l. douglas smith donald c. sweeney ii james f. campbell robert m. nauss

1Fraunhofer Institute, Dortmund, Germany, May 16, 2008Fraunhofer Institute, Dortmund, Germany, May 16, 2008

Center for Business and Industrial Studies

Center for Transportation

Studies

Analytical Modeling for Inland Waterway Traffic Management and Infrastructure: Experience from the Upper Mississippi

River Navigation System

L. Douglas Smith

Donald C. Sweeney II

James F. Campbell

Robert M. Nauss

College of Business Administration University of Missouri – St. Louis

One University Blvd.St. Louis MO 63121

Fraunhofer Institute, Dortmund, Germany, May 16, 2008Fraunhofer Institute, Dortmund, Germany, May 16, 2008 2



Studies

Upper Mississippi River (UMR) Navigation System

Extends 663 miles from St. Louis to Minneapolis.

Includes 29 lock and dam facilities to raise vessels 300 feet.




Studies

Commercial barge traffic

Carried 73.3 million tons in 2004.

Agricultural products travel downstream – most to New Orleans for export.

Other bulk commodities (petroleum, chemicals, etc.) travel back and forth in dedicated tows.

Barges measure 35 ft x 195 ft and hold 1500 tons.

UMR tows include up to 15 barges totaling nearly 1200 ft long.




Studies

Barges have great capacity but travel slowly (9 mph downstream, 5 upstream)

A 15-barge tow carries more than two unit trains.




Studies

Locks on the UMR vary in capacity

Old locks are 600-ft long, but some locks have been expanded to 1200-ft.

Locking a small tow in a 600-ft long lock takes about 30 minutes.

Locking a 1200-ft long tow in a 600-ft long lock takes about 2 hours because it has to be broken and winched through!

600 feet

1200 feet




Studies

Schematic of a lock service system

DownstreamMooring Buoy Recreational

DownstreamMooring Buoy Commercial

UpstreamMooring Buoy Recreational

UpstreamMooring Buoy Commercial

Lock Chamber Downstream DepartureUpstream Departure




Studies

The UMR is a series of interdependent service facilities (locks) with multiple queues that serve vessels and tows with highly seasonal traffic patterns and varying itineraries.

Five 600-foot locks in series between two 1200-foot locks north of St. Louis create traffic bottlenecks with seasonal delays.




Studies

Alternative remedies proposed to deal with the bottlenecks

U.S. Army Corps of Engineers (USACE) proposes to expand the five locks to 1200 feet (approx. $2.8 billion over five years).

National Research Council (NRC) proposed exploring less costly alternatives:

- Smaller infrastructure investments (more modest expenditure) to increase efficiency of existing assets.

- Alternative scheduling procedures (minimal expenditure).




Studies

Realistic models are needed to test the effects of scheduling rules and infrastructural improvements under different traffic scenarios.




Studies

Waiting times vary among the five locks

Different mixes of traffic, river conditions, and vessel maneuverability.

Upstream movements differ from downstream movements.

Itineraries, lockage times and pool transit times vary with tow configuration.

Occasional impairments to operations.

0

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LO

CK

_N

O




Studies

Considerations in locally sequencing vessel lockages

Immediate Efficiency

Equity to Users

Flexibility to derive future efficiency as succeeding events occur




Studies

Deterministic analysis of processing sequences to minimize total expecting waiting time of vessels when clearing current queues at a lock

Lockage times depend on changes in lock configuration (turnback or exchange) in addition to type of tow.

Nauss (2007 EJOR) used integer programming to create the optimal locking sequence for clearing all the queues at a lock.

- If waiting times were weighted equally for each towboat in the queue, solutions involved selecting vessels according to fastest locking time and may alternate upstream and downstream

Here, we add constraints for equity considerations

- Delay vessel in IP solution no more than a designated interval relative to its FIFO position (6 hours or 8 hours)

The new constraints are nonlinear and necessarily change the solution from FLT sequence




Studies

IP Problem parameters

ND: total number of TB’s in queue on the downstream side of the lock (headed upstream). NU: total number of TB’s in queue on the upstream side of the lock (headed downstream). N: total number of TB’s in queue on both sides of the lock (N = ND + NU).

itmdtr for i = 1, ...ND : expected lockage time for the ith TB on the downstream side if lockage is a turnback.

tmdex1 for i = 1, ...ND : expected lockage time for ith TB on the downstream side if lockage is an exchange. :N...,1for Ui itmutr expected lockage time for the ith TB on the upstream side if lockage is a turnback.

:N...,1for Ui itmuex expected lockage time for the ith TB on the upstream side if lockage is an exchange.




Studies

IP objective function and constraints

(1)

N

1jjENDLOCKMINIMIZE

subject to:

(2)

N

1jDijij N...1i 1 )EXDTRD( (downstream vessel i locked as turnback or exchange)

(3)

N

1

N...1 1 )( j

Uijij iEXUTRU (similarly for upstream vessel i)

(4) 1N,...1j 1 ZZZZ jUDjDUjDDjUU (jth lockage must be upstream or downstream

turnback or exchange)

(5)

D U

i ii ENDLOCKTRUtmutrtmdtr

N

11

N

111i11 *TRD* (start with turnback)




Studies

IP constraints (cont.)

(6) i

N

1i)1j( (ENDLOCK

D

tmdtr

TRD ij+ itmdex ijEXD ) +

UN

1ii(tmutr ijTRU itmuex ijEXU ) ≤ N,...2jfor ENDLOCKj

(calculate ending time for next lockage)

(7) 1N,...1j Z1TRD)TRDEXD( jDD

N

1i1j,iijij

N

1i

DD

with ZjDD ≤ 1N,...1 TRD Zand )TRDEXD(N

11,jDD

N

1

jUU

ijiijij

i

(force consistency in definition of downstream turnback)




Studies


(8) 1N,...1 1)(N

11,

N

1

jZTRUTRUEXU jUUi

jiijiji

UU

with ZjUU ≤ 1N,...1 TRU Zand )TRUEXU(N

11,jUU

N

1

jUU

ijiijij

i

(force consistency in definition for upstream turnback)

(9) 1N,...1j Z1EXU)TRDEXD( jDU1j,i

N

1iijij

N

1i

UD

(force consistency in definition for next lockage upstream as an exchange)

1N,...1 Zand)( with Z 1,

N

1jDU

N

1jDU

jEXUTRDEXD jii

ijiji

UD




Studies


(10) 1N,...1 1)(N

11,

N

1

jZEXDTRUEXU jUDi

jiijiji

DU

1N,...1 Zand)( with ZN

11,jUD

N

1jUD

jEXDTRUEXUDU

ijiijij

i

(force consistency in definition for next lockage downstream as an exchange)

(11) N,...1j 1)TRUEXU()TRDEXD( ij

N

1iijij

N

1iij

UD

(force jth lockage to be one of the four alternatives)




Studies

IP formulation (cont.)

(12) D1i N...,1i0EXD

U1i N...,1i0EXU

ijEXD = 0 or 1 N,...1jN,...1 ,Di

ijTRD = 0 or 1 N,...1jN,...1 ,Di

ijEXU = 0 or 1 N,...1jN,...1 ,Ui

(13) ijTRU = 0 or 1 N,...1jN,...1 ,Ui

1N,...1j 1or 0Z jDD

1N,...1j 1or 0Z jUU

1N,...1j 1or 0Z jDU

.1N,...1j 1or 0Z jUD




Studies

Additional nonlinear constraints for equity

(14) N,...1i FIFO)ENDLOCK()TRDEXD( D

N

1jiDjijij

waitlim

(15) .N,...1i FIFO)ENDLOCK()TRUEXU( U

N

1jiUjijij

waitlim




Studies

Random problem sets for peak traffic

20 random sets of single and double tows with 0.9 probability of a double tow; 20 random sets of single and double tows with 0.7 probability of a double tow

Problems solved with varying equity constraints

- Waitlim set very large (99999 minutes) to relax the constraint and revert to FLT

- Waitlim set to 6 hours (360 minutes)

- Waitlim set to 8 hours (480 minutes)




Studies

IP results for 90:10 ratio of double tows : single tows

Tow Configuration

Average Number

in Beginning

Queue

Av Total

Clearing Time FIFO

Av Total Time without

Displacement Restriction

(pct change in parentheses)

Av Total Time

with 480-min. Limit


Av. Total Time

with 360-min. Limit


Doubles Upstream 8.8 1174.1 580.3 (-50.6) 812.0 (-30.8) 933.7 (-20.5) Singles Upstream 1.1 1099.1 61.4 (-94,4) 64.0 (-94.2) 58.8 (-94.6) Doubles Downstream 9.15 1055.7 1612.8 (+52.8) 1400.3 (+32.6) 1309.3 (+24.0) Singles Downstream 0.95 1047.9 37.4 (-96.4) 33.8 (-96.8) 43.8 (-95.8) Doubles total 17.95 1115.5 1111.7 (-0.3) 1131.8 (+1.5) 1140.0 (+2.2) Singles total 2.05 1102.1 45.8 (-95.8) 46.0 (-95.8) 46.4 (-95.8) All vessels 20 1114.1 1004.2 (-9.9) 1022.5 (-8.2) 1029.8 (-7.6)




Studies

IP results for 70:30 ratio of double tows : single tows

Tow Configuration

Average Number

in Beginning

Queue

Av Total

Clearing Time FIFO

Av Total Time without

Displacement Restriction


Av Total Time

with 480-min. Limit


Av. Total Time

with 360-min. Limit


Doubles Upstream 6.55 892.0 603.1 (-32.4) 785.3 (-12.0) 853.3 (-4.3) Singles Upstream 2.75 808.7 146.1 (-81.9) 145.6 (-82.0) 141.2 (-82.5) Doubles Downstream 7 929.5 1347.5 (+45.0) 1210.6 (+30.2) 1162.8 (+25.1) Singles Downstream 3.7 873.3 111.6 (-87.2) 112.5 (-87.1) 122.6 (-86.0) Doubles total 13.55 913.7 998.7 (+9.3) 1016.0 (+11.2) 1021.2 (+11.8) Singles total 6.45 845.0 120.0 (-85.8) 120.7 (-85.7) 121.1 (-85.7) All vessels 20 897.9 714.6 (-20.4) 726.3 (-19.1) 729.9 (-18.7)




Studies

Summary of inferences from deterministic analysis

Without waitlim constraints to promote equity, optimal solution is FLT (if consider set-up and locking times that both depend on whether the lock is turned back)

As expected, greater diversity in vessel mix gives greater opportunity for improvement

Adding waitlim constraints has minor effect on total time in queue for all vessels

Must recognize that benefits will be less in slack periods




Studies

The system is nondeterministic and the objective is complicated

The queueing problem and optimal sequence can change with each arrival.

Actual activity times deviate from expected times used in the deterministic model.

Self-adapting behavior in periods of congestion can distort data and alleviate some problems without changing formal operating procedures.

First-come, first served is seen as a guiding principle that promotes equity (absent a priority charging scheme).




Studies

Scheduling rules need to be tested under stochastic conditions

For local scheduling, fastest locking time (FLT) is seen as promoting efficiency, FIFO is seen as promoting equity.

The barge industry demands simple rules that are easy to understand and implement without revealing proprietary information (including cargoes and destinations).

We developed a series of local scheduling rules with variants on FLT to consider efficiency and equity and tested their impact on the stochastic system.




Studies

Simulation model requirements

Must accommodate multiple classes of vessel traffic with different arrival patterns, itineraries and service characteristics.

Queueing and processing structure that captures physical realities of upstream and downstream traffic movements to and from the locks.

Detailed measures of system performance that show the mix of vessel traffic movements, facility utilization, waiting times and queue sizes in the vicinity at each lock at different times.

Tests of statistical significance of observed effects on system performance.




Studies

Discrete event simulation model infrastructure

SAS (Statistical Analysis System) front-end for historical analysis and generating equations for time and event-varying model parameters.

ARENA 10.0 discrete-event simulator to represent system behavior and generate experimental results under different rules and traffic scenarios.

SAS back-end for reporting and analysis of simulated system performance.




Studies

ARENA simulation model

Discrete-event simulation model with Markovian structure for generation of vessel itineraries and activity times and for exercising alternative traffic control policies.

Seasonal random arrivals generated with monthly effects, day-of-week effects, and time-of-day effects that differ according to vessel-tow characteristics.




Studies

Generating random arrivals

Nonstationary exponential distributions are used in conjunction with probabilistic intensification and thinning processes to impose differential arrival rates for various classes of vessel according to:

- Month of year

- Day of Week

- Time of day




Studies

Imposing other systematic variation

Itineraries and activity times differ according to vessel-tow configuration, sequence of lockage operations, traffic levels and river conditions.

Lock operations data were partitioned for different locks and vessel-tow combinations and 100+ regression and logistic models were created for dynamic setting of system parameters.




Studies

Lognormal distributions for conditional activity times

Raw lockage times Residuals of partitioned log regression

log(lockhrs for double lockage at 24U) = 0.599 - 0.096*feb + 0.080*jun-0.080*jul + 0.040*sep + 0.053*oct - 0.117*turnback




Studies

Simulated versus actual year 2000 arrivals by day of week (percent each tow type) in 100 replications

Day ofWeek

Double Singlewith Barges

Jack-knife Knock-out Singlew/o Barges

Rec’n

Sun 63.162.9

8.57.8

1.61.5

1.61.6

4.14.8

21.121.4

Mon 65.365.8

11.010.7

1.61.5

1.91.5

7.47.4

12.913.2

Tue 66.966.9

11.912.8

2.01.7

2.82.2

7.57.6

8.98.8

Wed 64.865.0

13.114.1

2.01.6

2.32.0

7.97.7

9.99.5

Thu 62.663.3

14.915.1

1.61.6

2.42.2

7.47.1

11.110.7

Fri 63.862.7

11.512.7

1.61.4

2.22.2

6.16.4

14.714.5

Sat 59.760.3

9.48.6

1.61.3

2.11.9

5.66.0

21.521.8

(Top number is percent from simulation; bottom number is year 2000 actual

percent.)




Studies

Simulated versus actual year 2000 arrivals by time of day (percent each tow type) in 100 replications

Hour of Day

Double Singlewith Barges

Jack-knife

Knock-out

Single w/o Barges

Rec’n

00 74.875.7

14.113.2

2.21.9

1.72.2

6.66.4

0.60.6

11 49.250.0

12.011.0

1.01.0

2.42.0

6.46.3

29.029.7

16 57.257.2

9.110.7

1.71.4

1.81.8

6.06.8

24.122.1

20 71.071.6

12.112.4

1.31.6

2.32.0

7.57.6

5.74.8

(Top number is percent from simulation; bottom number is year 2000 actual percent.)




Studies

Average monthly utilization for Lock 22

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

1 2 3 4 5 6 7 8 9 10 11 12

Month

Perc

en

t U

tiliza

tio

n

2000 OMNI

FIFO

RECPRIO




Studies

Comparisons of average monthly queue sizes upstream and downstream

Down Up Total Down Up TotalLock20 0.44 0.42 0.86 0.59 0.68 1.2721 0.48 0.44 0.92 0.46 0.49 0.9522 0.74 0.8 1.54 1.04 1.05 2.0924 0.65 0.82 1.47 0.94 0.94 1.8825 0.67 0.82 1.49 0.93 1.08 2.01

Average queue sizes in MayActual Year 2000 FIFORECPRIO Results




Studies

Alternative rules for sequencing lockages

FIFO (First In, First Out) - the traditional benchmark in the simulation literature.

FIFORECPRIO - a variation on FIFO where priority is given to recreational vessels (this policy closely matches the prevailing Corps guidelines).

FLTX – Fastest Locking time with priority escalation for vessels experiencing long delays.




Studies

Analysis

We used the results from 100 replications (years) of simulated activity to assess the impact of the alternative scheduling rules.

Experiments were also performed at different traffic levels




Studies

Mean wait and lock transit times (minutes) with Year 2000 traffic levels

Mean wait and transit times in minutes are for the study area over 100 simulated years of operation with current traffic levels

Vessel-tow Configuration

FIFO FIFORECPRIO FLTX 480 min

FLT FLTX 360 min

Wait Transit Wait Transit Wait Transit Wait Transit Wait Transit Double 161.1 275.7 162.9 277.5 168.3 281.9 170.6 284.2 164.5 278.2 Jackknife 178.9 262.6 183.5 267.2 123.6 205.9 101.3 183.5 125.4 208.0 Knockout 169.5 230.7 172.6 233.9 123.6 183.8 112.4 172.7 123.5 183.9 Single 161.0 192.0 163.9 194.9 109.3 139.8 94.6 125.0 113.4 143.9 X-Barge 155.8 179.3 157.8 181.4 97.7 121.3 86.1 109.6 101.7 125.5 Recreation 189.4 202.6 49.1 62.4 48.4 61.7 48.3 61.5 48.4 61.7 All Lockages 165.2 247.9 146.7 229.4 137.9 219.9 136.6 218.6 136.2 218.1 Replication Averages, Pairwise groupings (A, B, …) and Sequencing Impact from Basic ANOVA

A 247.5

(+18.2 Min.)

B 229.3

(0 Min.)

C 220.5

(-8.8 Min.)

C 219.1

(-10.1 Min.)

C 218.6

(-10.7 Min.)




Studies

Time savings are greater at increased traffic levels

We evaluated the sequencing alternatives with ranges in traffic level from -10% to +30% of year 2000 levels, while keeping the mix of vessel arrivals, seasonality and lockage types as observed in year 2000.

There was an increasing advantage of FLT as demand increases, particularly for the single tows, but an emerging need to deal with extreme waits for double tows.




Studies

TrafficLevels

NominalPolicy

(FIFORECPRIO)

SinglesPriority

(SINGPRIO)

FastestLocking

Time (FLT)

Time in Queue

Total Lock

TransitTime

Time inQueue

Total LockTransitTime

Time in Queue

Total LockTransitTime

Year 2000 D: 163S: 164

D: 277S: 195

D: 174S: 101

D: 289S: 131

D: 171S: 97

D: 284S: 125

Year 2000Plus 10%

D: 288S: 278

D: 402S: 308

D: 311S: 130

D: 425S: 159

D: 287S: 119

D: 399S: 149

Year 2000Plus 20%

D: 880S: 797

D: 992S: 827

D: 1003S: 177

D:1115S: 205

D: 794S: 152

D: 900S: 181

Effects on average times at locks (over 100 simulated years) differ greatly for double-tow (D) vs. single-tow (S) lockages

Average Times in Queue and at Lock (mins.)




Studies

Overall performance with 360 min. and 480 min. priority shifting criteria are quite similar

Medians and 95th Percentiles of Waiting Times

with YR 2000 Commercial Traffic Plus 20%

(without common random number streams for arrival generators)

FIFORECPRIO (benchmark)

FLTX (1yr - no priority shift)

FLTX 480 min

FLTX 360 min.


Median 95th Median 95th Median 95th Median 95th Double 327 3,689 165 3,688 401 3,283 385 2,902

Jackknife 378 3,645 116 705 200 3,029 211 2,667 Knockout 320 3,245 127 716 187 2,914 190 2,593

Single 293 3,411 106 630 157 2,920 161 2,598 Single ex Barge 271 3,079 92 573 137 2,997 140 2,639

Recreational 51 125 49 123 51 130 50 131 Average No.

Lockages 22,063 21,751 21,837 21,755

Resulting Averages of Total Transit Time All vessels

825 618 (-25%) 741 (-11%) 685 (-17%)




Studies

We had to use common number streams for arrival generators to get results completely consistent with the IP, further suggesting differences in performance of FLTX-360 and FLTX-480 would be hard to detect in practice.

Medians and 95th Percentiles of Waiting Times

with YR 2000 Commercial Traffic Plus 20%

(but without common random number streams for arrival generators)

FIFORECPRIO (benchmark)

FLTX (1yr - no priority shift)

FLTX 480 min

FLTX 360 min.


Median 95th Median 95th Median 95th Median 95th Double 314 3,694 164 3,385 377 3,120 386 3,224

Jackknife 365 3,641 117 721 199 2,787 217 3,045 Knockout 310 3,303 127 699 183 2,687 194 2,934

Single 281 3,481 105 628 152 2,734 162 2,984 Single ex Barge 269 3,243 91 572 134 2,767 144 3,006

Recreational 51 125 49 123 50 130 50 131 Average No. of

Lockages 21,810 21,730 21,770 21,770

Resulting Averages of Total Transit Time All vessels

818 A

586 C

(-28%) 713 B

(-13%) 729 B

(-11%)




Studies

Adding local queue balancing constraints for flexibility hurt system-wide performance in our experiments

Medians and 95th Percentiles of Waiting Times For Queue Balancing Variants with Year 2000 Commercial Traffic Plus 20%

FIFORECPRIO (bench mark)

BALQLCLX-5 (1yr - no priority

shift)

BALQLCLX-5 480 min.

BALQLCLX-5 360 min.

BALQLCLX-4 360 min


Median 95th Median 95th Median 95th Median 95th Median 95th Double 334 3,772 148 6,732 579 5,593 522 5,145 524 5,599

Jackknife 378 3,732 131 628 339 5,012 359 4,834 364 5,335 Knockout 324 3,322 117 546 242 4,521 258 4,399 256 4,726

Single 296 3,473 115 553 228 4,649 237 4,511 238 4,887 Single ex barge 275 3,062 101 549 199 4,426 203 4,180 210 4,529

Recreational 51 125 50 124 52 131 52 131 52 132




Studies

Using “helper boats” to speed lockages can greatly reduce congestion for moderate increases in traffic (with some capital investment required)

UMR Locks 20 through 25 - Mean Lock Transit Times in Minutes

0

100

200

300

400

500

600

700

800

900

1000

-20% -15% -10% -5% +0% +5% +10% +15% +20% +25% +30%

Mean Annual Total Number of Lockages as a Percentage of 2000 Lockages

Me

an

Tra

ns

it T

ime

pe

r L

oc

k in

Min

ute

s

FIFORECPRIO FLT FAST 1200 LOCKS SLOW 1200 LOCKS Historic Data 1992-2006 Helper Boats

Helper Boats

FIFORECPRIO FLT




Studies

New locks eliminate congestion under all traffic scenarios but at great capital cost

UMR Locks 20 through 25 - Mean Lock Transit Times in Minutes

0

100

200

300

400

500

600

700

800

900

1000

-20% -15% -10% -5% +0% +5% +10% +15% +20% +25% +30%

Mean Annual Total Number of Lockages as a Percentage of 2000 Lockages

Me

an

Tra

ns

it T

ime

pe

r L

oc

k in

Min

ute

s

FIFORECPRIO FLT FAST 1200 LOCKS SLOW 1200 LOCKS Historic Data 1992-2006

New 1200’ “Fast” Locks

New 1200’ “Slow” Locks

FIFORECPRIO FLT




Studies

Our Findings

The IP Model helped us develop scheduling rules for further testing via stochastic simulation.

Benefits (or costs) differ among classes of user.

The FLTX rule promotes immediate efficiency while imposing fairness, and results in improved system-wide performance under a range of priority-shifting intervals.

Adding constraints upon FLTX to keep local queues balanced harmed system-wide performance.




Studies

Findings (cont.)

Stochastic phenomena (variations in traffic intensity, traffic mix, activity times and random arrivals) mute the benefits of scheduling strategies inferred from deterministic optimizing models for clearing queues that exist at a point in time

Self-adapting behavior in extreme conditions eliminates (and hides) some of the stochastic problem – making it difficult to isolate the true benefits from scheduling solutions that may be implemented.




Studies

Strategic considerations for eliminating seasonal congestion

Fixed and variable costs under alternative remedies vary greatly and are incurred by stakeholders (public and private) in different proportions

Incidental economic effects differ

Environmental effects differ

Relative advantages depend heavily on future traffic scenarios




Studies

Political and economic issues

Infrastructure investments must be justified by the U.S. Army Corps of Engineers on the basis of net national economic benefit- How to estimate benefits from greater capacity

Market Benefits: Reduction in expected queue time with or without traffic displacement

Non-market Benefits: Carbon footprint for water transportation versus rail and highway

External Benefits: Congestion relief on railways and highways

Revenue sources for infrastructure improvements- Federal earmarks from general revenues- Existing fuel tax specific to the industry - Newly proposed lockage fees (risk of displacement as with the Chunnel if

competing modes adjust rates to retain or capture business) Containing Federal budgetary deficits versus economic stimulus Ethanol subsidies (corn for domestic bio-fuel instead of export for

food)




Studies

Future research

Exploring effects of alternative congestion charging mechanisms and priority booking fees

Developing other decision rules with consideration of conditions at adjacent locks

Investigating consequences of traffic restrictions during new construction

Extending the IP model to clearing a system of three locks to see if different rules emerge for clearing the middle lock versus the locks at both ends.- System-wide measures of queue balance- System-wide measures of dispersion in vessel mix at locks.

Integration of IP and simulation in various degrees.




Studies

Future research (cont.)

Improving IP heuristics- Recognize that vessels within a class will not be

reordered from upstream or downstream arrival sequence, as doing so will not generate efficiencies

- Possibly restricting attention to the first x lockages because new arrivals will change the problem.

Solving the IP over a range of anticipated future states of the system (and looking for commonalities in immediate action inferred from the different solutions).

Using time-discounted objectives in the IP solution (unfortunately adding additional nonlinearity).

Developing alternative metrics for flexibility that may be considered in setting IP boundary conditions or in the decision rules for stochastic analysis

l. douglas smith donald c. sweeney ii james f. campbell robert m. nauss

Documents

ft long tow

ft long lock

foot locks

capacityold locks

umr tows

traffic bottlenecks

barge tow

seasonal traffic patterns