Consistency in Time Weights

Modellers all learn about the different components of transit trip travel time, and the “perceived” weights that people put on them. It’s a useful insight into how transit works, and I find it’s a great exercise for testing how “useful” a new transit service is. The trouble is, after learning about weights, everyone wants to customize them – for their economic analysis, for one component of their model, etc.  And analysis quickly gets inconsistent. Here’s why I think that’s often a bad idea – and why I think the weights used in transit assignment should be applied, unchanged, for all other parts of analysis.  (And it’s not just me – the US Federal Transit Administration made this exact point in a 2006 discussion.)

The scenario

Suppose that we have a four-stage model with different transit time weights:

Walk Wait In Vehicle
Stage 3: Mode Choice 2.5 × 2.5 × 1.0 ×
Stage 4: Transit Assignment 1.5 × 1.5 × 1.0 ×

Suppose that we’re trying to analyze a new rapid transit line, intended to complement an existing bus service. Typically, rapid transit means wider stop spacing (more walking) and shorter travel times (among other things). We’ll be comparing a “no build” scenario where only the bus exists, and a “build” scenario where both bus and rapid transit are options.

We’ll focus on just one origin-destination pair.  Suppose that there are two paths from origin to destination, one using the existing local bus and one using the proposed rapid transit service. The travel times on each path are as follows:

Walk Wait In-Vehicle Weighted Total (assignment)
Bus Path 5 min 5 min 20 min 35.0 min
RT Path (rapid transit) 10 min 5 min 10 min 32.5 min

What assignment sees

In the “no build” scenario, only the Bus Path exists (local bus), and transit assignment stage says that  travel by transit takes 35.0 min.

In the “build” scenario, both the Bus Path and the RT Path are available. The transit assignment procedure will combine the two paths in some manner; assuming all-or-nothing assignment to the best path (for the sake of discussion), the RT Path will be the best option at 32.5 min.

So, in the transit assignment stage, the “build” scenario is about 2.5 min. faster for this O-D pair than the “no build” scenario because the rapid transit path is slightly faster. The longer walk time is justified by a faster in-vehicle time.

What mode choice sees

The transit assignment stage produces separate walk, wait and in-vehicle times for this O-D pair, and the individual components are fed to the mode choice stage. It then reweights the components with its own weights.

 Scenario Data from assignment Weighted Total (mode choice)
No Build Bus Path time components 45.0 min.
Build RT Path time components 47.5 min.

From the perspective of mode choice, the transit travel time is about 2.5 min. slower in the “build” scenario than the “no build” scenario.  The mode choice stage will then give this O-D pair lower transit mode share in the “build” scenario than the “no build” scenario. Travellers will abandon transit due to the addition of rapid transit.

What happened?

Before you start writing me nasty e-mails (back away from that caps lock key!) – yes, that result is clearly crazy. There’s no way that travel time would get worse.

This is all due to the mismatch of weights between assignment and mode choice. Transit assignment picked the best path between origin and destination based on the information it had available. Transit assignment is the only stage that has full information about different path options and the only stage that is in a position to trade off walk/wait/in-vehicle time.  By allowing mode choice to reweight these time components – without a full understanding of path alternatives – the story gets lost in translation.

Yes, it’s tempting to estimate the individual time weights in the mode choice model – they can be estimated statistically, while in the transit assignment stage the components have to be asserted. But it results in nonsensical behaviour.

Time weights in the real world

This is an artificial example, but I have seen versions of this happen in real life countless times. For any set of mismatched weights, you can construct examples where errors occur. It’s most obvious in an example like this where the “sign” changes, but it can just as easily get the magnitude of time savings wrong in the same manner.

In real life, these errors apply to millions of O-D pairs simultaneously.  The resulting error may well be inaccuracy (systematic bias in the errors), not just a problem of precision (errors that largely cancels out). In the example weights used above, the mode choice model would systematically understate mode shift for any “rapid transit” type projects that involve more walking and faster in-vehicle travel.

Over and out.

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