Generalized Model of Lockage Delay Based on Historic Data
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
Ohio River Navigation Investment Model (ORNIM) Random Closure Probabilities Reliability Estimates
• Goal: Maximize net benefits from national investments in infrastructure Repair Plans and Costs
Lock Risk Module
•50-70 year time horizon Cargo Forecasts
Optimal Investment Module
Waterway Supply and Demand Module Towboat/Barge Operations
Optimal Investment in Projects and Maintenance
2
Construction Plans
Managed by UT-Battelle for the U.S. Department of Energy
•Estimate waterway usage under future scenarios
Lock Operations River Network
Hilliard-Lock Delay Based on Historical Data
• Lock Transit time estimates determine delay costs and influence shipment levels.
Transit Curves are a foundation of analysis. • Systems approach requires curves for ALL locks in the system.
Transit Time (hours)
Theoretical Transit Estimation 3.5 3 2.5 2 1.5 1 0.5 0 0
1000
2000
3000
4000
5000
6000
7000
Number of Vessels Or Total Tonnage
Average_transit = 3
Managed by UT-Battelle for the U.S. Department of Energy
• Some locks are more critical for a given analysis. M/M/1 Queue
1 (Processing_rate — Arrival_rate) Hilliard-Lock Delay Based on Historical Data
Multiple Roads to Transit Curves Lockage Component Distributions Time Period Averages
Historic Lockage Data
Individual Lockage Estimates Lock Groups
4
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Simulation Results
Fitted Transit Curves
Simple Simulation Results
Multiple Roads to Transit Curves Lockage Component Distributions Time Period Averages
Historic Lockage Data
Individual Lockage Estimates Lock Groups
5
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Simulation Results
Fitted Transit Curves
Simple Simulation Results
6
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
7
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
8
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Multiple Roads to Transit Curves Lockage Component Distributions Time Period Averages
Historic Lockage Data
Individual Lockage Estimates Lock Groups
9
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Simulation Results
Fitted Transit Curves
Simple Simulation Results
More than 40 thousand cuts over ten years 400
Lagrange 2000-2009
Average Waiting Time
350 300 250 200
Annual Traffic
150
M/M/1 Estimate
100
M/G/1 Estimate
50 0 0
1,000 2,000 3,000 4,000 5,000 6,000 Cuts Per Year
10
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Some Locks have much less traffic Allegheny 6 (2000-2009) 0.16
Average Transit Time
0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0
50
100
150
Commercial Lockages
11
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
200
250
300
Multiple Roads to Transit Curves Lockage Component Distributions Time Period Averages
Historic Lockage Data
Individual Lockage Estimates Lock Groups
12
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Simulation Results
Fitted Transit Curves
Simple Simulation Results
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 13
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Transform and generalize the model Average_transit =
1 (Processing_rate — Arrival_rate)
Log(Average_transit) = -Log(Processing_rate — Arrival_rate)
Log(Average_transit) = C+B*Log(Processing_rate — Arrival_rate)
14
Managed by UT-Battelle for the U.S. Department of Energy
Linear Fit Hilliard-Lock Delay Based on Historical Data
D_Rate
Checking the Fit Graphically
15
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Many Fit Well
16
Managed 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
17
Managed 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
18
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Multiple Roads to Transit Curves Lockage Component Distributions Time Period Averages
Historic Lockage Data
Individual Lockage Estimates Lock Groups
19
Managed by UT-Battelle for the U.S. Department of Energy
• Size • Up/Down ratio • etc. Hilliard-Lock Delay Based on Historical Data
Simulation Results
Fitted Transit Curves
Simple Simulation Results
Currently experimenting with ways to use the parameters. Direct Formula
Simple Simulation
• Assume “consistent” arrivals • Assume average processing rate • Guaranteed to be a “nice” curve – Increasing delay – Accelerating – Limited capacity
20
Managed by UT-Battelle for the U.S. Department of Energy
• Spreadsheet based simulation • Arrival rate varies to match seasonality (with or without randomness) • Quick model of changes to processing times or planned closures.
Hilliard-Lock Delay Based on Historical Data
Ohio River Navigation Investment Model (ORNIM) Random Closure Probabilities Reliability Estimates
• Goal: Maximize net benefits from national investments in infrastructure Repair Plans and Costs
Lock Risk Module
•50-70 year time horizon Cargo Forecasts
Optimal Investment Module
Waterway Supply and Demand Module Towboat/Barge Operations
Optimal Investment in Projects and Maintenance
2
Construction Plans
Managed by UT-Battelle for the U.S. Department of Energy
•Estimate waterway usage under future scenarios
Lock Operations River Network
Hilliard-Lock Delay Based on Historical Data
• Lock Transit time estimates determine delay costs and influence shipment levels.
Transit Curves are a foundation of analysis. • Systems approach requires curves for ALL locks in the system.
Transit Time (hours)
Theoretical Transit Estimation 3.5 3 2.5 2 1.5 1 0.5 0 0
1000
2000
3000
4000
5000
6000
7000
Number of Vessels Or Total Tonnage
Average_transit = 3
Managed by UT-Battelle for the U.S. Department of Energy
• Some locks are more critical for a given analysis. M/M/1 Queue
1 (Processing_rate — Arrival_rate) Hilliard-Lock Delay Based on Historical Data
Multiple Roads to Transit Curves Lockage Component Distributions Time Period Averages
Historic Lockage Data
Individual Lockage Estimates Lock Groups
4
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Simulation Results
Fitted Transit Curves
Simple Simulation Results
Multiple Roads to Transit Curves Lockage Component Distributions Time Period Averages
Historic Lockage Data
Individual Lockage Estimates Lock Groups
5
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Simulation Results
Fitted Transit Curves
Simple Simulation Results
6
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
7
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
8
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Multiple Roads to Transit Curves Lockage Component Distributions Time Period Averages
Historic Lockage Data
Individual Lockage Estimates Lock Groups
9
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Simulation Results
Fitted Transit Curves
Simple Simulation Results
More than 40 thousand cuts over ten years 400
Lagrange 2000-2009
Average Waiting Time
350 300 250 200
Annual Traffic
150
M/M/1 Estimate
100
M/G/1 Estimate
50 0 0
1,000 2,000 3,000 4,000 5,000 6,000 Cuts Per Year
10
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Some Locks have much less traffic Allegheny 6 (2000-2009) 0.16
Average Transit Time
0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0
50
100
150
Commercial Lockages
11
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
200
250
300
Multiple Roads to Transit Curves Lockage Component Distributions Time Period Averages
Historic Lockage Data
Individual Lockage Estimates Lock Groups
12
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Simulation Results
Fitted Transit Curves
Simple Simulation Results
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 13
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Transform and generalize the model Average_transit =
1 (Processing_rate — Arrival_rate)
Log(Average_transit) = -Log(Processing_rate — Arrival_rate)
Log(Average_transit) = C+B*Log(Processing_rate — Arrival_rate)
14
Managed by UT-Battelle for the U.S. Department of Energy
Linear Fit Hilliard-Lock Delay Based on Historical Data
D_Rate
Checking the Fit Graphically
15
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Many Fit Well
16
Managed 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
17
Managed 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
18
Managed by UT-Battelle for the U.S. Department of Energy
Hilliard-Lock Delay Based on Historical Data
Multiple Roads to Transit Curves Lockage Component Distributions Time Period Averages
Historic Lockage Data
Individual Lockage Estimates Lock Groups
19
Managed by UT-Battelle for the U.S. Department of Energy
• Size • Up/Down ratio • etc. Hilliard-Lock Delay Based on Historical Data
Simulation Results
Fitted Transit Curves
Simple Simulation Results
Currently experimenting with ways to use the parameters. Direct Formula
Simple Simulation
• Assume “consistent” arrivals • Assume average processing rate • Guaranteed to be a “nice” curve – Increasing delay – Accelerating – Limited capacity
20
Managed by UT-Battelle for the U.S. Department of Energy
• Spreadsheet based simulation • Arrival rate varies to match seasonality (with or without randomness) • Quick model of changes to processing times or planned closures.
Hilliard-Lock Delay Based on Historical Data
