Post on 31-Mar-2015
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Simulation and Analysisof Entrance to DahlgrenNaval Base
Jennifer Burke
MSIM 752Final ProjectDecember 3, 2007
Background
Model the workforce entering the base Force Protection Status Security Needs Possibility of Re-Opening Alternate Gate 6am – 9am ~5000 employees
80% Virginia 20% Maryland
Arena 10.0
Map of Gates
Gate A
Gate B
Gate C
Probability Distributions
Employee arrival process Rates vary over time
How many people in each vehicle? Which side of base do they work
on? Which gate will they enter?
Vehicle Interarrival Rates
Cumulative Vehicle Arrivals
Modeling Employee Arrival Rates
First choice Exponential distribution with user-defined
mean Change it every 30 minutes
Wrong! Good if rate change between periods is
small Bad if rate change between periods is large
Modeling Employee Arrival Rates
Nonstationary Poisson Process (NSPP) Events occur one at a time Independent occurrences Expected rate over [t1, t2] Piecewise-constant rate function
NSPP using Thinning Method
Exponential distribution Generation Lambda <= Minimum
Lambda Accepts/Rejects entities
30 min period when entity created Expected arrival rate for that period Probability of Accepting Generated
EntityGeneration RateExpected Arrival
Rate
Carpooling
Discrete function Virginia
60% - 1 person 25% - 2 people 10% - 4 people 5% - 6 people
Maryland 75% - 1 person 15% - 2 people 5% - 4 people 5% - 6 people
~3000 vehicles
Side of Base
Gate A
Gate B
Gate C
Near Side = 70%
Far Side = 30%
Gate Choice
Gate A
Gate B
Gate C
Near Side = 70%
Far Side = 30%
Gate Delay Gate Delay =
MIN(GAMMA(PeopleInVehicle * BadgeTime/Alpha,Alpha),MaxDelay)
_______________________________________ GAMMA (Beta, Alpha)
α = 2 μ = αβ = α(PeopleInVehicle * BadgeTime)
β = (PeopleInVehicle * BadgeTime) α
MaxDelay = 360 seconds or 6 minutes
Baseline Model
Veh ic le Arri v a ls
A Ga te
Ente r Bas e
N S P P V ia ThinningTr ue
False
Enti tiesDis pos e Th inned
Attribu tesAs s ign Veh ic le S end V ehicles To G ates
Else
B Ga te Righ t L ine
B Ga te Left L ine
Inv a l id En ti ty
0
0
0
0
0
0
0
0
Added Gate
Ve h i c l e Arri v a l s
A Ga te
En te r Ba s e
NSPP Via ThinningTr ue
False
En ti t i e sDis p o s e Th i n n e d
Attri b u te sAs s i g n Ve h i c l e Send Vehic les To Gates
Pr im ar yG at e==1Pr im ar yG at e==2Pr im ar yG at e==3Pr im ar yG at e==4Else
B Ga te Rig h t L in e
B Ga te L e ft L i n e
C Ga te
In v a l i d En ti ty
0
0
0
0
0
0
0
0
0
Results
Baseline model Avg # vehicles entering base = 3065
Avg wait time (seconds) All gates = 0.007
Max wait time (seconds) Gate A = 5.481 Gate B (right lane) =
5.349 Gate B (left lane) = 4.726
Avg vehicles in queue All gates = 0.001
Max vehicles in queue Gate A = 5 Gate B (right lane) = 3 Gate B (left lane) = 5
Veh ic le Arri v a ls
A Ga te
En te r Ba s e
N S P P V ia ThinningTr ue
False
Enti tie sDis p os e Th inn ed
Attribu te sAs s ign Ve h ic le S end V ehicles To Gates
Else
B Ga te Rig h t L ine
B Ga te L eft L in e
Inv a l id En ti ty
0
0
0
0
0
0
0
0
Results (cont.) Added security model
Only completed 2 runs before crashing Avg # of vehicles entering base = 3034
Avg wait time (seconds) Gate A = 53.507 Gate B (right lane) = 54.229 Gate B (left lane) = 54.306
Max wait time (seconds) Gate A = 243.33 Gate B (right lane) = 242.66 Gate B (left lane) = 242.19
Avg vehicles in queue Gate A = 8.720 Gate B (right lane) = 1.933 Gate B (left lane) = 4.488
Max vehicles in queue Gate A = 86 Gate B (right lane) = 27 Gate B (left lane) = 50
Veh ic le Arri v a ls
A Ga te
En te r Ba s e
N S P P V ia ThinningTr ue
False
Enti tie sDis p os e Th inn ed
Attribu te sAs s ign Ve h ic le S end V ehicles To Gates
Else
B Ga te Rig h t L ine
B Ga te L eft L in e
Inv a l id En ti ty
0
0
0
0
0
0
0
0
Results (cont.)
Added gate model Avg # vehicles entering base = 3065
Ve h i c l e Arri v a ls
A Ga te
En te r Ba s e
NSPP Via ThinningTr ue
False
En ti t i e sDis p o s e Th in n e d
Attri b u te sAs s ig n Ve h i c l e Send Vehic les To Gates
Pr im ar yG at e==1Pr im ar yG at e==2Pr im ar yG at e==3Pr im ar yG at e==4Else
B Ga te Rig h t L in e
B Ga te L e ft L i n e
C Ga te
In v a l id En ti ty
0
0
0
0
0
0
0
0
0
Avg wait time (seconds) All gates = 0.007
Max wait time (seconds) Gate A = 5.481 Gate B (right lane) = 5.349 Gate B (left lane) = 4.726 Gate C = 4.605
Avg vehicles in queue All gates = 0.001
Max vehicles in queue Gate A = 5 Gate B (right lane) = 3 Gate B (left lane) = 4 Gate C = 3
Results (cont.) Added gate, added security model
Only completed 2 runs before crashing Avg # of vehicles entering base = 3034
Avg wait time (seconds) Gate A = 53.507 Gate B (right lane) = 54.229 Gate B (left lane) = 54.177 Gate C = 54.572
Max wait time (seconds) Gate A = 243.33 Gate B (right lane) = 242.66 Gate B (left lane) = 242.63 Gate C = 242.19
Avg vehicles in queue Gate A = 8.720 Gate B (right lane) = 1.933 Gate B (left lane) = 3.001 Gate C = 1.478
Max vehicles in queue Gate A = 86 Gate B (right lane) = 27 Gate B (left lane) = 36 Gate C = 18
Ve h i c l e Arri v a ls
A Ga te
En te r Ba s e
NSPP Via ThinningTr ue
False
En ti t i e sDis p o s e Th in n e d
Attri b u te sAs s ig n Ve h i c l e Send Vehic les To Gates
Pr im ar yG at e==1Pr im ar yG at e==2Pr im ar yG at e==3Pr im ar yG at e==4Else
B Ga te Rig h t L in e
B Ga te L e ft L i n e
C Ga te
In v a l id En ti ty
0
0
0
0
0
0
0
0
0
Hypothesis of Wait Time H0: μbaseline = 3 seconds Ha: μbaseline < 3 seconds
H0: μadded security = 60 seconds Ha: μadded security < 60 seconds
H0: (μadded security – μbaseline) = 0 seconds Ha: (μadded security – μbaseline) > 0 seconds
H0: (μadded security w/gate – μbaseline) = 0 seconds Ha: (μadded security w/gate – μbaseline) < 0 seconds
Example CalculationAnalysis of Wait Time
Added security model – Gate A = 53.5 seconds = 58.43 seconds
Z = 53.5 – 60 58.43/1.4142
X–
σ̂ Z = X – μ σ / n^
–
Z = -0.157
Fail to Reject H0-zα > Z to Reject
H0
-zα = -6.314 -6.314 < -0.157
Hypothesis of Vehicles in Line H0: μbaseline = 3 vehicles in line Ha: μbaseline < 3 vehicles in line
H0: μadded security = 5 vehicles in line Ha: μadded security > 5 vehicles in line
H0: (μadded security – μbaseline) = 0 vehicles in line Ha: (μadded security – μbaseline) > 0 vehicles in line
H0: (μadded security w/gate – μbaseline) = 0 vehicles Ha: (μadded security w/gate – μbaseline) < 0 vehicles
Example CalculationAnalysis of Vehicles in Line
Added security model – Gate A compared to baseline mode – Gate A = μ1 – μ2 = 8.72 vehicles = 1.73
T = 8.72 – 0 1.73/1.4142
d–
σd
T = d – D0
σd / n
–
T = 7.129
Reject H0
tα < T to Reject H0
tα = 6.314 6.314 < 7.129
Comparing Results For each model the expected wait time was
approximately even for all the gates Could not provide confidence intervals to test all
hypotheses since variances were 0
No difference was seen when adding gate C Badge read time = 1 sec No significant
changes
Badge read time of 4 seconds Both simulations crashed due to entity limits
Average Wait and Line Length Increased Very minor changes adding gate C
Lessons Learned Like to get exact census data Thinning method is very helpful Arena
Need full version Possible improvements would include
traffic patterns to control gate entry Gate C Unavailable to South-bound traffic
Comparison of Dahlgren Base entry to other government installations