Simulation and Analysis of Entrance to Dahlgren Naval Base

1. Simulation and Analysisof Entrance to DahlgrenNaval 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. 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 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. 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. 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 • Avg vehicles in queue • Gate A = 8.720 • Gate B (right lane) = 1.933 • Gate B (left lane) = 4.488 • Max wait time (seconds) • Gate A = 243.33 • Gate B (right lane) = 242.66 • Gate B (left lane) = 242.19 • 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 • 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 wait time (seconds) • Gate A = 243.33 • Gate B (right lane) = 242.66 • Gate B (left lane) = 242.63 • Gate C = 242.19 • 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 • H0: μbaseline = 3 seconds • Ha: μbaseline < 3 seconds • H0: μadded security = 60 seconds • Ha: μadded security < 60 seconds • H0: (μadded security – μbaseline) = 0 seconds • Ha: (μadded security – μbaseline) > 0 seconds • H0: (μadded security w/gate – μbaseline) = 0 seconds • Ha: (μadded security w/gate – μbaseline) < 0 seconds

21. – X – Z = X – μ σ / n ^ σ ^ Example CalculationAnalysis of Wait Time • Added security model – Gate A • = 53.5 seconds • = 58.43 seconds Fail to Reject H0 Z = 53.5 – 60 58.43/1.4142 -zα> Z to Reject H0 -zα = -6.314 -6.314< -0.157 Z = -0.157

22. Hypothesis of Vehicles in Line • H0: μbaseline = 3 vehicles in line • Ha: μbaseline < 3 vehicles in line • H0: μadded security = 5 vehicles in line • Ha: μadded security > 5 vehicles in line • H0: (μadded security – μbaseline) = 0 vehicles in line • Ha: (μadded security – μbaseline) > 0 vehicles in line • H0: (μadded security w/gate – μbaseline) = 0 vehicles • Ha: (μadded security w/gate – μbaseline) < 0 vehicles

23. – 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 = 8.72 vehicles • = 1.73 σd Reject H0 tα< T to Reject H0 tα = 6.314 6.314< 7.129 T = 8.72 – 0 1.73/1.4142 T = 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