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L. Douglas Smith Donald C. Sweeney II James F. Campbell Robert M. Nauss

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

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L. Douglas Smith Donald C. Sweeney II James F. Campbell Robert M. Nauss

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  1. 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, 2008

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

  3. 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. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  4. Barges have great capacity but travel slowly (9 mph downstream, 5 upstream) A 15-barge tow carries more than two unit trains. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  5. Locks on the UMR vary in capacity 600 feet 1200 feet • 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! Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  6. Schematic of a lock service system Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  7. 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. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  8. 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). Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  9. Realistic models are needed to test the effects of scheduling rules and infrastructural improvements under different traffic scenarios. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  10. 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. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  11. Considerations in locally sequencing vessel lockages • Immediate Efficiency • Equity to Users • Flexibility to derive future efficiency as succeeding events occur Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  12. 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 Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  13. IP Problem parameters Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  14. IP objective function and constraints Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  15. IP constraints (cont.) Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  16. IP constraints (cont.) Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  17. IP constraints (cont.) Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  18. IP formulation (cont.) Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  19. Additional nonlinear constraints for equity Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  20. 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) Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  21. IP results for 90:10 ratio of double tows : single tows Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  22. IP results for 70:30 ratio of double tows : single tows Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  23. 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 Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  24. 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). Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  25. 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. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  26. 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. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  27. 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. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  28. 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. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  29. 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 Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  30. 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. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  31. 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 Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  32. Simulated versus actual year 2000 arrivals by day of week (percent each tow type) in 100 replications (Top number is percent from simulation; bottom number is year 2000 actual percent.) Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  33. Simulated versus actual year 2000 arrivals by time of day (percent each tow type) in 100 replications (Top number is percent from simulation; bottom number is year 2000 actual percent.) Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  34. Average monthly utilization for Lock 22 Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  35. Comparisons of average monthly queue sizes upstream and downstream Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  36. 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. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  37. 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 Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  38. 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 Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  39. 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. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  40. 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.) Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  41. 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) Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  42. 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) Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  43. Adding local queue balancing constraints for flexibility hurt system-wide performance in our experiments Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  44. Using “helper boats” to speed lockages can greatly reduce congestion for moderate increases in traffic (with some capital investment required) FIFORECPRIO FLT Helper Boats Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  45. New locks eliminate congestion under all traffic scenarios but at great capital cost FIFORECPRIO FLT New 1200’ “Slow” Locks New 1200’ “Fast” Locks Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  46. 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. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  47. 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. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  48. 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 Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  49. 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) Fraunhofer Institute, Dortmund, Germany, May 16, 2008

  50. 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. Fraunhofer Institute, Dortmund, Germany, May 16, 2008

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