Simulation and Analysis of Entrance to Dahlgren Naval Base Jennifer Burke MSIM 752 Final Project December 7, 2007

Simulation and Analysisof Entrance to DahlgrenNaval Base

Jennifer Burke

MSIM 752Final ProjectDecember 7, 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 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

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

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)

Added Security – Gates A & B

Added Security – Gates A, B, & C

Added Gate – Gates A, B, & C

Baseline – Gates A & B

Results

Baseline model Avg # vehicles entering base = 3065

0600-0900 Maximums


A Ga te

En te r Ba s e


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

Results (cont.)

Added security model Avg # of vehicles entering base =

3034

0600-0900 Maximums


A Ga te

En te r Ba s e


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


242.66 Gate B (left lane) = 242.19

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


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




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


5.349 Gate B (left lane) = 4.726 Gate C = 4.605

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


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




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

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

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

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

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

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

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


H0: μcars = 1car

Ha: μcars < 1car

0600-0700 None(0 variance)

N/A

H0: μcars = 1car

Ha: μcars < 1car


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


H0: μcars, w/ security - μcars, baseline = 0Ha: μcars, w/ security - μcars, baseline > 0

0600-0700


H0: μcars, w/ security - μcars, baseline = 0Ha: μcars, w/ security - μcars, baseline > 0

0700-0900


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


H0: μcars, w/ security & gate – μcars, w/ security = 0Ha: μcars, w/ security & gate – μcars, w/ security < 0

0600-0700


H0: μcars, w/ security & gate – μcars, w/ security = 0Ha: μcars, w/ security & gate – μcars, w/ security < 0

0700-0900


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


H0: μwait, w/ security – μwait, w/o security = 0Ha: μwait, w/ security – μwait, w/o security > 0

0700-0900


H0: μcars, w/ security – μcars, w/o security = 0Ha: μcars, w/ security – μcars, w/o security > 0

0600-0700


H0: μcars, w/ security – μcars, w/o security = 0Ha: μcars, w/ security – μcars, w/o security > 0

0700-0900


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

Documents

Simulation and Analysis of Entrance to Dahlgren Naval Base Jennifer Burke MSIM 752 Final Project December 7, 2007