1. Simulation and Analysis of Entrance to Dahlgren Naval 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. Map of Gates Gate A Gate B Gate C

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 [t 1, t 2 ] 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. Side of Base Gate A Gate B Gate C Near Side = 70% Far Side = 30%

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

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 Security – Gates A & B Added Security – Gates A, B, & C Added Gate – Gates A, B, & C Baseline – 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, t alpha t alpha = (1.671 + 1.684)/2 = 1.6775

23. Hypothesis of Wait Times (seconds) H 0 : μ gate A, baseline = 1 H a : μ gate A, baseline < 1 H 0 : (μ gate A, added security – μ gate A, baseline ) = 0 H a : (μ gate A, added security – μ gate A, baseline ) > 0 H 0 : (μ gate B, added security, added gate – μ gate B, added security ) = 0 H a : (μ gate B, added security, added gate – μ gate B, added security ) < 0 H 0 : (μ gate C, added security, added gate – μ gate C, added gate ) = 0 H a : (μ gate C, added security, added gate – μ gate C, added gate ) > 0

24. Example Calculation Analysis of Wait Times Gate A – Baseline model = 0.004572 seconds = 0.008355 seconds Z = 0.004572 – 1 0.008355/7.071 X – σ ^ Z = X – μ σ /  n ^ – Z = -842.4479 Reject H 0 -z α < Z to Reject H 0 Z = - 842.4479 - 842.45 < -0.16775

25. Hypothesis of Vehicles in Line H 0 : μ gate A, baseline = 1 H a : μ gate A, baseline < 1 H 0 : (μ gate A, added security – μ gate A, baseline ) = 0 H a : (μ gate A, added security – μ gate A, baseline ) > 0 H 0 : (μ gate B, added security, added gate – μ gate B, added security ) = 0 H a : (μ gate B, added security, added gate – μ gate B, added security ) < 0 H 0 : (μ gate C, added security, added gate – μ gate C, added gate ) = 0 H a : (μ gate C, added security, added gate – μ gate C, added gate ) > 0

26. Example Calculation Analysis of Vehicles in Line Added security model – Gate A compared to baseline mode – Gate A = μ 1 – μ 2 = 12.185 vehicles = 23.27 vehicles T = 12.185 – 0 23.27/7.071 d – σdσd T = d – D 0 σ d /  n – T = 3.7025 Reject H 0 t α < T to Reject H 0 T = 3.7025 3.7025 > 1.6775

27. Gate A: Baseline Testing Hypothesis Test Time Interval Test Statistic Results H 0 : μ wait = 1sec H a : μ wait < 1sec 0600-0700-45186Reject Null Hypothesis H 0 : μ wait = 1sec H a : μ wait < 1sec 0700-0900-842Reject Null Hypothesis H 0 : μ cars = 1car H a : μ cars < 1car 0600-0700None (0 variance) N/A H 0 : μ cars = 1car H a : μ cars < 1car 0700-0900-875Reject Null Hypothesis

28. Gate A w/Security Compared to Gate A Baseline Hypothesis TestTime Interval Test Statistic Results H 0 : μ wait, w/ security - μ wait, baseline = 0 H a : μ wait, w/ security - μ wait, baseline > 0 0600-07006.414Reject Null Hypothesis H 0 : μ wait, w/ security - μ wait, baseline = 0 H a : μ wait, w/ security - μ wait, baseline > 0 0700-09003.614Reject Null Hypothesis H 0 : μ cars, w/ security - μ cars, baseline = 0 H a : μ cars, w/ security - μ cars, baseline > 0 0600-07004.103Reject Null Hypothesis H 0 : μ cars, w/ security - μ cars, baseline = 0 H a : μ cars, w/ security - μ cars, baseline > 0 0700-09003.703Reject Null Hypothesis

29. Gate B w/Security & Added Gate Compared to Gate B w/Security Hypothesis TestTime Interval Test Statistic Results H 0 : μ wait, w/ security & gate – μ wait, w/ security = 0 H a : μ wait, w/ security & gate – μ wait, w/ security < 0 0600-0700-4.644Reject Null Hypothesis H 0 : μ wait, w/ security & gate – μ wait, w/ security = 0 H a : μ wait, w/ security & gate – μ wait, w/ security < 0 0700-0900-3.567Reject Null Hypothesis H 0 : μ cars, w/ security & gate – μ cars, w/ security = 0 H a : μ cars, w/ security & gate – μ cars, w/ security < 0 0600-0700-2.236Reject Null Hypothesis H 0 : μ cars, w/ security & gate – μ cars, w/ security = 0 H a : μ cars, w/ security & gate – μ cars, w/ security < 0 0700-0900-3.62Reject Null Hypothesis

30. Gate C w/Security Compared to Gate C w/o Security Hypothesis TestTime Interval Test Statistic Results H 0 : μ wait, w/ security – μ wait, w/o security = 0 H a : μ wait, w/ security – μ wait, w/o security > 0 0600-07002.666Reject Null Hypothesis H 0 : μ wait, w/ security – μ wait, w/o security = 0 H a : μ wait, w/ security – μ wait, w/o security > 0 0700-09003.602Reject Null Hypothesis H 0 : μ cars, w/ security – μ cars, w/o security = 0 H a : μ cars, w/ security – μ cars, w/o security > 0 0600-07002.236Reject Null Hypothesis H 0 : μ cars, w/ security – μ cars, w/o security = 0 H a : μ cars, w/ security – μ cars, w/o security > 0 0700-09003.622Reject Null Hypothesis

31. Lessons Learned Like to get exact census data Hypothesis testing for a defined increase in wait time or vehicles in line H 0 : μ wait, w/ security – μ wait, 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