simulation and analysis of entrance to dahlgren naval base jennifer burke msim 752 final project...
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Simulation and Analysisof Entrance to DahlgrenNaval Base
Jennifer Burke
MSIM 752Final ProjectDecember 7, 2007
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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
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Map of Gates
Gate A
Gate B
Gate C
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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?
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Vehicle Interarrival Rates
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Cumulative Vehicle Arrivals
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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
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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
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NSPP using Thinning Method
Exponential distribution Generation Rate Lambda >=
Maximum Rate Lambda Accepts/Rejects entities
30 min period when entity created Expected arrival rate for that period Probability of Accepting Generated
EntityExpected Arrival RateGeneration Rate
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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
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Side of Base
Gate A
Gate B
Gate C
Near Side = 70%
Far Side = 30%
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Gate Choice
Gate A
Gate B
Gate C
Near Side = 70%
Far Side = 30%
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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
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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
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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
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Batching Results Temporal-based batching 5 minutes per batch 2 significant time periods (due to
queues emptying during 0630-0700 time frame) 0600-0700
Removed initial 10 minutes (before queue becomes significant)
0700-0900 Removed initial 5 minutes (before queue
becomes significant)
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Added Security – Gates A & B
Added Security – Gates A, B, & C
Added Gate – Gates A, B, & C
Baseline – Gates A & B
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Results
Baseline model Avg # vehicles entering base = 3065
0600-0900 Maximums
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
Max vehicles in queue Gate A = 5 Gate B (right lane) = 3 Gate B (left lane) = 5
Max wait time (seconds) Gate A = 5.481 Gate B (right lane) =
5.349 Gate B (left lane) = 4.726
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Results (cont.)
Added security model Avg # of vehicles entering base =
3034
0600-0900 Maximums
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
Max vehicles in queue Gate A = 86 Gate B (right lane) = 27 Gate B (left lane) = 50
Max wait time (seconds) Gate A = 243.33 Gate B (right lane) =
242.66 Gate B (left lane) = 242.19
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Results (cont.)
Added gate model Avg # vehicles entering base = 3065
0600-0900 Maximums
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
Max vehicles in queue Gate A = 5 Gate B (right lane) = 3 Gate B (left lane) = 4 Gate C = 3
Max wait time (seconds) Gate A = 5.481 Gate B (right lane) =
5.349 Gate B (left lane) = 4.726 Gate C = 4.605
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Results (cont.)
Added gate, added security model Avg # of vehicles entering base = 3034
0600-0900 Maximums
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
Max vehicles in queue Gate A = 86 Gate B (right lane) = 27 Gate B (left lane) = 36 Gate C = 18
Max wait time (seconds) Gate A = 243.33 Gate B (right lane) = 242.66 Gate B (left lane) = 242.63 Gate C = 242.19
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Running Tests 50 Replications Compared
Wait times at the gates Number of cars in line at the gates
Hypothesis testing 95% confidence interval Single tail test, talpha
talpha = (1.671 + 1.684)/2 = 1.6775
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Hypothesis of Wait Times (seconds) H0: μgate A, baseline = 1 Ha: μgate A, baseline < 1
H0: (μgate A, added security – μgate A, baseline) = 0 Ha: (μgate A, added security – μgate A, baseline) > 0
H0: (μgate B, added security, added gate – μgate B, added security) = 0 Ha: (μgate B, added security, added gate – μgate B, added security) < 0
H0: (μgate C, added security, added gate – μgate C, added gate) = 0 Ha: (μgate C, added security, added gate – μgate C, added gate) > 0
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Example CalculationAnalysis of Wait Times
Gate A – Baseline model = 0.004572 seconds = 0.008355 seconds
Z = 0.004572 – 1 0.008355/7.071
X–
σ̂ Z = X – μ σ / n^
–
Z = -842.4479
Reject H0
-zα < Z to Reject H0
Z = - 842.4479 - 842.45 < -0.16775
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Hypothesis of Vehicles in Line H0: μgate A, baseline = 1 Ha: μgate A, baseline < 1
H0: (μgate A, added security – μgate A, baseline) = 0 Ha: (μgate A, added security – μgate A, baseline) > 0
H0: (μgate B, added security, added gate – μgate B, added security) = 0 Ha: (μgate B, added security, added gate – μgate B, added security) < 0
H0: (μgate C, added security, added gate – μgate C, added gate) = 0 Ha: (μgate C, added security, added gate – μgate C, added gate) > 0
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Example CalculationAnalysis of Vehicles in Line
Added security model – Gate A compared to baseline mode – Gate A = μ1 – μ2 = 12.185 vehicles = 23.27 vehicles
T = 12.185 – 0 23.27/7.071
d–
σd
T = d – D0
σd / n
–
T = 3.7025 Reject H0
tα < T to Reject H0
T = 3.7025 3.7025 > 1.6775
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Gate A: Baseline Testing
Hypothesis Test
Time Interval
Test Statistic
Results
H0: μwait = 1sec
Ha: μwait < 1sec
0600-0700 -45186 Reject Null Hypothesis
H0: μwait = 1sec
Ha: μwait < 1sec
0700-0900 -842 Reject Null Hypothesis
H0: μcars = 1car
Ha: μcars < 1car
0600-0700 None(0 variance)
N/A
H0: μcars = 1car
Ha: μcars < 1car
0700-0900 -875 Reject Null Hypothesis
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Gate A w/Security Compared to Gate A Baseline
Hypothesis Test Time Interva
l
Test Statisti
c
Results
H0: μwait, w/ security - μwait, baseline = 0Ha: μwait, w/ security - μwait, baseline > 0
0600-0700
6.414 Reject Null Hypothesis
H0: μwait, w/ security - μwait, baseline = 0Ha: μwait, w/ security - μwait, baseline > 0
0700-0900
3.614 Reject Null Hypothesis
H0: μcars, w/ security - μcars, baseline = 0Ha: μcars, w/ security - μcars, baseline > 0
0600-0700
4.103 Reject Null Hypothesis
H0: μcars, w/ security - μcars, baseline = 0Ha: μcars, w/ security - μcars, baseline > 0
0700-0900
3.703 Reject Null Hypothesis
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Gate B w/Security & Added Gate Compared to Gate B w/Security
Hypothesis Test Time Interv
al
Test Statisti
c
Results
H0: μwait, w/ security & gate – μwait, w/ security = 0Ha: μwait, w/ security & gate – μwait, w/ security < 0
0600-0700
-4.644 Reject Null Hypothesis
H0: μwait, w/ security & gate – μwait, w/ security = 0Ha: μwait, w/ security & gate – μwait, w/ security < 0
0700-0900
-3.567 Reject Null Hypothesis
H0: μcars, w/ security & gate – μcars, w/ security = 0Ha: μcars, w/ security & gate – μcars, w/ security < 0
0600-0700
-2.236 Reject Null Hypothesis
H0: μcars, w/ security & gate – μcars, w/ security = 0Ha: μcars, w/ security & gate – μcars, w/ security < 0
0700-0900
-3.62 Reject Null Hypothesis
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Gate C w/Security Compared to Gate C w/o Security
Hypothesis Test Time Interva
l
Test Statisti
c
Results
H0: μwait, w/ security – μwait, w/o security = 0Ha: μwait, w/ security – μwait, w/o security > 0
0600-0700
2.666 Reject Null Hypothesis
H0: μwait, w/ security – μwait, w/o security = 0Ha: μwait, w/ security – μwait, w/o security > 0
0700-0900
3.602 Reject Null Hypothesis
H0: μcars, w/ security – μcars, w/o security = 0Ha: μcars, w/ security – μcars, w/o security > 0
0600-0700
2.236 Reject Null Hypothesis
H0: μcars, w/ security – μcars, w/o security = 0Ha: μcars, w/ security – μcars, w/o security > 0
0700-0900
3.622 Reject Null Hypothesis
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Lessons Learned Like to get exact census data Hypothesis testing for a defined
increase in wait time or vehicles in line H0: μwait, w/ security – μwait, w/o security = N
Thinning method is very helpful 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