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Practical Implications of Finding Consistent Route Flows Hillel BarGera Purdue University, and BenGu

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Title: Practical Implications of Finding Consistent Route Flows Hillel BarGera Purdue University, and BenGu


1
Practical Implications of Finding Consistent
Route Flows Hillel Bar-GeraPurdue University,
and Ben-Gurion University of the Negev, Israel
Yu Nie and David BoyceNorthwestern
UniversityMay 20, 2009
  • FHWA 2008 TRANSPORTATION PLANNING COOPERATIVE
    RESEARCH (DTFH61-08-R-00011)

2
Acknowledgements
Sponsor and study participants FHWA Office of
Environment and Planning and six collaborating
transportation planning organizations ____________
__________________________________________________
__________________________________________________
Other research team members Yang Liu, Yucong
Hu _______________________________________________
__________________________________________________
_______________ Volunteers Jeffrey Casello,
Birat Pandey, Robert Tung ________________________
__________________________________________________
______________________________________ Software
vendors Caliper, Citilabs, INRO,
PTV ______________________________________________
__________________________________________________
________________ The authors alone are
responsible for the content and views expressed
in this presentation.
3
Travel forecasting challenges
  • Influence decisions, be useful!
  • Data, data and data, particularly travel times.
  • Model choice and model assumptions.
  • Calibration and validation.
  • Computational quality challenges
  • Sufficient precision (convergence) for scenario
    comparisons
  • Reasonable and consistent route flows.

4
Comparing total link flows and link costs between
FW (10 iterations) and TAPAS for the Chicago
regional network
5
Distribution of deviations in link flowsfor the
Chicago regional network
6
Distribution of deviations in link flowsfor the
Chicago regional network
7
Solutions evaluated in this study
Six solutions for Chicago are evaluated in this
study, produced by six tools CUBE, EMME-LA,
TransCAD-FW, TransCAD-OUE, VISUM (RB), and
TAPAS. Commercial tools that are not evaluated
are EMME-PG (RB) ESTRAUS (FW, OB) SATURN
(FW, OB, RB) VISUM-Lohse (FW), VISUM-LUCE
(OB).
8
Precision of evaluated solutions
  • All evaluated solutions are converged to 1E-4.
  • A very precise solution (1e-12) produced by
    TAPAS is used as a reference, when needed.
  • Definitions of convergence are not identical,
    but are within the same order of magnitude.
  • Convergence of 1e-4 is chosen because
  • Scenario comparisons require at least this
  • level of convergence.
  • All commercial tools can achieve it.
  • This is the current best practice.

9
Precision of total link flows
Comparison of total link flows to precise link
flows
10
Distribution of residuals of total link flow
11
Comparison of convergence of research tools for
the Chicago regional network
12
Precision of solutions used in this study
  • It is important to separate the discussion of
    precision of specific solutions from the
    discussion of precision of methods.
  • All solutions have similar level of precision,
    with residuals less than 10 vph on the majority
    of links.
  • Proper precision comparison between methods is
    beyond the scope of the current project.
  • Precision performance of FW-type tools (CUBE,
    EMME-LA, TransCAD-FW) is very different from
    quick-precision tools (TransCAD-OUE, VISUM).

13
Multiple UE route flow solutions
A
2
100
40
40
160
4
D
1
120
60
120
B
3
14
Who needs route flows?
  • Multi-class models
  • Select Link Analysis determine the
    distribution of link flows by their origins and
    destinations
  • Estimation of OD flows from link flows
  • Derivation of OD flows for a subarea of a region,
    e.g. for micro-simulation
  • License plates surveys
  • Validate model results against survey data
  • Design a survey to capture travelers at least
    twice, or as much travel as possible.

15
OD flows through North Ave. Bridge WB
Each point represents vehicle flow per hour for
one OD pair. X - reference solution (TAPAS-3057
ODs) Y - evaluated solution (RG 1e-4)
16
OD flows through North Ave. Bridge EB
Each point represents vehicle flow per hour for
one OD pair. X - reference solution (TAPAS-3,376
ODs) Y - evaluated solution (RG 1e-4)
17
OD flows through Harlem Ave. SB
Each point represents vehicle flow per hour for
one OD pair. X - reference solution (TAPAS-4,752
ODs) Y - evaluated solution (RG 1e-4)
18
OD flows through Harlem Ave. NB
Each point represents vehicle flow per hour for
one OD pair. X - reference solution (TAPAS-5,034
ODs) Y - evaluated solution (RG 1e-4)
19
How to choose a single route flow solution?
The condition of Proportionality Same proportions
apply to all travelers facing a choice between a
pair of alternative segments.
Consider the pair of segments 1,2,4 and
1,3,4. First segment proportion is
40/(40120)1/4.
20
How to choose a single route flow solution?
The condition of Proportionality Same proportions
apply to all travelers facing a choice between a
pair of alternative segments.
Consider the pair of segments 1,2,4 and
1,3,4. First segment proportion is
40/(40120)1/4.
For travelers from A to D the proportion is
25/(2575)1/4.
21
How to choose a single route flow solution?
The condition of Proportionality Same proportions
apply to all travelers facing a choice between a
pair of alternative segments.
Consider the pair of segments 1,2,4 and
1,3,4. First segment proportion is
40/(40120)1/4.
For travelers from B to D the proportion is
15/(1545)1/4.
22
The condition of proportionality
Same proportions for the two segments. Origin and
destination do not matter. Previous or subsequent
decisions do not matter.
By proportionality, flow on designated route is
200 (150/200) (160/200) (180/200) 108
23
The condition of proportionality
  • Reasons
  • Simple, reasonable, consistent, stable, and
    therefore useful.
  • Proportionality is testable.
  • Are there any other practical suggestions?

Implications The set of routes should be
consistent, meaning that any route that can be
used while keeping the same total link flows,
should be used. No route is left behind
(without a reason).
24
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25
Paired Alternative Segments near Lake Shore Drive
Each point represents vehicle flow per hour for
one OD pair. X - Segment 1 Y - Segment 2 all
solutions converged to RG 1e-4.
26
Paired Alternative Segments near Lake Shore Drive
Each point represents vehicle flow per hour for
one OD pair. X - seg. 1 flow seg. 2 flow Y
Log (seg. 1 flow / seg. 2 flow)
27
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28
Paired Alternative Segments near North Ave.
Bridge
Each point represents vehicle flow per hour for
one OD pair. X - Segment 1 Y - Segment 2 all
solutions converged to RG 1e-4.
29
Paired Alternative Segments near North Ave.
Bridge
Each point represents vehicle flow per hour for
one OD pair. X - seg. 1 flow seg. 2 flow Y
Log (seg. 1 flow / seg. 2 flow)
30
Effect of convergence on consistency in TAPAS
Each point represents vehicle flow per hour for
one OD pair. X - seg. 1 flow seg. 2 flow Y
Log (seg. 1 flow / seg. 2 flow)
31
Conclusions FW-type methods
  • Solutions tend to satisfy the condition of
    proportionality, although deviations do occur.
  • Route set consistency is problematic due to small
    flows on non-optimal routes.
  • To achieve the precision needed for scenario
    comparisons (1E-4 or better), hundreds of
    iterations may be necessary, implying relatively
    long computation times. 

32
Commercial quick precision methods
  • Available in VISUM and TransCAD soon in EMME and
    CUBE
  • Important for scenario comparisons of total link
    flows
  • Do not satisfy proportionality and route
    consistency, which could be problematic in select
    link and similar analyses. 

33
Research progress
  • A new method, TAPAS, has been developed
  • Quick-precision assignment
  • Reasonably consistent set of routes, mainly at
    higher levels of convergence
  • Satisfaction of the condition of proportionality
  • Functionality is limited to research purposes
  • Additional experiments are on-going

34
Summary
  • Route flows are used often in practical
    applications, at various levels of aggregation.
  • Results of select link and similar analyses are
    quite different from software to software.
  • The set of routes should be consistent No
    route is left behind.
  • The assumption of proportionality ensures unique,
    consistent and stable route flows.

35
Software vendor reactions
  • Quick precision is more important than
    proportionality. Select flows are more meaningful
    at aggregate levels e.g., flow through a
    selected link on other nearby links, rather than
    by OD. (PTV)
  • Lack of proportionality for a tiny amount of
    traffic is insignificant. (Citilabs)
  • Proportionality is a potentially useful mechanism
    for rendering path flows unique applications for
    multi-class assignments as well as behavioral or
    empirical validation would lend it credibility.
    (INRO)

36
Discussion What makes a model useful?
  • Proper sensitivity to policy decisions
  • Reasonably accurate (i.e. realistic) predictions
  • Ability to obtain needed data for inputs,
    as well as for calibration and validation
  • Stability, repeatability, and consistency
  • Computational efficiency
  • Insights, understanding and accessibility
  • Convincing

37
Slide Notes
38
  • Slide 1
  • This research is about route flows in the static
    deterministic UE model. The research is funded by
    FHWA. It began in September 2008, and is
    scheduled for one year. The research is conducted
    by Marco Nie, David Boyce, and Hillel Bar-Gera.
  • Slide 2
  • Our purpose in this research is to support
    decisions about future improvements to travel
    forecasting practices. I am glad to say that the
    software vendors, who are important leaders of
    progress in this field, took a similar point of
    view. They offered us help in various ways,
    including many useful and productive comments,
    which we highly appreciate.
  • Of course, this does not mean that they
    necessarily agree with the content of this
    presentation.
  • We also want to acknowledge the contribution of
    several people that worked very hard with us to
    prepare the results presented here
  • Yang Liu and Yucong Hu, Northwestern University
  • Jeffrey Casello, Assistant Professor of Planning
    and Civil Engineering, University of Waterloo,
    Ontario
  • Birat Pandey, Senior Engineer, PBSJ, Austin,
    Texas
  • Robert S. Tung, RST International, Inc.

39
  • Slide 3
  • The main focus of this research is finding route
    flows, which is a computational challenge. We
    realize that you, as travel forecasting
    practitioners, devote most of your time and
    efforts to address other important challenges.
    Among the many difficult decisions you need to
    make, you need to choose which assignment method
    to use and for how long to let it run. This is
    why practitioners should be aware of assignment
    computational challenges.
  • The main computational challenges in the static,
    deterministic, user equilibrium (UE) model are
    precision and route flows. In some ways these two
    issues are quite intertwined, while in other ways
    they are completely orthogonal.
  • In particular, as far as we know, not much has
    been done in practice regarding route flows. On
    the other hand, there has been a remarkable
    change, almost a revolution, regarding precision
    over the last five years or so.
  • From our point of view, when we asked
    practitioners five years ago how many iterations
    they use, the answers were 10, or 20, or
    sometimes 5. If we suggested that more iterations
    might be helpful, the response was that this
    would be a complete waste of computer time.
  • This presentation starts with evaluation of the
    precision of a solution obtained by the FW
    algorithm in 10 iterations. During the last year
    we showed this evaluation to several
    practitioners, and they immediately jumped and
    said that 10 FW iterations do not provide
    sufficient precision for any analysis.
  • We think that in order to put in context the
    issue of route flows, it should be discussed
    together with precision. This is why nearly half
    of this presentation will be devoted to
    precision, and only then we will discuss route
    flows.

40
  • Slide 4
  • This is a comparison of a solution obtained by
    the FW algorithm in 10 iterations with a very
    precise solution obtained by TAPAS, which is
    converged to a Relative Gap of 1e-12.
  • In theory, total link flows and link costs are
    uniquely determined by a UE assignment. Indeed we
    see a good match between the link flow results,
    but it is not perfect the link cost results are
    more problematic.
  • Slide 5
  • We can examine the comparison under the
    microscope by considering the distribution of
    the differences between the two solutions. Notice
    that the difference in flow on the horizontal
    axis is in log scale. We see that a difference of
    10vph or more, which is not trivial, occurs for
    40 of the links. In many applications this
    precision is not enough, so more iterations are
    needed.
  • Slide 6
  • As the number of iterations increases, the
    precision increases, and the differences become
    smaller, as expected.
  • The needed level of precision depends on the
    application. One way to choose is to pick a
    threshold and choose a solution with sufficiently
    small tail beyond that threshold. If the
    threshold is 10 vph, then 10-iterations solution
    is clearly not good enough, but 1000-iterations
    solution probably is.
  • Slide 7
  • FW The Frank-Wolfe or Linear Approximation (LA)
    method
  • RB route-based method
  • OB origin-based method
  • Slide 9
  • As you can see, the match in total link flows,
    with the reference TAPAS solution (1e-12), is
    quite good in all six evaluated solutions.

41
  • Slide 8
  • The level of convergence is defined in term of
    the Relative Gap (RG).
  • Slide 9
  • As you can see, the match in total link flows,
    with the reference TAPAS solution (RG 1E-12),
    is quite good in all six evaluated solutions.
  • Slide 10
  • Examination of the differences in total link
    flows from the reference solution shows that all
    six solutions are fairly precise, with only a
    small tail of differences above 10 vph. This
    evaluation gives us the confidence that the
    conversion of inputs to all the software was done
    properly, which is not a trivial thing, and that
    the subsequent comparison of select link analyses
    results are valid.
  • According to this figure the precision of all six
    solutions is in the same order of magnitude. This
    does not mean that the methods have similar
    precision performance, because in order to
    compare methods we need to consider CPU time.
    Performing such a comparison between commercial
    software in a proper manner is far beyond the
    scope of this project. To give you an idea about
    the possible differences between methods we show
    here a comparison of convergence vs. CPU time for
    several research tools.
  • Slide 11
  • We can see here that modest levels of precision
    can be obtained fairly quickly by several
    different methods, including FW. When higher
    precision is needed, the computation time for FW
    increases dramatically, while other methods can
    achieve high precision fairly quickly. We refer
    to such methods as quick-precision methods.
  • Slide 12
  • To summarize our discussion about precision, here
    are the main conclusions.

42
  • Slide 12
  • To summarize our discussion about precision, here
    are the main conclusions.
  • Slide 13
  • It is quite well known that under the UE
    assumption route flows are not unique. Here is a
    simple example to explain why. Suppose that the
    total link flows indicated here represent perfect
    UE solution, for which the two segments from 1 to
    4 have exactly the same cost. If we switch one
    vehicle from A that uses the segment through 2
    with a vehicle from B that uses the segment
    through 3 the total link flows remain the same,
    so link costs remain the same and the perfect
    equilibrium situation also remains. In this table
    we can see 3 different route flow solutions and
    all of them correspond exactly to the same total
    link flows shown above.
  • Slide 14
  • In many practical applications, for example in
    most cost-benefit analyses, we are interested
    only in the full aggregation of route flows to
    total link flows. It is quite rare to find
    practical application where fully disaggregate
    route flows are needed. But there are quite a few
    applications where various different intermediate
    levels of aggregation are needed. A few of them
    are listed here. The important point is that
    different route flow solutions may lead to
    different answers in each of these partially
    aggregated analyses.
  • Slide 15
  • One of the most typical partially aggregated
    analyses is select link analysis. In this
    analysis we want to know the breakdown of a flow
    on a single link by OD pair. We can see here a
    comparison for one link in the Chicago network
    between the six evaluated solutions and the
    reference solution. OD flows on both axes are in
    log scale. Points along the axes represent values
    below 1E-4, including zeros. On the left you see
    the three FW-type methods, and on the right you
    see the quick-precision methods.

43
  • Slide 15 (continued)
  • If we compare the number of ODs identified by
    the various solutions, these numbers are quite
    different from each other. (In the reference
    solution there are 3,057 ODs that use this
    link.) So clearly the sets of ODs using this
    link are quite different in all the solutions.
  • If we focus on the comparison of OD flows through
    this link, and particularly the larger flows,
    evaluated solutions from the three FW-type
    methods as well as from TransCAD OUE and TAPAS
    are quite similar to the reference solution,
    while the Visum solution is slightly different.
  • Slide 16
  • Considering the same link in the other direction
    we see that a match with the FW type methods and
    a mismatch with the quick-precision methods. (In
    the reference solution there are 3376 ODs that
    use this link.)
  • Slide 17
  • For a completely different link on Harlem Ave. we
    get fairly similar patterns. (In the reference
    solution there are 4752 ODs that use this link.)
  • Slide 18
  • Considering the same link on Harlem Ave. in the
    opposite direction we find a mismatch with all
    the methods. (In the reference solution there are
    5034 ODs that use this link.)
  • This small sample of 4 links out of 40,000 was
    chosen fairly arbitrarily, and is not necessarily
    statistically representative. Even so, it is
    enough to conclude that differences between
    solutions at the select link analysis level do
    occur.

44
  • Slides 19-22
  • It would be useful to find a way to choose one
    specific solution out of all the many options.
  • One way to do that is by the condition of
    proportionality, which is explained in these four
    slides.
  • Slide 23
  • The main reasons to adopt proportionality are 1)
    a reasonable condition that is easy to
    understand, implying consistent treatment which
    may be important when equity issues are present,
    and 2) provision of stable solutions with respect
    to model inputs. All of these properties make the
    resulting model quite useful.
  • As we will see soon, it is possible to test
    whether any particular method satisfies
    proportionality or not.
  • And the only other existing alternative is to
    make a completely arbitrary choice.
  • An important implication of proportionality is
    that any route that can be used under the UE
    condition, should be used. For example, in the
    previous slide there are 8 routes under
    proportionality all of them are used. So a
    precondition to satisfying proportionality is to
    make sure that no route is left behind, unless
    of course it is not a minimum cost route. We
    refer to this property of the set of routes as
    consistency.
  • Slide 24
  • The assumption of proportionality is based on
    pairs of alternative segments. In the Chicago
    model there are 5000 basic pairs of alternative
    segments, which can be used to construct all
    other pairs of alternative segments. Here is one
    of them.

45
  • Slide 25
  • In each evaluated solution we found the breakdown
    of the flow on the two segments by OD. So each
    point here represents a single OD, and the
    horizontal and vertical axes represent the flows
    on segments 1 and 2 respectively. If the same
    proportions apply to all OD pairs, all the points
    should fall on a straight line (with a slope of
    45 degrees). Both axes are in log scale. Points
    along the axes represent values below 1E-4,
    including zeros.
  • A fairly straight line is observed for all
    FW-type solutions, especially for higher flows,
    as well as the evaluated TAPAS solution (RG
    1E-4).
  • For TransCAD OUE we see three main lines, each
    line corresponds to a different origin. This
    means that within each origin proportionality is
    maintained, but between origins proportions are
    not the same. The Visum solution in this case is
    quite extreme, where only one OD pair uses both
    segments.
  • Slide 26
  • Another way to look at the same data is shown
    here, where the horizontal axis shows the sum of
    flow on both segments in log scale, and the
    vertical axis shows the log of the flow ratio.
    Under proportionality the flow ratio should be
    constant, so the log of the flow ratio should be
    constant, so all OD pairs should be on a
    horizontal line. This is pretty much the case for
    TAPAS. It is more or less the case in the FW-type
    solutions for the higher flow values.
  • For the VISUM solution most OD pairs have all
    their flow either on segment 1, with log ratio of
    infinity, or on segment 2, with log ratio of
    minus infinity. So clearly proportionality does
    not hold. In the TransCAD solution we see a group
    of ODs that use only segment 1, and three other
    groups corresponding to three origins, each
    having its own ratio.

46
  • Slide 27
  • Here is another pair of alternative segments we
    examined.
  • Slide 28
  • Again we see linear lines for all FW-type
    methods, but not for the three quick-precision
    methods, including the evaluated TAPAS solution
    (1E-4).
  • Slide 29
  • Using the log ratio plots further enhance the
    same conclusions regarding FW type solutions. All
    three quick-precision methods suffer from
    substantial inconsistency, as many ODs use only
    one segment out of the two. When ODs use both
    segment, in the TAPAS solution the proportions
    are the same, while in the commercial
    quick-precision methods each OD has its own
    proportion.
  • The two pairs of alternative segments do not
    necessarily represent all 5000 other pairs in
    this model. They do offer an idea for what might
    be expected in other cases.
  • Slide 30
  • Consistency in TAPAS solutions improves
    considerably with convergence. Nearly perfect
    consistency is shown here at relative gap around
    1E-9, and a noticeable progress is shown already
    at relative gap around 1E-7. Notice that reaching
    these higher levels of precision does not require
    too much computation time.
  • Preliminary experiments with commercial
    quick-precision tools did not demonstrate
    improvement in consistency or proportionality at
    higher levels of precision, but additional
    exploration is needed to verify these
    observations.

47
  • Slide 33
  • At present, TAPAS exists only as a research code.
    As such its functionality is limited to research
    needs. It did not go through the extensive
    testing expected from commercial products. The
    results from TAPAS demonstrate the potential of
    incorporating proportionality into assignment
    methods. The results are not perfect, so there
    are possibilities for future improvements.
  • Slide 35
  • We agree that quick precision is more important
    than proportionality, but proportionality is also
    important.
  • We plan to study other levels of aggregation in
    the future.
  • We agree that small flow values are less
    important, the problem in practice is how to tell
    whether the flows are small and should be
    attributed to solution imprecision, or whether
    they are not so small and represent something
    else.
  • We certainly appreciate the positive reaction
    from INRO.
  • Slide 36
  • We think that the main consideration when
    choosing a model is its usefulness. The main
    criterion for usefulness is the model ability to
    support decision processes. All other criteria
    are derived from this one. Reasonable realism is
    obviously important. All else being equal, a more
    realistic model should be preferred. However,
    there are many other considerations, so in most
    cases not all else is equal. As a result, in some
    cases a more realistic model is not more useful.
    More important to our discussion, if several
    methods produce solutions that are equally
    realistic, other criteria should be considered to
    choose the most useful method. We believe that
    all other considerations, and particularly the
    ability to understand why the method chose a
    specific solution, and the ability to explain
    that to others, indicate that solutions that
    follow the proportionality condition are more
    useful. Thank you.
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