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

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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

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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.

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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.

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

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

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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!

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Schematic of a lock service system

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• 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.

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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).

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

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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.

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Considerations in locally sequencing vessel
lockages

• Immediate Efficiency
• Equity to Users
• Flexibility to derive future efficiency as
  succeeding events occur

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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

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IP Problem parameters
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IP objective function and constraints
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IP constraints (cont.)
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IP constraints (cont.)
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IP constraints (cont.)
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IP formulation (cont.)
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Additional nonlinear constraints for equity
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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)

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IP results for 9010 ratio of double tows
single tows
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IP results for 7030 ratio of double tows
single tows
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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

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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).

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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.

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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.

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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.

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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.

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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

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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.

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Lognormal distributions for conditional activity
times

Raw lockage times
Residuals of partitioned log regression
log(lockhrs for double lockage at 24U) 0.599 -
0.096feb 0.080jun -0.080jul 0.040sep
0.053oct - 0.117turnback
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Simulated versus actual year 2000 arrivals by day
of week (percent each tow type) in 100
replications
Day of Week Double Single with Barges Jack-knife Knock-out Single w/o Barges Recn
Sun 63.1 62.9 8.5 7.8 1.6 1.5 1.6 1.6 4.1 4.8 21.1 21.4
Mon 65.3 65.8 11.0 10.7 1.6 1.5 1.9 1.5 7.4 7.4 12.9 13.2
Tue 66.9 66.9 11.9 12.8 2.0 1.7 2.8 2.2 7.5 7.6 8.9 8.8
Wed 64.8 65.0 13.1 14.1 2.0 1.6 2.3 2.0 7.9 7.7 9.9 9.5
Thu 62.6 63.3 14.9 15.1 1.6 1.6 2.4 2.2 7.4 7.1 11.1 10.7
Fri 63.8 62.7 11.5 12.7 1.6 1.4 2.2 2.2 6.1 6.4 14.7 14.5
Sat 59.7 60.3 9.4 8.6 1.6 1.3 2.1 1.9 5.6 6.0 21.5 21.8
(Top number is percent from simulation bottom
number is year 2000 actual percent.)
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Simulated versus actual year 2000 arrivals by
time of day (percent each tow type) in 100
replications
Hour of Day Double Single with Barges Jack-knife Knock- out Single w/o Barges Recn
00 74.8 75.7 14.1 13.2 2.2 1.9 1.7 2.2 6.6 6.4 0.6 0.6
11 49.2 50.0 12.0 11.0 1.0 1.0 2.4 2.0 6.4 6.3 29.0 29.7
16 57.2 57.2 9.1 10.7 1.7 1.4 1.8 1.8 6.0 6.8 24.1 22.1
20 71.0 71.6 12.1 12.4 1.3 1.6 2.3 2.0 7.5 7.6 5.7 4.8
(Top number is percent from simulation bottom
number is year 2000 actual percent.)
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Average monthly utilization for Lock 22
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Comparisons of average monthly queue sizes
upstream and downstream
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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.

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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

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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
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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.

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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.)
Traffic Levels Nominal Policy (FIFORECPRIO) Nominal Policy (FIFORECPRIO) Singles Priority (SINGPRIO) Singles Priority (SINGPRIO) Fastest Locking Time (FLT) Fastest Locking Time (FLT)
Traffic Levels Time in Queue Total Lock Transit Time Time in Queue Total Lock Transit Time Time in Queue Total Lock Transit Time
Year 2000 D 163 S 164 D 277 S 195 D 174 S 101 D 289 S 131 D 171 S 97 D 284 S 125
Year 2000 Plus 10 D 288 S 278 D 402 S 308 D 311 S 130 D 425 S 159 D 287 S 119 D 399 S 149
Year 2000 Plus 20 D 880 S 797 D 992 S 827 D 1003 S 177 D1115 S 205 D 794 S 152 D 900 S 181
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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)

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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)

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Adding local queue balancing constraints for
flexibility hurt system-wide performance in our
experiments
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Using helper boats to speed lockages can
greatly reduce congestion for moderate increases
in traffic (with some capital investment required)

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

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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.

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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

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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)

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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.

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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