Simulation and Analysis of Entrance to Dahlgren Naval Base

1. Simulation and Analysisof Entrance to DahlgrenNaval Base Jennifer Burke MSIM 752 Final Project December 7, 2007

2. 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

3. Gate C Map of Gates Gate B Gate A

4. 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?

5. Vehicle Interarrival Rates

6. Cumulative Vehicle Arrivals

7. 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

8. 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

9. 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

10. 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

11. Gate C Side of Base Far Side = 30% Gate B Near Side = 70% Gate A

12. Gate C Gate Choice Far Side = 30% Gate B Near Side = 70% Gate A

13. 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

14. Baseline Model

15. Added Gate

16. 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)

17. Added Gate – Gates A, B, & C Baseline – Gates A & B Added Security – Gates A, B, & C Added Security – Gates A & B

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. – 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

25. 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

26. – 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

27. Gate A: Baseline Testing

28. Gate A w/Security Compared to Gate A Baseline

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

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

31. 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