Generalized Model of Lockage Delay Based on Historic Data Michael R. Hilliard, Ph.D. Center for Transportation Analysis Oak Ridge National Laboratory Smart Rivers, 2011 New Orleans

2Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data Optimal Investment in Projects and Maintenance Random Closure Probabilities Reliability Estimates Repair Plans and Costs Construction Plans Cargo Forecasts Lock Operations Towboat/Barge Operations Lock Risk Module Optimal Investment Module Waterway Supply and Demand Module Ohio River Navigation Investment Model (ORNIM) River Network Goal: Maximize net benefits from national investments in infrastructure Estimate waterway usage under future scenarios year time horizon Lock Transit time estimates determine delay costs and influence shipment levels.

3Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data Transit Curves are a foundation of analysis. 1 (Processing_rate — Arrival_rate) Average_transit = Number of Vessels Or Total Tonnage Transit Time (hours) Systems approach requires curves for ALL locks in the system. Some locks are more critical for a given analysis. M/M/1 Queue

4Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data Multiple Roads to Transit Curves Historic Lockage Data Lockage Component Distributions Time Period Averages Individual Lockage Estimates Simulation Results Fitted Transit Curves Simple Simulation Results Simple Simulation Results Lock Groups

5Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data Multiple Roads to Transit Curves Historic Lockage Data Lockage Component Distributions Time Period Averages Individual Lockage Estimates Simulation Results Fitted Transit Curves Simple Simulation Results Simple Simulation Results Lock Groups

6Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data

7Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data

8Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data

9Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data Multiple Roads to Transit Curves Historic Lockage Data Lockage Component Distributions Time Period Averages Individual Lockage Estimates Simulation Results Fitted Transit Curves Simple Simulation Results Simple Simulation Results Lock Groups

10Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data More than 40 thousand cuts over ten years

11Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data Some Locks have much less traffic

12Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data Multiple Roads to Transit Curves Historic Lockage Data Lockage Component Distributions Time Period Averages Individual Lockage Estimates Simulation Results Fitted Transit Curves Simple Simulation Results Simple Simulation Results Lock Groups

13Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data Individual Estimations Each transit record becomes a data item Error checking on data Rolling average of arrival and processing rates Arrival rate = average arrival rate of last 20 tows Processing Rate = average of last 20 lockages Benefits Seasonality captured Variations in processing over time allowed Fitting to 1000s of points—Trade details for large numbers

14Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data Transform and generalize the model 1 (Processing_rate — Arrival_rate) Average_transit = Log(Average_transit) = C+B*Log(Processing_rate — Arrival_rate) Log(Average_transit) = -Log(Processing_rate — Arrival_rate) D_Rate Linear Fit

15Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data Checking the Fit Graphically

16Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data Many Fit Well

17Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data But sometimes they don’t Construction & closures Changes to lock structures Very low traffic levels

18Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data Some locks may be too complex for this approach

19Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data Multiple Roads to Transit Curves Historic Lockage Data Lockage Component Distributions Time Period Averages Individual Lockage Estimates Simulation Results Fitted Transit Curves Simple Simulation Results Simple Simulation Results Lock Groups Size Up/Down ratio etc.

20Managed by UT-Battelle for the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data Currently experimenting with ways to use the parameters. Direct Formula Assume “consistent” arrivals Assume average processing rate Guaranteed to be a “nice” curve – Increasing delay – Accelerating – Limited capacity Assume “consistent” arrivals Assume average processing rate Guaranteed to be a “nice” curve – Increasing delay – Accelerating – Limited capacity Simple Simulation Spreadsheet based simulation Arrival rate varies to match seasonality (with or without randomness) Quick model of changes to processing times or planned closures. Spreadsheet based simulation Arrival rate varies to match seasonality (with or without randomness) Quick model of changes to processing times or planned closures.