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

2 Managed by UT-Battellefor the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data

Optimal Investmentin Projects andMaintenance

Random ClosureProbabilities Reliability Estimates Repair Plans

and Costs

ConstructionPlans

Cargo Forecasts

Lock Operations

Towboat/BargeOperations

Lock Risk Module

Optimal Investment

Module WaterwaySupply 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

• 50-70 year time horizon

• Lock Transit time estimates determine delay costs and influence shipment levels.

3 Managed by UT-Battellefor 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 =

0

0.5

1

1.5

2

2.5

3

3.5

0 1000 2000 3000 4000 5000 6000 7000

Theoretical Transit Estimation

Number of VesselsOr

Total Tonnage

Tra

nsit

Tim

e (h

ours

)

• Systems approach requires curves for ALL locks in the system.

• Some locks are more critical for a given analysis.

M/M/1Queue

4 Managed by UT-Battellefor 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

ResultsLock Groups

5 Managed by UT-Battellefor 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

ResultsLock Groups

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

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

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

9 Managed by UT-Battellefor 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

ResultsLock Groups

10 Managed by UT-Battellefor the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data

More than 40 thousand cuts over ten years

0

50

100

150

200

250

300

350

400

0 1,000 2,000 3,000 4,000 5,000 6,000

Aver

age

Wai

ting

Tim

e

Cuts Per Year

Lagrange 2000-2009

Annual Traffic

M/M/1 Estimate

M/G/1 Estimate

11 Managed by UT-Battellefor the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data

Some Locks have much less traffic

0 50 100 150 200 250 3000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Allegheny 6 (2000-2009)

Commercial Lockages

Aver

age

Tran

sit T

ime

12 Managed by UT-Battellefor 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

ResultsLock Groups

13 Managed by UT-Battellefor 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

14 Managed by UT-Battellefor 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

15 Managed by UT-Battellefor the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data

Checking the Fit Graphically

16 Managed by UT-Battellefor the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data

Many Fit Well

17 Managed by UT-Battellefor 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

18 Managed by UT-Battellefor the U.S. Department of Energy Hilliard-Lock Delay Based on Historical Data

Some locks may be too complex for this approach

19 Managed by UT-Battellefor 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

ResultsLock Groups

• Size• Up/Down

ratio• etc.

20 Managed by UT-Battellefor 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

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.