Simulation and analysis of entrance to dahlgren naval base
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Simulation and Analysis of Entrance to Dahlgren Naval 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

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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


Gate C

Map of Gates

Gate B

Gate A


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 Entity

Expected Arrival Rate

Generation 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


Gate C

Side of Base

Far Side = 30%

Gate B

Near Side = 70%

Gate A


Gate C

Gate Choice

Far Side = 30%

Gate B

Near Side = 70%

Gate A


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


Added Gate


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 Gate – Gates A, B, & C

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


Gate A: Baseline Testing


Gate A w/Security Compared to Gate A Baseline


Gate B w/Security & Added Gate Compared to Gate B w/Security


Gate C w/Security Compared to Gate C w/o Security


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


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