1. Simulation and Analysis of Entrance to Dahlgren Naval Base Jennifer Burke MSIM 752 Final Project December 3, 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 Lambda <= Minimum Lambda Accepts/Rejects entities 30 min period when entity created Expected arrival rate for that period Probability of Accepting Generated Entity Generation Rate Expected Arrival 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. Results Baseline model Avg # vehicles entering base = 3065 Avg wait time (seconds) All gates = 0.007 Max wait time (seconds) Gate A = 5.481 Gate B (right lane) = 5.349 Gate B (left lane) = 4.726 Avg vehicles in queue All gates = 0.001 Max vehicles in queue Gate A = 5 Gate B (right lane) = 3 Gate B (left lane) = 5

17. Results (cont.) Added security model Only completed 2 runs before crashing Avg # of vehicles entering base = 3034 Avg wait time (seconds) Gate A = 53.507 Gate B (right lane) = 54.229 Gate B (left lane) = 54.306 Max wait time (seconds) Gate A = 243.33 Gate B (right lane) = 242.66 Gate B (left lane) = 242.19 Avg vehicles in queue Gate A = 8.720 Gate B (right lane) = 1.933 Gate B (left lane) = 4.488 Max vehicles in queue Gate A = 86 Gate B (right lane) = 27 Gate B (left lane) = 50

18. Results (cont.) Added gate model Avg # vehicles entering base = 3065 Avg wait time (seconds) All gates = 0.007 Max wait time (seconds) Gate A = 5.481 Gate B (right lane) = 5.349 Gate B (left lane) = 4.726 Gate C = 4.605 Avg vehicles in queue All gates = 0.001 Max vehicles in queue Gate A = 5 Gate B (right lane) = 3 Gate B (left lane) = 4 Gate C = 3

19. Results (cont.) Added gate, added security model Only completed 2 runs before crashing Avg # of vehicles entering base = 3034 Avg wait time (seconds) Gate A = 53.507 Gate B (right lane) = 54.229 Gate B (left lane) = 54.177 Gate C = 54.572 Max wait time (seconds) Gate A = 243.33 Gate B (right lane) = 242.66 Gate B (left lane) = 242.63 Gate C = 242.19 Avg vehicles in queue Gate A = 8.720 Gate B (right lane) = 1.933 Gate B (left lane) = 3.001 Gate C = 1.478 Max vehicles in queue Gate A = 86 Gate B (right lane) = 27 Gate B (left lane) = 36 Gate C = 18

20. Hypothesis of Wait Time H 0 : μ baseline = 3 seconds H a : μ baseline < 3 seconds H 0 : μ added security = 60 seconds H a : μ added security < 60 seconds H 0 : (μ added security – μ baseline ) = 0 seconds H a : (μ added security – μ baseline ) > 0 seconds H 0 : (μ added security w/gate – μ baseline ) = 0 seconds H a : (μ added security w/gate – μ baseline ) < 0 seconds

21. Example Calculation Analysis of Wait Time Added security model – Gate A = 53.5 seconds = 58.43 seconds Z = 53.5 – 60 58.43/1.4142 X – σ ^ Z = X – μ σ / n ^ – Z = -0.157 Fail to Reject H 0 -z α > Z to Reject H 0 -z α = -6.314 -6.314 < -0.157

22. Hypothesis of Vehicles in Line H 0 : μ baseline = 3 vehicles in line H a : μ baseline < 3 vehicles in line H 0 : μ added security = 5 vehicles in line H a : μ added security > 5 vehicles in line H 0 : (μ added security – μ baseline ) = 0 vehicles in line H a : (μ added security – μ baseline ) > 0 vehicles in line H 0 : (μ added security w/gate – μ baseline ) = 0 vehicles H a : (μ added security w/gate – μ baseline ) < 0 vehicles

23. Example Calculation Analysis of Vehicles in Line Added security model – Gate A compared to baseline mode – Gate A = μ 1 – μ 2 = 8.72 vehicles = 1.73 T = 8.72 – 0 1.73/1.4142 d – σdσd T = d – D 0 σ d / n – T = 7.129 Reject H 0 t α < T to Reject H 0 t α = 6.314 6.314 < 7.129

24. Comparing Results For each model the expected wait time was approximately even for all the gates Could not provide confidence intervals to test all hypotheses since variances were 0 No difference was seen when adding gate C Badge read time = 1 sec No significant changes Badge read time of 4 seconds Both simulations crashed due to entity limits Average Wait and Line Length Increased Very minor changes adding gate C

25. Lessons Learned Like to get exact census data Thinning method is very helpful Arena Need full version 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