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