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

2. 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.

3. 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.

4. 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.

5. Fraunhofer Institute, Dortmund, Germany, May 16, 2008 5 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

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

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

8. 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).

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

10. 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.

11. 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

12. 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

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

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

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

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

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

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

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

20. 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)

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

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

23. 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

24. 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).

25. 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.

26. 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.

27. 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.

28. 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.

29. 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

30. 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.

31. 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

32. 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 Day of Week DoubleSingle with Barges Jack-knifeKnock-outSingle w/o Barges Rec’n Sun63.1 62.9 8.5 7.8 1.6 1.5 1.6 4.1 4.8 21.1 21.4 Mon65.3 65.8 11.0 10.7 1.6 1.5 1.9 1.5 7.4 12.9 13.2 Tue66.9 11.9 12.8 2.0 1.7 2.8 2.2 7.5 7.6 8.9 8.8 Wed64.8 65.0 13.1 14.1 2.0 1.6 2.3 2.0 7.9 7.7 9.9 9.5 Thu62.6 63.3 14.9 15.1 1.6 2.4 2.2 7.4 7.1 11.1 10.7 Fri63.8 62.7 11.5 12.7 1.6 1.4 2.2 6.1 6.4 14.7 14.5 Sat59.7 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.)

33. 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 Hour of Day DoubleSingle with Barges Jack- knife Knock- out Single w/o Barges Rec’n 0074.8 75.7 14.1 13.2 2.2 1.9 1.7 2.2 6.6 6.4 0.6 1149.2 50.0 12.0 11.0 1.0 2.4 2.0 6.4 6.3 29.0 29.7 1657.2 9.1 10.7 1.7 1.4 1.8 6.0 6.8 24.1 22.1 2071.0 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.)

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

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

36. 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.

37. 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

38. 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

39. 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.

40. Fraunhofer Institute, Dortmund, Germany, May 16, 2008 40 Traffic Levels Nominal Policy (FIFORECPRIO) Singles Priority (SINGPRIO) Fastest Locking Time (FLT) Time in Queue Total Lock Transit Time Time in Queue Total Lock Transit Time Time in Queue Total Lock Transit Time Year 2000D: 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 D:1115 S: 205 D: 794 S: 152 D: 900 S: 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.)

41. Fraunhofer Institute, Dortmund, Germany, May 16, 2008 41 Overall performance with 360 min. and 480 min. priority shifting criteria are quite similar Medians and 95 th Percentiles of Waiting Times with YR 2000 Commercial Traffic Plus 20% (without common random number streams for arrival generators)

42. 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)

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

44. 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) Helper Boats FIFORECPRIO FLT

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

46. 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.

47. 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.

48. 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

49. 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)

50. 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.

51. Fraunhofer Institute, Dortmund, Germany, May 16, 2008 51 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