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Simulation and Analysis of Entrance to Dahlgren Naval Base Jennifer Burke MSIM 752 Final Project December 3, 2007

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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

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Map of Gates Gate A Gate B Gate C

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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?

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Vehicle Interarrival Rates

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Cumulative Vehicle Arrivals

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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

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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

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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

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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

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

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

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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

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Baseline Model

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Added Gate

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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