31 July 2010

If We Had Four Billion Dollars...

The recent Executive / Administrative Committee meeting featured an interesting memo regarding the application for another $2.3 billion of HSR federal funding to be distributed nationwide. Last time around, the CHSRA bagged $1.85 billion out of $8 billion of ARRA stimulus funding distributed nationwide. The additional funding, if CHSRA continues to bat .231, is on the order of $530 million.

The memo examines various scenarios where ARRA funding and Prop 1A bonds, of which a total of $3.3 billion is claimed to be available, are combined with new federal funding to reach a threshold of "independent utility" for one of the many segments of the California high-speed rail project.

If the San Francisco to San Jose segment were chosen as the initial recipient of this funding, then nearly $4 billion would become available for construction, still quite short of what will ultimately be necessary. The hypothetical question examined in the memo is how this money would be spent.

Salient points:
  • the CHSRA is starting to realize that they can't use a "Big Bang" approach where everything is constructed at once. For the first time, there is talk of phasing and a "building block" approach within the peninsula segment.
  • phasing means construction would start first on the ~26 mile stretch between San Francisco and Redwood City, avoiding the controversy in PAMPA (Palo Alto - Menlo Park - Atherton).
  • $4 billion would only cover elevated grade separations; trenches through Burlingame and San Mateo would not be included.
  • ERTMS is mentioned in the same breath as CBOSS, an encouraging first baby step in the right direction.
  • FRA would likely frown on using high-speed rail funds to provide "independent utility" for what is primarily a commuter rail corridor, not an intercity corridor
Of course, all this is purely hypothetical. Consider that (1) only one single segment could be started as the marquee project for California high-speed rail; (2) the high level of controversy on the peninsula makes it highly unlikely that the environmental clearance will be obtained on schedule; and (3) short-term improvements that benefit primarily Caltrain will be difficult to pass off as "independent utility" for intercity rail service. The likelihood of $4 billion suddenly hitting the peninsula is fairly close to zero.

27 July 2010

Odd Stacking

The odd stacked alternatives shown in the figure at right (ripped out of a recent technical working group presentation) make little sense, for a number of reasons that were previously discussed.

Recall that track stacking, besides entailing very intensive and profitable construction of complicated earthquake-resistant civil structures on the taxpayer's dime, is intended to reduce the right-of-way width required to build a four track corridor, presumably to appease neighbors and minimize residential property takes. A brief glance at the above drawing (which should also reinforce fears of a separate-but-equal approach that is disastrous for Caltrain) necessarily leads to ONE of the following two conclusions:
  1. The planners have lost sight of what they were trying to achieve, in effect destroying our village in order to save it. The stacked solution on the left requires "only" 87 feet of ROW width, while the one on the right requires 119 feet of ROW to make room for a Caltrain platform down in the trench. These elephantine structures, making use of enormous amounts of concrete, seem to miss the whole point of stacking: to save space. If you were to nibble back just 4 feet out of the 13 feet (thirteen!) devoted to drainage and third-party utility easements, you could simply stick all four tracks down in that trench on 15-foot centers. Dear peninsula communities: do you prefer 13 feet for drainage and utilities, and oh, by the way, a viaduct that looms 30 feet above ground level (16 feet of road vehicle clearance, 10 feet of viaduct box + rails, and 4 feet of sound wall) with another 30 feet of overhead wires towering above that? Or would you rather we cut back to 9 feet for drainage and utilities, and the viaduct disappears entirely? Let's think it over, for about a microsecond.

  2. The planners are not so subtly trying to sand-bag the stacked options to gain community buy-in for property takes. Making the stacked alternative look this bad on paper fulfills the dual goal of giving it environmental due diligence under CEQA and ensuring that public opinion will be "stacked" against it, setting it up for being "not carried forward" in a way that is impervious to future litigation. These are the lengths to which we must go to take 5 feet of somebody's back yard.
Since one would prefer to assume that planners are not stupid, and that they don't take peninsula residents for idiots, #2 seems more likely. Stay tuned for the answer: the supplementary alternatives analysis report for the peninsula high-speed rail project is scheduled to be revealed to the public on Thursday, August 5th in San Francisco.

23 July 2010

Metrics That Matter

The future of Caltrain (if it doesn't go bankrupt first) is likely to hinge on the quality of the service provided. Even if they don't ride the train, all peninsula residents can still benefit from quality train service that vacuums traffic off the road. So how exactly does one define and measure Quality?

From the point of view of a Caltrain rider, quality can be defined in terms of just four Metrics That Matter.
  1. What is the average trip time between my origin and my destination?
  2. What is the best trip time between my origin and my destination?
  3. At my origin, how long is the average waiting time between trains that go to my destination?
  4. At my origin, what is the longest waiting time between trains that go to my destination?
The first two metrics measure trip time on board the train, and the next two can be used to measure waiting time on the platform, which is just as important, and often perceived as longer than it really is. Notice that all four metrics are measured in units of time, between a specific origin and destination. These metrics don't measure operating cost. Not ease of maintenance. Not reduced emissions or noise. Not electricity or diesel. Not seats per hour. Not consist utilization. All those other metrics are important to a train operator, but riders don't understand them, and frankly don't care. Riders care primarily about time.

Figuring the Metrics

The four metrics that matter are objective measures that are reasonably straightforward to extract from a timetable. A computer can churn through a timetable to extract the metrics for every possible origin & destination pair, by making a few simple assumptions about rider behaviors as shown in the graphic at left.

For example, we can crunch the current Caltrain timetable (with 90 trains per weekday and 5 trains per peak hour), with the result shown at right. For simplicity, the graphic shows a limited sample of ten stations; simply follow the blue lines to find the intersection of the desired origin and destination, and read off the four metrics. A more complete version of this table is provided below.

Effective Trip Time

The four metrics are useful to consider separately, but ultimately we'd like to compare entire timetables to determine which timetable is better. To do this, we need to consolidate the four metrics that matter into a single "effective trip time" metric for each origin and destination pair. Thus far, the four metrics required very few assumptions and could be quantified quite objectively. As we construct an effective trip time metric, things get a bit more subjective and debatable.

The effective trip time is not the trip time experienced by any particular passenger; rather, it is a single figure of merit that reflects a global average of trip times taken by all passengers between a given origin and destination.

If a passenger showed up randomly, the effective trip time would simply be the average trip time plus 50% of the average wait time. However, most passengers don't show up randomly. They tend to show up before their train, and they also tend to prefer faster express trips. Therefore, we can create a reasonable measure of effective trip time as the sum of:
  • 70% of the average trip time
  • 30% of the best trip time (to favor express service)
  • 20% of the mean wait between trains (far less than the random arrival figure of 50%)
  • 15% of the maximum service gap (to penalize very large gaps between trains)
The first two terms of this sum (70% + 30%) bias the on-board portion of the trip toward express service. The last two (adding up to 35% of headway if the timetable is regularly spaced) reflect the time waiting at the station, with most but not all passengers showing up some minutes before their train. The combination of the four metrics that matter into a single effective trip time allows us to represent the current Caltrain timetable as shown in the graphic at right.

Notice that the effective trip time metric is constructed so as to punish very large service gaps. Due to the speed / frequency trade-off that Caltrain currently must contend with, many smaller stops are severely under-served during rush hour, commonly with gaps of 40 minutes or more, to clear the tracks for Baby Bullets. This is reflected in the table: for example, Palo Alto to 4th & King (the highest traffic and best-served O&D pair) is covered in 47 minutes, but the similar distance between California Ave and 22nd Street (an under-served O&D pair) effectively takes 67 minutes.

Whether or not you agree with the exact weighting used to construct the effective trip time metric, the fact remains that with some optimally chosen weights, the metric is a valid one. The numbers can easily be recalculated using different weighting assumptions.

Measuring the Quality of an Entire Timetable

Now that we have a single number that describes the effective trip time between any given O&D pair, it's time to generalize the approach to encompass all O&D pairs and to construct a single figure of merit that captures the service performance of an entire timetable. Obviously, not all O&D pairs can be served optimally: any timetable is inherently a trade-off between minimizing trip times for most riders at the cost of longer trip times for some riders. Figuring out what works best thus requires ridership weighting.

Ridership weights can be derived from actual weekday ridership data, shown as blue bars in the chart at right (these weights have been scaled such that they add up to one). Unfortunately, actual ridership is not always an exact reflection of underlying travel demand. Some stations suffer from a vicious circle; they have poor ridership in large part because they are poorly served. A good example of such a station is California Avenue in Palo Alto, where average weekday ridership was 1225 riders in 2002 before service was cut to make way for the Baby Bullet, dropping to 891 riders in 2010. This 27% drop occurred at the same time as overall ridership increased by 19%, and is unlikely to have been caused by any shifts in employment or residential patterns in the rather thriving vicinity of this station.

The most desirable approach would be to implement a full-featured ridership model, of the sort that has recently generated so much controversy for the state-wide high-speed rail project. That is unfortunately beyond our means, so we will simply use direct ridership weighting, with some filling in where service currently isn't provided (e.g. Transbay or Atherton).

The ridership weight of an O&D pair is the product of origin ridership and destination ridership (a measure of how many people travel on that O&D pair) and is shown by the light blue circles in the figure at left. Big circles mean heavy ridership, small circles mean light ridership. An optimal timetable will seek to provide the best effective trip time for O&D pairs where a big circle represents heavy ridership.

To construct a single figure of merit for an entire timetable, we first need to come up with a new, ridership-weighted service score for each O&D pair. This score, where higher is better, is the product of origin and destination ridership (the size of the blue circle), divided by effective trip time. Dividing by effective trip time means that shorter trip times increase the score for that O&D pair. Now all that's left to do is to sum up all the O&D service scores, and presto, we've got ourselves a single figure of merit. This allows us to compare timetables and, provided that we agree on the method used to construct that figure of merit, to determine objectively which of two timetables is the better one.

Any disagreements about which is the best timetable can then be reduced to disagreements over the scoring method. Planners tend to fall in love with their favorite solution, so taking the discussion away from the solution and focusing instead on the scoring method allows a dispassionate debate that is less colored by subjective preferences. Indeed, without an agreed-upon scoring framework (clearly defined metrics), comparing timetables is a subjective and useless exercise.

The Great Timetable Shoot-Out

Enough with metrics, are we ready for some fun, or rather, as much fun as can be had with timetables? Let's put three different timetables through their paces, and see how they stack up in terms of service quality.

Contestant #1: today's 90-train-per-day, 5-train-per-hour Caltrain timetable, to which we will assign a score of 100 for the purpose of comparison.
Contestant #2: the official Caltrain 2025 timetable published in Appendix K of the Preliminary Alternatives Analysis. This 162-train-per-day timetable shows 10 trains per hour in each direction at peak times, with every train performing a skip-stop pattern to keep the entire end-to-end run under 65 minutes--about ten minutes slower than today's Baby Bullet.
Contestant #3: a plain vanilla takt-timetable featuring only 6 trains per hour in each direction at peak times. Four of those trains are all-stops locals (running at regular 15-minute intervals, with a 93-minute run from Transbay to Tamien) and two of them are expresses, which take advantage of the four-track peninsula rail corridor to overtake locals. One of those overtakes occurs at the middle of the line at the Redwood City station, where the local and the express stop simultaneously on opposite sides of the same platform and exchange passengers--at this stop only, we make an exception to the 3-minute transfer rule. This cross-platform transfer extends the benefits of express service to a much wider selection of O&D pairs than today's Baby Bullet.
While Contestant #2 takes first place, Contestant #3 is competing with a huge handicap of 40% fewer trains per hour, but comes in just 1% behind in service quality. That's right: there exists a SIX train per hour time table that provides nearly the same quality of service as Caltrain's TEN train per hour timetable. How can that possibly be?

The secret weapon: the mid-line overtake.

The Trickle Down Effect

With the peninsula being reconfigured to four tracks for high-speed rail, it would be a terrible shame not to take advantage of some of that new track capacity to run better and more efficient local service, providing measurable benefits to local peninsula communities. Better service just might be the sugar coating to make the bitter pill of high-speed rail go down a little bit easier in places like Palo Alto, Atherton, Belmont, or Burlingame. Otherwise, why even bother?