model
We see that given baselines of 30 shelter rooms and 30 hotel rooms, the church rooms are
important in terms of keeping families off the street. It appears that a key number of
church rooms to be able to marshal at any given time is 7 as anything less will likely
leave a family stuck on the street at sometime throughout the year. Being able to call
upon a sufficient and consistent supply of church shelter rooms is imperative; for
example, only having one or two rooms to call on at any given time could leave
anywhere from 24 to 50 families on the street during the course of the year as demand
exceeds supply during peak periods.
Scenarios: Varying RoomChurch
Controls Responses
# Reps #RoomShelter #RoomHotel #RoomChurch
# Unhelped
Families
RoomChurch.N
umberSeized
30 30 30 10 0 99
30 30 30 9 0 99
30 30 30 8 0 99
30 30 30 7 0 99
30 30 30 6 1 96
30 30 30 5 3 98
30 30 30 4 6 91
30 30 30 3 14 90
30 30 30 2 24 70
30 30 30 1 50 58
!4

5. The importance of having a good source of church rooms as back-up for shelters and
hotel rooms is evident by the fact that the other options tend to provide for longer periods
of shelter meaning more of them are needed to meet demand. For example, if we
couldn't count on any church rooms as back-up (as shown above) but still wanted to
reduce the number of families who don’t receive aid to near zero, we would need a steady
source of 40 hotel rooms to compensate for the lost church rooms.
Scenarios: Varying Hotel Rooms and Zero Church Rooms
Controls Responses
# Reps #RoomShelter #RoomHotel #RoomChurch
# Unhelped
Families
30 30 20 0 96
30 30 21 0 87
30 30 22 0 74
30 30 23 0 65
30 30 24 0 60
30 30 25 0 49
30 30 26 0 44
30 30 27 0 39
30 30 28 0 35
30 30 29 0 24
30 30 30 0 20
30 30 40 0 1
!5

6. Appendix A: Conceptual Model of Homeless Shelter Supply and Demand
!6

7. We are interested in analyzing the Hampton Roads region in terms of demand for
temporary homeless shelter by families. Each city has a unique rate in terms of
generating demand that also varies season. The families enter the system by contacting a
telephone help line. (The actual call center is not included in the model as they act
merely as a facilitator in terms of the shelter selection – which is the variable we are most
interested in analyzing). We shall assume our rates of demand creation based on a study
of call volume as tracked by the help line and creating the demand distributions is
discussed in more detail below.
Upon creation of each family entity, an attempt is made to put the family in any available
space in a shelter, in this case a “room.” If space is not available in the shelter, an attempt
is made to put the family in a hotel room. If a hotel room is not available, an attempt is
made to put them in a church shelter. If a room in a church shelter is not available, the
family is marked as “unserved” and leave the system. The length of stay at each option is
based on a unique triangular distribution.
Questions to Answer
What is the needed number of back-up church shelter rooms needed to ensure that
families seeking a place to stay get it?
If back-up church shelters are not available, how many hotel rooms are needed to ensure
that families seeking a place to stay get it?
Key Metrics
Number of people left unserved
Number of church rooms needed to ensure people have a place to stay
Assumptions
The model runs 24 hours per day and for 365 days before resetting.
Families contacting the call center help line is represented by their creation in the
individual city modules.
Each family is either served or not served but none have an unknown status.
There can be no more than one person in a queue for any type of shelter.
Families first try to fill the space available at shelters, then at hotels, then at church
shelters; if none of these are available they exit the system without finding shelter.
Families stay at each type of shelter for based on specified durations which vary by type
of shelter. Once a family’s stay is over, they leave the system.
Data Sources
Data about the creation of families needing shelter was based culled from call-log records
of a local help-line. The Triangular distributions used to determine the duration of stays
at the various shelter options were derived from historical averages. The quantity of
resources available were based on current estimations by help line management.
!7

8. Entities
Family
Represents families who have called the help-line in need of assistance finding shelter
Important attributes of Family:
Time @ Creation
Current station assignment
Arrival Process
The following creation rates were used as part of an Exponential distribution and
schedule:
Justification for chosen rates
An analysis using the Welch t Test for Independent Samples was conducted to determine
if there was a significant difference between the mean arrival rate for each of the four
seasons. This method was chosen for our statistical analysis as the Welch t Test for
Independent Samples can account for unequal sample sizes and unequal variances.
Welch's t-test defines the statistic t by the following formula:
The degrees of freedom ν associated with this variance estimate is approximated using:
v=
Once t and ν have been computed, these statistics can be used with
the t-distribution to test the null hypothesis that the two population means are equal
Mean Arrival Rate
Winter Spring Summer Fall
Chesapeake 3.8 5.2 9.0 7.7
VA Beach 7.3 10.0 11.7 14.5
Norfolk 4.4 5.8 10.2 8.7
Portsmouth 2.7 3.8 6.5 4.2
Suffolk 3.6 3.7 4.6 5.9
Hampton 0.9 1.2 2.1 1.8
Newport News 1.3 1.8 3.1 2.6
!8

9. (using a two-tailed test), or the null hypothesis that one of the population means is greater
than or equal to the other (using a one-tailed test). In particular, the test will yield a p-
value which might or might not give evidence sufficient to reject the null hypothesis.
This method was used in the following comparisons. In each case, zero does not fall
between the upper and lower confidence intervals allowing us to say that the mean of
each is significantly different. Therefore it is appropriate to model the changing rate of
demand across the seasons.
Comparison 1: Winter Spring
mean 0.55 0.32
standard deviation 0.92 0.61
n 163.00 282.00
degrees of freedom 246.92
t-value 0.05
Welch upper C.I. (3c & 3cv ) @ 95% 0.227
Welch lower C.I. (3c & 3cv ) @ 95% 0.219
Comparison 2: Spring vs. Summer Spring Summer
mean 0.32 0.24
standard deviation 0.61 0.63
n 282.00 391.00
degrees of freedom 616.65
t-value 0.05
Welch upper C.I. (3c & 3cv ) @ 95% 0.090
Welch lower C.I. (3c & 3cv ) @ 95% 0.085
Comparison 3: Summer vs. Fall Summer Fall
mean 0.24 2.81
standard deviation 0.63 29.27
n 391.00 270.00
!9

10. degrees of freedom 704.69
t-value 0.05
Welch upper C.I. (3c & 3cv ) @ 95% 0.051
Welch lower C.I. (3c & 3cv ) @ 95% 0.046
Comparison 4: Fall vs. Winter Fall Winter
mean 0.19 0.55
standard deviation 0.52 0.92
n 316.00 163.00
degrees of freedom 704.69
t-value 0.05
Welch upper C.I. (3c & 3cv ) @ 95% -0.356
Welch lower C.I. (3c & 3cv ) @ 95% -0.362
!10

11. Justification for chosen distributions
The Kolmogorov-Smirnov Test was used to decide if our hypothesized exponential
distributions accurately describe the data. Our null and the alternative hypotheses are:
H0: the data follow the specified distribution;
H1: the data do not follow the specified distribution.
A value of 0.05 our chosen significance level as is typically used for most applications.
The null hypothesis (H0) will be accepted for all values of ! less than the P-value. In
the cases below, all of the p-values were over our .05 thresh-hold; meaning they met our
accepted levels for variance. As such, exponential distributions were chosen to generate
the arrival rates of families into the system.
!
!11

12. !
Resources
Shelter Rooms
Baseline Capacity: 30
Delay distribution: TRIA (1,29,30)
Hotel Rooms
Baseline Capacity: 20
Delay distribution: TRIA (1,29,30)
Church Rooms
Baseline Capacity: 10
Delay distribution: TRIA (1,1,3)
Queues
Queue for each of the three shelter resource types
FIFO type
Capacity limit = 1
Variables
!12

13. The number of families that are not served is initially set at 0 and added to by intervals of
1 as families leave the system without receiving shelter.
Actions/Activities
Family seizes type of shelter resources
Flow Control
There is conditional branching on which type of shelter resource is available for a family.
Families entering the system are first directed toward the shelter; if this resource is full,
the family will balk and attempt to seize a hotel room; if this resource is full, the family
will balk and attempt to seize a church shelter room; if this resource is full, the family
will balk and leave the system without receiving any assistance.
Appendix B: Implementation of Conceptual Model in Arena
The following steps were used to implement the conceptual model in Arena modeling
software which is designed for business consultants and business analysts. It can also be
widely deployed as a desktop tool and is most effective when modeling and analyzing
business, service, or (non material handling intensive) manufacturing processes or flows.
Arena Flowchart
Modules & Blocks
“Create” Module
Each of the seven cities is represented by a create module that creates a “family”
based on varying Exponential distributions as discussed previously
“Queue” Block
Queue limited to 1 so that family entity will balk to the next label as specified
!13
Ch e s a p e a k e Dis p o s e 1
Sh e lte r.Qu e u e
Queue
Ro o m Sh e lte r
Seize
TRIA(1 ,2 9 ,3 0 )
Delay
Ro o m Sh e lte r
Release
Ho te l.Qu e u e
Queue
Ro o m Ho te l
Seize
TRIA(1 ,2 9 ,3 0 )
Delay
Ro o m Ho te l
Release
Ch u rc h .Qu e u e
Queue
Ro o m Ch u rc h
Seize
TRIA(1 ,1 ,3 )
Delay
Ro o m Ch u rc h
Release
Virg in ia Be a c h
No rfo lk
Po rts m o u th
Su ffo lk
Ha m p to n
Ne wp o rt Ne ws
Assign
Un h e lp e d
Re c o rd 1
0 0
0
0
0
0
0
0

14. “Seize” Block
Family entity seizes 1 unit of appropriate resource, i.e. room in a shelter, hotel, or
church
“Delay” Block
Family entity is delayed for a period of time as determined by a specified random
distribution of duration times.
“Release” Block
Family entity releases 1 unit of appropriate resource, i.e. room in a shelter, hotel,
or church
“Assign” Block
Assign value of variable Unhelped +1 as family entities leave the system without
finding shelter
“Record” Module
Record newly assigned value of variable Unhelped as family entities leave the
system without finding shelter
“Dispose” Module
Family entitiy leaves system
SIMAN .mod & .exp files
Model statements for module: BasicProcess.Create 1 (Chesapeake)
2$ CREATE, 1,DaysToBaseTime(0.0),Family:DaysToBaseTime(EXPO(ScheduleChesapeake)):NEXT(3$);
3$ ASSIGN: Chesapeake.NumberOut=Chesapeake.NumberOut + 1:NEXT(QueueShelter);
QueueShelter QUEUE, Shelter.Queue,1,QueueHotel;
SeizeShelter SEIZE, 1,Other:
RoomShelter,1:NEXT(StayShelter);
StayShelter DELAY: TRIA(1,29,30),,Other:NEXT(ReleaseShelter);
ReleaseShelter RELEASE: RoomShelter,1:NEXT(0$);
;
; Model statements for module: BasicProcess.Dispose 1 (Dispose 1)
;
0$ ASSIGN: Dispose 1.NumberOut=Dispose 1.NumberOut + 1;
6$ DISPOSE: Yes;
QueueHotel QUEUE, Hotel.Queue,1,QueueChurch;
SeizeHotel SEIZE, 1,Other:
RoomHotel,1:NEXT(StayHotel);
StayHotel DELAY: TRIA(1,29,30),,Other:NEXT(ReleaseHotel);
ReleaseHotel RELEASE: RoomHotel,1:NEXT(0$);
QueueChurch QUEUE, Church.Queue,1,AssignUnelped;
SeizeChurck SEIZE, 1,Other:
RoomChurch,1:NEXT(StayChurch);
StayChurch DELAY: TRIA(1,1,3),,Other:NEXT(ReleaseChurch);
ReleaseChurch RELEASE: RoomChurch,1:NEXT(0$);
AssignUnelped ASSIGN: Unhelped=Unhelped+1:NEXT(1$);
;
;
; Model statements for module: BasicProcess.Record 1 (Record 1)
!14

15. ;
1$ COUNT: Record 1,Unhelped+1:NEXT(0$);
;
;
; Model statements for module: BasicProcess.Create 2 (Virginia Beach)
;
7$ CREATE,
1,DaysToBaseTime(0.0),Family:DaysToBaseTime(EXPO(ScheduleVirginiaBeach)):NEXT(8$);
8$ ASSIGN: Virginia Beach.NumberOut=Virginia Beach.NumberOut + 1:NEXT(QueueShelter);
;
;
; Model statements for module: BasicProcess.Create 3 (Norfolk)
;
11$ CREATE, 1,DaysToBaseTime(0.0),Family:DaysToBaseTime(EXPO(ScheduleNorfolk)):NEXT(12$);
12$ ASSIGN: Norfolk.NumberOut=Norfolk.NumberOut + 1:NEXT(QueueShelter);
;
;
; Model statements for module: BasicProcess.Create 4 (Portsmouth)
;
15$ CREATE,
1,DaysToBaseTime(0.0),Family:DaysToBaseTime(EXPO(SchedulePortsmouth)):NEXT(16$);
16$ ASSIGN: Portsmouth.NumberOut=Portsmouth.NumberOut + 1:NEXT(QueueShelter);
;
;
; Model statements for module: BasicProcess.Create 5 (Suffolk)
;
19$ CREATE, 1,DaysToBaseTime(0.0),Family:DaysToBaseTime(EXPO(ScheduleSuffolk)):NEXT(20$);
20$ ASSIGN: Suffolk.NumberOut=Suffolk.NumberOut + 1:NEXT(QueueShelter);
;
;
; Model statements for module: BasicProcess.Create 6 (Hampton)
;
23$ CREATE, 1,DaysToBaseTime(0.0),Family:DaysToBaseTime(EXPO(ScheduleHampton)):NEXT(24$);
24$ ASSIGN: Hampton.NumberOut=Hampton.NumberOut + 1:NEXT(QueueShelter);
;
; Model statements for module: BasicProcess.Create 7 (Newport News)
;
27$ CREATE,
1,DaysToBaseTime(0.0),Family:DaysToBaseTime(EXPO(ScheduleNewportNews)):NEXT(28$);
28$ ASSIGN: Newport News.NumberOut=Newport News.NumberOut + 1:NEXT(QueueShelter);
PROJECT, "Unnamed Project","George",,,No,Yes,Yes,Yes,No,No,No,No,No,No;
SCHEDULES:
ScheduleNewportNews,TYPE(Arrival),FORMAT(Duration),FACTOR(1.0),UNITS(Days),DATA(1.32,91),DATA(1.77,
91),DATA(3.1,91),
DATA(2.64,92):
ScheduleSuffolk,TYPE(Arrival),FORMAT(Duration),FACTOR(1.0),UNITS(Days),DATA(3.6,91),DATA(3.7,91),DAT
A(4.61,91),
DATA(5.89,92):
SchedulePortsmouth,TYPE(Arrival),FORMAT(Duration),FACTOR(1.0),UNITS(Days),DATA(2.69,91),DATA(3.78,91
),DATA(6.53,91),
DATA(4.16,92):
ScheduleChesapeake,TYPE(Arrival),FORMAT(Duration),FACTOR(1.0),UNITS(Days),DATA(3.85,91),DATA(5.16,91
),DATA(9.02,91),
DATA(7.68,92):
ScheduleNorfolk,TYPE(Arrival),FORMAT(Duration),FACTOR(1.0),UNITS(Days),DATA(4.35,91),DATA(5.84,91),D
ATA(10.21,91),
DATA(8.7,92):
ScheduleHampton,TYPE(Arrival),FORMAT(Duration),FACTOR(1.0),UNITS(Days),DATA(.
92,91),DATA(1.23,91),DATA(2.15,91),
DATA(1.83,92):
ScheduleVirginiaBeach,TYPE(Arrival),FORMAT(Duration),FACTOR(1.0),UNITS(Days),DATA(7.25,91),DATA(10,9
1),DATA(11.74,91),
DATA(14.46,92);
!15

16. VARIABLES: Suffolk.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Portsmouth.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Hampton.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Virginia Beach.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Dispose 1.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Unhelped,CLEAR(System),CATEGORY("User Specified-User Specified"),DATATYPE(Real),0:
Newport News.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Norfolk.NumberOut,CLEAR(Statistics),CATEGORY("Exclude"):
Chesapeake.NumberOut,CLEAR(Statistics),CATEGORY("Exclude");
QUEUES: Hotel.Queue,FIFO,,AUTOSTATS(Yes,,):
Church.Queue,FIFO,,AUTOSTATS(Yes,,):
Shelter.Queue,FIFO,,AUTOSTATS(Yes,,);
PICTURES: Picture.Airplane:
Picture.Green Ball:
Picture.Blue Page:
Picture.Telephone:
Picture.Blue Ball:
Picture.Yellow Page:
Picture.EMail:
Picture.Yellow Ball:
Picture.Bike:
Picture.Report:
Picture.Van:
Picture.Widgets:
Picture.Envelope:
Picture.Fax:
Picture.Truck:
Picture.Person:
Picture.Letter:
Picture.Box:
Picture.Woman:
Picture.Package:
Picture.Man:
Picture.Diskette:
Picture.Boat:
Picture.Red Page:
Picture.Ball:
Picture.Green Page:
Picture.Red Ball;
RESOURCES: RoomChurch,Capacity(10),,,COST(0.0,0.0,0.0),CATEGORY(Resources),,AUTOSTATS(Yes,,):
RoomShelter,Capacity(30),,,COST(0.0,0.0,0.0),CATEGORY(Resources),,AUTOSTATS(Yes,,):
RoomHotel,Capacity(20),,,COST(0.0,0.0,0.0),CATEGORY(Resources),,AUTOSTATS(Yes,,);
COUNTERS: Record 1,,,,DATABASE(,"Count","User Specified","Record 1");
REPLICATE, 1,,DaysToBaseTime(365),Yes,Yes,,,,24,Days,No,No,,,Yes,No;
ENTITIES: Family,Picture.Woman,0.0,0.0,0.0,0.0,0.0,0.0,AUTOSTATS(Yes,,);
!16

17. Appendix C: Experimental Design
Our null hypothesis is that changing the number of church shelter rooms available as
back-up will not affect the number of families on average that do not receive aid finding
shelter.
We write this as:
Ho: u1=u2
H1: u1/=u2
Appendix D: Data Output & Analysis
Based on our analysis of the data (as presented below), we can reject the null and state with
confidence that the average number of families left without service is not the same if the number
of church shelter rooms is changed.
In both comparisons below, the range between upper and lower confidence intervals does not
contain zero. This indicates that the average number of families that do not find shelter in the
system is significantly different depending on how many church rooms are regularly available
and can be called upon when needed. The less church rooms are available, the more families will
wind up on the street.
!17
ChurchRooms(7) ChurchRooms(6) ChurchRooms(5)
0.60 1.17 3.37
1.89 2.89 4.60
30 30 30
Comparison 1: Church Rooms = 7 vs. Church Rooms =6
50
0.056
-0.532
-0.602
Comparison 2: Church Rooms = 6 vs. Church Rooms =5
49
0.056
-2.145
-2.255
Welch upper C.I. (3c & 3cv ) @ 95%
Welch lower C.I. (3c & 3cv ) @ 95%
degrees of freedom
t-value
degrees of freedom
t-value
Welch upper C.I. (3c & 3cv ) @ 95%
Welch lower C.I. (3c & 3cv ) @ 95%