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Simulation and Analysis of Entrance to Dahlgren Naval BasePowerPoint Presentation

Simulation and Analysis of Entrance to Dahlgren Naval Base

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Simulation and Analysis of Entrance to Dahlgren Naval Base

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Simulation and Analysis of Entrance to Dahlgren Naval Base

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Simulation and Analysisof Entrance to DahlgrenNaval Base

Jennifer Burke

MSIM 752

Final Project

December 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

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?

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 Entity

Expected Arrival Rate

Generation Rate

Carpooling

- Discrete function
- Virginia
- 60% - 1 person
- 25% - 2 people
- 10% - 4 people
- 5% - 6 people

- Virginia

- Maryland
- 75% - 1 person
- 15% - 2 people
- 5% - 4 people
- 5% - 6 people

~3000 vehicles

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

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)

- 0600-0700

Baseline – Gates A & B

Added Security – Gates A, B, & C

Added Security – Gates A & B

Results

- Baseline model
- Avg # vehicles entering base = 3065

- 0600-0900 Maximums

- 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

- 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

Results (cont.)

- Added gate model
- Avg # vehicles entering base = 3065

- 0600-0900 Maximums

- 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

Results (cont.)

- Added gate, added security model
- Avg # of vehicles entering base = 3034

- 0600-0900 Maximums

- 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

X

–

Z = X – μ

σ / n

^

σ

^

Example CalculationAnalysis of Wait Times- Gate A – Baseline model
- = 0.004572 seconds
- = 0.008355 seconds

Z = 0.004572 – 1

0.008355/7.071

-zα< Z to Reject H0

Z = - 842.4479

- 842.45< -0.16775

Z = -842.4479

Reject H0

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

d

–

T = d – D0

σd / n

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

σd

tα< T to Reject H0

T = 3.7025

3.7025> 1.6775

T = 12.185 – 0

23.27/7.071

T = 3.7025

Reject H0

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