MSA Feedback

Background

Travel demand models generally follow a sequential process wherein person travel demand is generated and then assigned to a network with fixed capacity. A key challenge associated with the sequential processing is that the congestion generated by assigning demand to the network is also an input to the models used to estimate demand. A generally accepted solution to this problem is to iterate the model system, where network level-of-service from assignment is "fed back" to demand generation. After network assignment, new travel time matrices are generated, the person travel models are re-run and new destination, modes, etc. are chosen and the trips are re-loaded onto the network. This process is repeated until an acceptable level of convergence is achieved. It is insufficient to simply feed back the congested skims, since the model system may oscillate between iterations and never converge. Using warm start assignment methods at each iteration of the model system, in Visum or other assignment package, is not mathematically guaranteed to reach convergence.

MSA Implementation in SOABM

For SOABM, the Method of Successive Averages (MSA) is used to achieve convergence. The MSA method computes a new average solution at every iteration as a function of the number of iterations being carried out. The function is shown below:

New Solution = Previous Solution * (1 - 1/N) + Current Solution * (1/N)

where, N is the iteration count.

From a model design perspective, there are a few options when it comes to the choice of a solution to be averaged. In most cases, the final choice of an averaging strategy depends on a mix of practical and theoretical reasons. The MSA averaging of link volumes is considered the best practice method (TMIP, 1996). Typically, MSA averaging of link volumes can be implemented as an extension of the link-based assignment. The average link volumes become an input to the model VDF, which yields the adjusted link times for next iteration. Trip table averaging is another option. The research literature suggests that trip table averaging might work better with path-based assignment algorithms (Boyce et. al., 2006). Some studies conclude that trip table averaging might benefit link volume averaging but may not be very effective on its own (Slavin et. al., 2015). For bigger complex models, trip table averaging might result in excessive storage and computational time as well. Another option is to average impedance matrices (Slavin et. al., 2015). This method is in use by many MPOs and research suggest that this method can also be effective in achieving convergence. Link times is also an option to implement feedback. The drawback of using link times is that the average times do not correspond to any consistent set of link flows that are produced by a traffic assignment. This can be resolved by storing average times in temporary fields to implement feedback and then discard them at the end of the final feedback iteration. With any strategy, there is always the question of implementability within the given modeling framework.

For the Visum-based SOABM, MSA feedback was implemented on link times. Link volumes and link times are read-only variables in Visum. Link volumes are computed by the assignment module and the link times are computed using a volume-delay function. Therefore, direct averaging of link volumes or times is not possible in Visum. However, MSA-averaged travel time skims can be computed from a user-defined MSA link time variable. Therefore the assignment-skimming process was updated to calculate MSA link times and compute shortest path skims. The updated assignment-skimming steps (taz_skim entry point in the SOABM.py script) are as follows:

For each ABM feedback iteration and time-of-day period:

• Call the MSA Preparation function which does the following:
  • Create link-level user-defined-attributes (UDA) to store previous iteration link times for each demand segment (DSeg)
    tCur_SOV, tCur_SOVToll, tCur_HOV2, tCur_HOV2Toll, tCur_HOV3, tCur_HOV3Toll, tCur_TRUCK, tCur_TRUCKToll
  • Set travel time UDAs to previous iteration link times. For the first iteration, these are set to zero
• Perform assignment and skimming by running the procedures stored in config/visum/taz_skim_[TOD].xml
• Generate initial skims for each DSeg (demand segment) as described here. The skim numbers must match the skim numbers specified in CT-RAMP UECs
• For each DSeg:
  • Compute MSA link times as:
    t_MSA = t_previous * (1-1/iteration) + t_current * (1/iteration)
    The t_previous is zero for the 1st iteration as initialized in the initial preparation step. For 1st iteration, t_MSA simply becomes:
    t_MSA = 0 * (1-1/1) + t_current * (1/1) = t_current
  • Compute MSA generalized cost using t_MSA as follows:
    Generalized Cost = 1 * t_MSA + (3600/[VOT]) * Toll_PrTSys([DSEG]) + (3600 * [AOC]/[VOT] * Length)
    Detailed information on generalized cost can be found here
  • Compute shortest path skims using MSA generalized cost. Compute t_MSA skim in addition to all other skims
  • Since all other skims already exist, they get overwritten by the skimming process
  • Overwrite the tCur skim with the newly computed t_MSA skim to be used by person travel demand process in next iteration

The model is currently configured to run 5 feedback iterations. The ABM sample rate is increased steadily from 10% in the first iteration to 100% in the last iteration. Generally, 5 feedback loops are sufficient to achieve convergence. Convergence can be checked by computing %RMSE between the current and previous link volumes for the peak period. A %RMSE value of less than 5% indicates that convergence has reached.

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References

1. Boyce, D. and Bar-Gera, H. (2006) Solving the Sequential Travel Forecasting Procedure with Feedback. 16th PTV Vision User Group Meeting 2006
2. Slavin, H., Lam, J., Nanduri, K. (2015) Traffic Assignment and Feedback Research to Support Improved Travel Forecasting. 2015. Federal Transit Administration (FTA), Final Report accessed from https://www.transit.dot.gov/sites/fta.dot.gov/files/traffic-assignment-and-feedback-research-to-support-improved-travel-forecasting.pdf
3. Travel Model Improvement Program (TMIP). (1996) Incorporating Feedback in Travel Forecasting: Methods, Pitfalls and Common Concerns, March 1996