Simulation and Analysis of Entrance to Dahlgren Naval Base Jennifer Burke MSIM 752 Final Project December 7, 2007

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

Map of Gates Gate A Gate B Gate C

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?

Vehicle Interarrival Rates

Cumulative Vehicle Arrivals

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

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

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

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

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

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

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

Baseline Model

Added Gate

Batching Results Temporal-based batching 5 minutes per batch 2 significant time periods (due to queues emptying during time frame) Removed initial 10 minutes (before queue becomes significant) Removed initial 5 minutes (before queue becomes significant)

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

Results Baseline model Avg # vehicles entering base = Maximums Max vehicles in queue Gate A = 5 Gate B (right lane) = 3 Gate B (left lane) = 5 Max wait time (seconds) Gate A = Gate B (right lane) = Gate B (left lane) = 4.726

Results (cont.) Added security model Avg # of vehicles entering base = Maximums Max vehicles in queue Gate A = 86 Gate B (right lane) = 27 Gate B (left lane) = 50 Max wait time (seconds) Gate A = Gate B (right lane) = Gate B (left lane) =

Results (cont.) Added gate model Avg # vehicles entering base = 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 = Gate B (right lane) = Gate B (left lane) = Gate C = 4.605

Results (cont.) Added gate, added security model Avg # of vehicles entering base = 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 = Gate B (right lane) = Gate B (left lane) = Gate C =

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 = ( )/2 =

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

Example Calculation Analysis of Wait Times Gate A – Baseline model = seconds = seconds Z = – /7.071 X – σ ^ Z = X – μ σ /  n ^ – Z = Reject H 0 -z α < Z to Reject H 0 Z = <

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

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

Gate A: Baseline Testing Hypothesis Test Time Interval Test Statistic Results H 0 : μ wait = 1sec H a : μ wait < 1sec Reject Null Hypothesis H 0 : μ wait = 1sec H a : μ wait < 1sec Reject Null Hypothesis H 0 : μ cars = 1car H a : μ cars < 1car None (0 variance) N/A H 0 : μ cars = 1car H a : μ cars < 1car Reject Null Hypothesis

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 > Reject Null Hypothesis H 0 : μ wait, w/ security - μ wait, baseline = 0 H a : μ wait, w/ security - μ wait, baseline > Reject Null Hypothesis H 0 : μ cars, w/ security - μ cars, baseline = 0 H a : μ cars, w/ security - μ cars, baseline > Reject Null Hypothesis H 0 : μ cars, w/ security - μ cars, baseline = 0 H a : μ cars, w/ security - μ cars, baseline > Reject Null Hypothesis

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 < Reject 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 < Reject 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 < Reject 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 < Reject Null Hypothesis

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 > Reject 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 > Reject 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 > Reject 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 > Reject Null Hypothesis

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