It's the Trip Time, Stupid

Components of trip time.
Electrification only improved
time in motion. Photos by
Mliu92, Evan0512, SaarPro.

Marco Chitti recently penned a great piece about Why Speed Matters, a critique of Toronto's recently opened and glacially slow Finch West light rail. It echoes some of the themes that have infused discussions about how best to improve Caltrain, and what to focus on next. Electrification had obvious speed benefits that have now been realized, resulting in a ridership boost recently recognized by an industry group as "America's Fastest-Growing Transit Agency." But what now? As the accolades die down and the catenary fades into the scenery, will Caltrain lose its sense of purpose and fall asleep on its laurels?

Their relentless focus must remain on trip time, which comprises more than the time in motion, the component of trip time that was so remarkably improved by electrification. Trip time also includes time at rest, made up of all those station dwell times, and time waiting for the train, which depends on service frequency. The peninsula rail corridor's entire capital program should be organized around reducing trip time; instead, we see attention and funding being scattered among an incoherent set of gold-plated projects that produce no discernible trip time improvements:

• stupendously expensive grade separation projects such as Broadway in Burlingame ($615M to $889M) or Rengstorff Ave in Mountain View ($395M to $453M) masquerading as train projects are actually massive road traffic sewer expansions that provide negligible benefit to the average train passenger, especially after Caltrain recently demonstrated major reductions in cars-on-tracks incidents.
  
  
• like the White House ballroom, a grandiose remodel of the San Jose station (the "Diridon Integration Station Concept Plan") will plow under (literally!) 3 to 6 billion dollars to over-deliver on Caltrain's need for a single island platform at this not particularly remarkable train stop.

None of these shameful nine- and ten-figure megaprojects do anything to attack the components of trip time. To improve trip time, these are the projects that actually matter, in order of small to large:

1. Fixed EMU door software to reduce each station dwell time by about ten seconds (the cost rounds to zero, serving as a useful litmus test of Caltrain's faith in trip time). Reduces time at rest.
    
2. Updated EMU step design, a prerequisite for the transition to level boarding. The prototype cost is $3M and fleet-wide deployment likely less than $10M. This is currently the most important capital project at Caltrain, whether the college intern assigned to it knows this or not. Enables future reduction of time at rest.
    
3. Twenty-minute base frequency, improved from today's half-hour, when the fleet grows to 21 (reliable!) trains. The capital cost is ~$0.4B but is already sunk. This adds operating cost, but only marginally since Caltrain has high fixed costs that can be better amortized over more riders. Reduces time waiting.
    
4. Level boarding, not as a consultant-bloated megaproject where all platforms are replaced, but as a simple and incremental project using the existing platforms as foundation slab with modular, lightweight elements added to raise the height up by two steps (14 inches). This is likely < $0.5B system-wide and reduces time at rest.
    
5. The four-track hub station in Redwood City, preferably with quadruple approach tracks (for simultaneous local+express arrivals and departures) from CP Dumbarton to San Carlos. This is the only grade separation project on the corridor that has any value for trip time. This one is likely about $1B. Reduces both time at rest (for the local being overtaken, thanks to the quadruple approach tracks) and time in motion (via cross-platform transfer to/from an express).
    
6. The SF downtown extension, another dazzlingly expensive megaproject that will only be worth its cost (>$10B) if San Francisco downtown office towers fill up again, if service is extended through a new Transbay Tube to destinations eastward as part of Link21, and if the federal government ever funds big transit projects again. Compared to a two-seat ride, a direct connection reduces time in motion, time at rest, and time waiting for a transfer.

Ridership and revenue follows from trip time, another way of saying that time is money. All other capital projects are at best value-maintaining, not value-adding.

Note: Trip time forms the basis of timetable scoring in the Taktulator, with the nerdy details laid out in the formulation of a service quality metric and the posts linked therefrom. Reading this material over a decade later, it still rings just as true.

Capital Spending for Better Service

Wouldn't it be great if you could quantify the service benefit of capital improvements, to compare and prioritize them by how much better train service results?  We can, and using our handy Taktulator, we will. This service pattern evaluation tool was formulated around time-based service quality metrics. We use it to explore future improvements to the peninsula rail corridor.

Today's 2022 Timetable: 94 service points -- The current peak schedule with four diesel trains per hour features very generous padding and SF - SJ trip times ranging from 66 minutes (express) to 99 minutes (local). The less-than-100 score indicates that service quality has dropped since 2011 when there were five trains per peak hour. The Taktulator score is calibrated such that the 2011 Caltrain timetable scores exactly 100 points.

Caltrain's 2040 service vision foresees eight trains per peak hour per direction (not counting HSR). Let's start with a service frequency of 8 trains per hour-- except for the sake of exploring and quantifying the value of capital improvements, we'll start from a hypothetical case that will never happen: eight trains per hour of today's diesel service, making all local stops.

Hypothetical diesel all-stops local, 8 tph: Score = 109 service points (+16%) -- The doubling of hourly frequency improves the service score by 16%, despite each train being slower. The extra time riding an all-stops trains is more than offset by the much shorter wait time at the station. For example, maximum wait times in Belmont plummet from one hour to just 7.5 minutes. Unfortunately, this service pattern would take an unrealistic 32 trains to operate, because each train takes 94 minutes to go between SF and SJ. The hypothetical scenario still illustrates the magnitude of the effect of doubling frequency.

Add electrification: Score = 121 service points (+11%) -- Electrification is worth another +12 points relative to diesel, thanks to the shorter trip times that come from the higher acceleration capability of EMUs. Those savings accrue to a full ten minutes between SF and SJ for an all-stops local. Station dwell times are still booked at 45 seconds, a longer duration that reflects the lack of level boarding. Thanks to the faster trip times, the fleet requirement has dropped from 32 trains to 28 trains. Service speed saves money, not just on fleet size but also by increasing the hourly productivity of train crews (in terms of passenger-miles served).

Add Redwood City hub station: Score = 131 service points (+8%) -- If trains cannot pass each other, there is no room in such a frequent timetable for express service. A new four-track station at Redwood City, where express trains can overtake locals on opposite sides of the same station platform (so that passengers may transfer seamlessly between local and express) gives the best of both worlds: frequent service AND express service. For now, we'll assume this station has only two-track approaches, requiring trains to arrive and depart serially. In practice, this means every local must wait more than 5 minutes or the equivalent of two signal headways to let the express catch up before RWC and then pull ahead after RWC. The stopping patterns start to look like Caltrain's 2040 service vision.

Add Redwood City quadruple approach tracks: Score = 138 service points (+5%) -- If quadruple tracks are added approaching Redwood City from the north and south, then local and express trains can make parallel moves into and out of the hub station, removing the requirement for every local to wait there for five wasteful minutes. To unlock this benefit, the quadruple track overtake section needs to extend to one station on either side of RWC, so every local train can make productive use of those five minutes. In the Taktulator, we simulate this by having every local train stop at San Carlos and Atherton, which (despite its closure) stands in for a new Fair Oaks infill station at 5th Avenue. This suggests a hub station is about 1.7x more effective if it forms the center of a three-station quadruple track section. Having fully half your trains save five minutes is a huge service improvement!

Add level boarding: Score = 147 service points (+7%) -- Where electrification saved time in motion, level boarding saves time at rest by shaving 15 seconds of dwell time at each station, as step-free access smooths passenger boarding and alighting. Level boarding gives not only short dwell times but predictable dwell times (for example, wheelchairs don't take longer to board) so we can also tighten up the padding margin in the timetable, cut in this example from 12% to 7%. Interestingly, the end-to-end corridor times fall below a threshold that allows turning a train sooner, reducing fleet requirement from 28 to 24 trains. This isn't necessarily an effect of level boarding itself, and only illustrates that a series of small improvements can result in a discontinuous benefit when a certain threshold is reached.

Add SF Downtown Extension: Score = 250 service points (+70%) -- There are more jobs (over 100,000) located within a half mile of the Transbay Transit Center than there are jobs within a half mile of every other Caltrain station combined. This makes downtown SF a dominant node if added to the system, a fact that is reflected in our census-based weighting of available trips. No other improvement comes close.

Here is how these service improvements stack up against each other, plotted as the logarithm of the ratio of after/before scores, which gives you their relative impact. They can be constructed in a different order than imagined above, but the relative proportion of each improvement should remain approximately similar:

Bar graph of the relative service quality improvement of Caltrain capital projects

Here are some key takeaways:

1. Grade separation projects do not improve train service. Exceedingly rarely, they do prevent a train delay, something that is not captured in this analysis. On the basis of the time metrics of a typical trip, however, the service improvement of grade separations is ZERO. This should factor strongly into how many billions we are collectively willing to spend on them relative to the other capital improvements discussed here.
    
   
2. The benefits of electrification alone (without other improvements) are mediocre at best. On the basis of our time metrics, service quality is only improved by about 11% relative to an equivalent diesel scenario. Caltrain can't just finish the electrification project and call it good enough.
    
   
3. The Redwood City hub station now in the planning stages is surprisingly beneficial to service quality. While packaged and sold as a grade separation with a bonus of expanding the train station, it is hard to overstate the service quality benefit of the new hub station. Even as planned by Caltrain (with two-track approaches from the north and south) the new station produces nearly as much service improvement as the entire electrification project.
    
   
4. The Redwood City hub station as planned by Caltrain with two-track approaches is operationally ineffective. It can be juiced up to 1.7x more benefit to service quality by making it the center of a four-track overtake facility spanning just three stations: San Carlos, Redwood City and a new Fair Oaks infill station at 5th Ave. The southern portion of this four-track facility already exists today. Together with 4-track approaches, the Redwood City hub improves service quality by a greater proportion than the entire electrification project! That's why it is critical that planning for the Redwood City grade separations allow for four tracks throughout.
    
   
5. Level boarding provides over half the service quality improvement of electrification, and is likely to be a much cheaper capital investment. However, it makes sense to do it after the hub station.
    
   
6. The downtown extension in San Francisco will be a game changer for service quality. The transportation industrial complex knows this and will make us pay dearly for the DTX project. However, the additional billions for the PAX (Pennsylvania Avenue Extension, a city-desired grade separation) add absolutely nothing to service quality, and should never be allowed to be bundled with the DTX project. Every capital dollar should improve service quality.
    
   
7. The Redwood City hub station (with four tracks, not two!) is worth one fourth of the service benefit of the DTX. That means we should (a) not be shy about spending capital dollars to build it and (b) stop selling it as a grade separation, because that isn't the story here-- it should be about a new infill station, seamless transfers, and better service quality system-wide.
   

As always, the analysis provided here can be quibbled with and improved upon, and you are encouraged to "do your own research" by trying out your own service patterns in the Taktulator.

Electric Timetable Contest

The coveted Takt Cup

Timetable planning has long been a staple of this blog, with the support of rapid prototyping tools like Richard Mlynarik's excellent Taktulator, a calculator for "Taktverkehr," the German term for clockface timetabling. While it may take a few minutes to learn how to use the tool, you can easily punch in a stopping pattern into the Taktulator to get an instant score, based on well-researched quality metrics and train performance calculations described here almost a decade ago. The service quality score is normalized so that the 2011 timetable, not much different from today's, earns 100 points.

Working back from its long term service vision, Caltrain has started planning for the near term timetable change that will occur with the start of electric service. Through a process of elimination, Caltrain has settled on two candidate service patterns, each with six trains per peak hour per direction, linked below in the Taktulator. You can verify that the resulting string line diagrams match extremely closely with the last couple of slides in Caltrain's presentation.

Two Zone with Express
Score: 123.3
Fleet: 13 EMU + 7 diesel

Distributed Skip Stop
Score: 124.1
Fleet: 13 EMU + 7 diesel
This timetable has a bit of a "can't get there from here" problem.

Can YOU beat those scores with a better concept?

Of course, scores depend on the assumptions you make. If you assume that the downtown extension is built into San Francisco Transbay, that all the diesels are replaced by EMUs, that dwell times are shortened by system-wide level boarding, that operating practices are reformed to allow better punctuality with less padding of the timetable, that terminal turn times are shortened to match foreign practice, and that a cross-platform transfer station is built in Redwood City with a short four-track section from just north of San Carlos into Redwood City (most of these contemplated in Caltrain's long-term planning), then you can set a sky-high score. In fact, using the Taktulator, you can even quantify the service benefit of each separate improvement. If we're allowed to dream, surely this is one of the most efficient:

Richard's Finest
Score: 230.2
Fleet: 16 EMU

Unfortunately, for the start of electric service in 2023, we'll have to settle for a bit less. There is no service to San Francisco Transbay, there is a fleet of 19 EMUs available of which you probably don't want to operate more than 17 at any given time, dwell times are still long (for simplicity, assume 45 seconds everywhere), timetable padding is ample (assume 10%), terminal turns are slow (assume 15 minutes), and there are no expanded stations or passing tracks. So, with those assumptions input into the Taktulator, can you beat Caltrain's score and win the coveted Takt Cup?

Please post your suggested Taktulator timetables and scores (and your supporting rationale) below in the comments. In your comment, use a clickable hyperlink, in the format <a href="your-taktulator-link">your timetable title<\a>, for brevity and clarity.

Here's my first entry for this contest, to kick things off:

Silicon Valley All Stop
Score: 126.9
Fleet: 17 EMU + 4 diesel

This improves on Caltrain's concept by admitting what census data and Caltrain's presentation tells us: all of Silicon Valley has enormous ridership potential, and running skip-stop express service south of Menlo Park is harmful to overall service quality. In short, the Baby Bullet is bad. This timetable also makes better use of the EMU fleet, as was intended when additional trains were ordered, by running 5 EMU + 1 diesel per hour per direction, instead of 4 EMU + 2 diesel.

Can you beat my score subject to the assumptions above?

The Capacity Problem

These days, Caltrain is breaking a ridership record nearly every month.  Rush hour trains are running with standing-room-only crush loads, measured by Caltrain's statistics as a percentage of seating capacity.  The most recent ridership counts (tallied during the low-ridership season in the first quarter of 2016) showed several trains running at 125% of seated capacity, even after the addition of a sixth car.  Capacity, or the lack of it, is becoming a problem and Caltrain will need to do more about it before 2020.

A montage of what a Caltrain EMU
by Stadler might look like,
based on a photo by Yevgeny Gromov

The recent award of electrification contracts, including an order for sixteen new six-car EMU trains from rail vehicle manufacturer Stadler, has brought this issue to the forefront.  Caltrain's Chief Operating Officer for Rail, Michelle Bouchard, had to concede in front of the Caltrain board of directors that the new EMUs would initially have a lower seat count than the diesel trains they will replace. The argument was that increased capacity could be achieved by increasing train frequency from 5 to 6 trains per peak hour per direction, and ultimately by lengthening the EMUs from 6 cars to 8 cars, something that can be done to an EMU without loss of performance or track capacity, unlike a diesel train.

Here are some thoughts about the capacity problem.

Capacity is measured in people, not seats.  Measuring passenger load factors as a percentage of seated capacity works well for airplanes, but doesn't quite do the trick for a transportation mode where passengers routinely stand.  The design of a train, including the number of seats, the interior layout, and accommodations for standees (handrails, poles, straps, etc.) has an enormous effect on the level of comfort experienced by passengers when the car operates at "125% seated capacity."  In rail vehicle A, filled with seats and with few places to stand, 125% feels uncomfortably crowded.  In rail vehicle B, with a lower seat count and large areas where passengers can comfortably stand, 125% of seated capacity feels just fine. A better metric of the true capacity of a rail vehicle is the number of seats plus some number of standees per unit of usable floor area (typically 4 standees per square meter); with such a metric, "100% capacity" feels like the same crowding regardless of train design.

Load factors over 100% seated capacity are desirable.  While this may be news to the person crushed between two sweaty people in the vestibule of a rush hour train, sizing the train fleet so that everyone can get a seat during the peak leads to a lot of empty seats running around the system or idling in yards during off-peak hours. This can be mitigated by changing the length of train consists (like BART), but unless trains are designed for this to begin with, it can't be done in daily practice.  Caltrain's new fleet of EMUs will not be easily reconfigurable unless two EMUs are coupled together; plans for this are not evident in the train configurations discussed in the EMU Request for Proposals (6 cars and 8 cars).  With fixed train consists, there is necessarily a sweet spot where a balance is achieved between two undesirable conditions: too many bums and not enough seats during the peak, and too many seats and not enough bums off-peak.  That sweet spot will mean peak load factors should very well be over 100% when measured as a fraction of seating capacity.

LIRR M-7 rail car with 5-abreast,
by Lexcie via Wikimedia Commons

Middle seats are seats, too.  The idea of 3+2 seating (five abreast) is usually batted away with a summary argument that passengers don't like middle seats, but it undeniably results in more seating capacity.  The question is, do passengers dislike middle seats more than they dislike standing? Commuter railroads on the East Coast seem to know the answer: the Long Island Rail Road M-7, the Metro North M-8, and the SEPTA Silverliner V, (to cite only the most modern examples) all feature 3+2 seating areas.  If providing seated capacity is so important, and if load factors are going to be measured as a percentage of seated capacity, then that middle seat is worth an easy 25% additional capacity.  The Caltrain EMU contract could be changed to require 3+2 seating; Stadler has already built a 3+2 bi-level EMU for a Russian client.

Fewer seats can actually increase passenger capacity.  If Caltrain stays with 2+2 seating and a lower seat count, the additional space for standees can provide greater passenger capacity if standees are properly accommodated.  The new EMUs should be configured with poles, handrails, grab handles or straps as necessary to allow standees to travel comfortably when no seats are available.  During the platform height transition period when Caltrain will be operating dual boarding heights (two sets of doors), the number of seats will temporarily drop after seats are removed from the high door boarding vestibules.  This may increase the load factor when measured as a percentage of seated capacity, but it will actually increase passenger capacity by opening up more room for standees.  Comfort may suffer, but only temporarily.

Caltrain should find a way to buy 8 car trains right away.  If some trains are already running at 125% seated capacity in 2016 during the winter low season, they are probably running at 150% seated capacity during the summer.  Seasonal load factor will go even higher if ridership continues to increase between now and 2020 when the new EMUs arrive.  By then, even with the entire Caltrain diesel fleet at six cars per train, the system will likely be bursting at the seams.  The step change in service quality thanks to the new EMU fleet will trigger another ridership increase.  Taking into consideration those three factors (high season peak, continued ridership escalation and better EMU service), it seems likely that six-car EMUs will be overcrowded from day one.  If Caltrain can scrape together another ~$150 million (another 7% of the total tab for modernization) to exercise an option on the Stadler contract, all EMUs can enter service in 2020 as 8-car trains.  Short platforms can be dealt with by prohibiting boarding and alighting from the front or rear cars at the few stations that cannot berth a 200-meter train.  An eight-car Stadler KISS with 2+2 seating will accommodate about 750 seated passengers and another 1000 standees.

Special Provision SP01040

Buried deep in the fine print of Caltrain's electrification Request For Proposals, Volume 3, Part C, Paragraph 1.04, you will encounter Special Provision SP01040.  It defines where and when the electrification contractor will be allowed access to Caltrain's tracks to perform the work of re-signaling and electrifying the railroad.  These are known as "work windows" and are tabulated at right, as extracted from the RFP.

What follows is an analysis of the far-reaching cost and schedule implications of Special Provision SP01040.

Temporal Windows

Special Provision SP01040 imposes the following time restrictions:

• No work during weekday peak hours (6 - 10 AM and 4 - 8 PM)
• No work on Tuesdays and Wednesdays overnight, for track maintenance
• Only one track available mid-day, evenings and weekends
• Two tracks will only be available in the early morning hours Friday - Tuesday.

The limits defined in SP01040 do not include time for sending crews and equipment to or from the work site, known in construction jargon as "mobilization" and "demobilization".  An hour is eaten away from the beginning and end of each work window for this purpose.

If you want to analyze a typical work week on an hour-by-hour basis, you can define six different track availability states.  Each state has associated to it an availability factor, which you can think of as how many tracks are available to perform productive work (i.e. re-signaling or constructing the overhead contact system).

Availability State	Availability Factor
No access	0
Mob/Demob for 1 track	0
Mob/Demob for 2 tracks	0
Single track available for work	0.75
Mob/Demob for 2 tracks with 1 track already available	1
Both tracks available for work	2

During periods of mobilization or demobilization, the work window is technically open to the contractor, but no useful work can occur since crews are busy moving equipment and materials to/from the work site.  When a single track is available for work, trains passing on the other track will occasionally interrupt the work, which is why the availability factor is 0.75 rather than 1.  This typically accounts for 2 trains passing the work site every hour, causing work to cease for 15 minutes due to worker safety protocols.  When mobilizing both tracks for the contractor, these passing trains cease and the availability factor increases to 1.  The ideal situation is when both tracks are shut down and the contractor has full control of the work site.

Geographical Windows

The corridor has been divided into geographical segments, at least some of which must remain open at all times to allow northbound and southbound trains to meet and run past each other.  Each segment has a certain length (measured in route-miles).

Segment	Length (miles)
Segment #1, MP 0.3 - 8.0 (CP 4th to CP Sierra)	7.7
Segment #2, MP 8.0 - 29.1 (CP Sierra to CP Alma)	21.1
Segment #3, MP 29.1 - 44.5 (CP Alma to CP De La Cruz)	14.8
Segment #4a, MP 44.5 - 47.5 (CP De La Cruz - CP Alameda)	3.0
Segment #4b, MP 47.5 - 51.1 (CP Alameda - Tamien)	3.6
Yard Facilities (4th & King, CEMOF, San Jose)	3.0

Note that various yard facilities are assigned 3 route miles (6 track miles).

During the first phase of electrification, work may only occur in segments 2 and 4, with both tracks open in segments 1 and 3 to allow trains to meet.  Then, following an adjustment to the timetable, the second phase of the work will occur in segments 1 and 3, with both tracks open in segments 2 and 4 to allow trains to meet.  This allows Caltrain to maintain hourly service in both directions during mid-day, evening and weekend periods, single-tracking as needed around electrification work sites.

Labor Costs

Let us loosely define a unit of labor to perform electrification work on one mile of track for one hour (however many people that may actually take).  One labor unit is multiplied by the number of track miles and the number of hours to calculate a burn rate, or how much the labor will cost during any given period of time, assuming the contractor makes full use of the work windows.

We will assume that when both tracks are open, efficiencies can be realized so that only 1.5 labor units (rather than 2) are required to work on 1 route-mile (2 track-miles).  We can then assign a labor cost for each track availability state defined above:

Availability State	Hourly Labor Rate (per route mile)
No access	0
Mob/Demob for 1 track	1
Mob/Demob for 2 tracks	1.5
Single track available for work	1
Mob/Demob for 2 tracks with 1 track already available	1.5
Both tracks available for work	1.5

The work is performed by skilled union workers, whose hourly cost is not always the same.  While weekday work can be performed in shifts at no additional hourly expense, weekend work is another matter.  Depending on the union and the trade (the RFP contains hundreds of pages of union wage rate tables), weekend work can cost up to twice the rate of weekday work.  Let us assume overtime cost factors in as follows:

Day of Week	Overtime Factor
Monday - Friday	1
Saturday	1.5
Sunday	2

 

Efficiency Metrics

Now let's pull all these assumptions together and come up with three metrics.

1. The first metric is average track avaibility, measured in track-miles.  It measures how much of the railroad is available for actual productive electrification work, as opposed to shuffling workers and equipment or dodging out of the way of trains.  Average track availability is inversely proportional to how long it will take to complete the work.  If you double the amount of available track, the job can be done in half the number of weeks.  There are limits to this assumption, of course, but for sequential tasks requiring direct access to track, such as re-signaling and constructing the overhead contact system, this inverse relationship is quite reasonable.
   
   The way to compute average track availability is to assign each hour of the week a track availability state, based on the rules set out in SP01040.  Then, we multiply the availability factor (associated to that state) by the number of route-miles in that segment to calculate how many track-miles are available for work in that particular hour in that particular segment.  We can repeat this calculation for every hour of the week (24 x 7 = 168 hours) and for every segment.  Finally, we can add it all up and divide by the total number of hours in a week to figure how many miles of track are available on average.
   
   But it's not quite that simple.  Since the work is divided into two geographical phases, we must first add up the availability for segments 2 and 4 (Phase 1) and then separately add up the availability for segments 1 and 3 and the yards (Phase 2).  The average track availability for Phase 1 and Phase 2 is then averaged; this average is weighted by segment lengths to serve as a proxy for duration of each phase.
    
2. The second metric is burn rate, measured in labor units per week.  It measures the rate at which money is spent on all the work, including not just actual productive electrification work but also the shuffling of workers and equipment and the dodging out of the way of trains.  This metric assumes that the contractor makes full use of the available windows, and that no additional hourly expenses are incurred outside of the work windows (e.g. due to the work not filling a full 8-hour union shift).
   
   The way to compute burn rate is to multiply the hourly labor rate (associated to each hour's track availability state) by the number of route-miles in that segment and the overtime factor for that particular day of the week, to calculate how many labor units are expended in that particular hour in that particular segment.  Once again, we need to be careful how we add up the labor for Phases 1 and 2, using the same partial sums and weighted averages as for track availability.
    
3. The third metric is installation efficiency, measured in labor units per week per available track mile.  It measures how much of the labor is expended on actual productive electrification work, as opposed to unproductive tasks such as the shuffling of workers and equipment and the dodging out of the way of trains.  It serves a rough measure of the overall cost of tasks requiring access to the track, such as building the overhead contact system and re-signaling.  It is defined simply as burn rate divided by average track availability.  A lower number is better, indicating that a given length of track can be completed using less labor.

Four Scenarios

Armed with these metrics, we can analyze and compare a variety of electrification scenarios, including the baseline scenario specified in the RFP per Special Provision SP01040, and other scenarios of our choosing.

For the detailed calculations that support each scenario, or to explore your own scenarios and change any of the assumptions, you can download this Excel spreadsheet.

1. Baseline Scenario: Let us scrupulously apply the work window restrictions from Caltrain's RFP, per SP01040.  Phase 1 has an average track availability of 13.3 track miles, while Phase 2 comes out to 12.1 track miles.  The weighted average of the two phases yields an average track availability of 12.7 track miles.  Bearing in mind that Caltrain has over 100 track miles to be electrified, this works out to a paltry ~12% of the railroad being available, a reflection of the extremely restrictive work windows.  This does not bode well for the program schedule, since having so little of the railroad available to the contractor will draw out the duration of all activities requiring access to the tracks.
   
   The burn rate works out to 3934 labor units per week, much of which is spent on mobilization and demobilization, as well as on weekend overtime work.
   
   The installation efficiency is 309 labor units per week per track mile.  When you consider that there are only 168 hours in a week, that is a terrible score indeed.
    
2. Weekend Shutdown Scenario: One way to improve the average track availability is to completely shut down the railroad on weekends.  While this concentrates the majority of labor onto weekends when overtime rates are high, it opens up a 54-hour long period of uninterrupted access to segments 1 through 4a, while segment 4b and the yards remain partially open (to support tenant railroads and Caltrain maintenance activities).  This allows weekend work to be performed simultaneously in all segments, during both Phase 1 and Phase 2.
   
   Not surprisingly, average track availability improves considerably, with 35.3 track miles for Phase 1, 35.6 track miles for Phase 2, and a weighted average of 35.4 track miles.  By shutting down the railroad on weekends, we effectively tripled the amount of track access afforded to the contractor.
   
   The burn rate goes up quite a bit, because the entire railroad is being worked on every weekend.  The total works out to 8044 labor units per week.
   
   The installation efficiency is 227 labor units per week per track mile, a savings of 27%.
    
3. Friday + Weekend Shutdown Scenario: The next possible step is to shut down the railroad on Fridays to extend the weekend work window to three days.  This has the advantage of increasing availability during a non-overtime weekday, but it is disruptive to riders who need to commute five days a week.  Weekend access increases from 54 hours to 78 hours, again with all four segments being worked simultaneously.
   
   Average track availability increases to 45.4 track miles.  Burn rate increases to 9144 labor units per week.  Installation efficiency improves to 201 labor units per week per track mile, a savings of 35%.
    
4. Total Shutdown Scenario: The most draconian possibility is to shut down the railroad entirely.  It would be extremely disruptive for riders.  It could very well gridlock the highway 101 corridor, and in so doing, drive home the value of Caltrain for hundreds of thousands of commuters who never use Caltrain.  It would leave freight customers high and dry.  On the plus side, it would enable a coordinated construction "blitz" to complete the work at lower cost and far faster.  Electrification could even be combined with other projects such as grade separations.  Segment 4b and the yards would remain partially open (single-tracked) for the tenant railroads that use the southern end of the corridor.
   
   Average track availability would shoot up to 98.2 track miles.  Burn rate increases to 15600 labor units per week.  Installation efficiency improves to just 159 labor units per week per track mile, a savings of 49% (half off!)

Here are some graphs to summarize the results of this analysis.

You might wonder about the point of this exercise.  The RFP is closed and all the bids are in, so isn't all this overcome by events?

Word has it that the bids came in much higher than Caltrain expected, with contractors blaming the restrictive work windows for the higher cost.  Caltrain is now scrambling to scrape together even more funding than the $958M they thought electrification would cost (not including new vehicles).  Recall about half of that sum was estimated for re-signaling and building the overhead contact system, tasks where cost and schedule are strongly driven by work windows.

Shut Down This Railroad!

The right answer isn't to go digging between couch cushions for another several hundred million dollars.  The right answer is to shut down this railroad, because trying to electrify without shutting it down is like trying to change a flat tire without stopping your car.  A weekend shutdown would speed the work by a factor of nearly three, and reduce cost by about $150 million.  Shut down three days, save $200 million.  Shut everything down, save nearly $300 million.  Okay, maybe don't shut everything down, but at the very least, the weekends must go.

Formulation of a Service Quality Metric

The quantitative formulation of an overall quality metric, which can be extracted from an arbitrary timetable, is necessary to objectively answer the question “is proposed timetable A better than proposed timetable B?”

Such metrics facilitate the trade-study and optimization process of planning a new timetable, and must take into account several factors, including not just the quality of the service provided to passengers but also other factors that passengers don’t think about, such as robustness to disruption, fleet size and crew time considerations.

For today, however, we will focus exclusively on quantifying the quality of the service provided to passengers.  This particular formulation proceeds in eight reasonably simple steps, pulling together earlier information on timetable metrics and demographics.  It is only one example of how one might formulate a service quality metric, something that Caltrain has never explicitly done and could benefit greatly from doing as they share the pros and cons of various blended service plans.  This is one way to do it; what's theirs?

Step 1: Extract trip time and wait time statistics for each origin and destination pair.  By straightforward analysis of the timetable, one can figure all the possible trips between any origin station A and destination station B (including transfers) during a one-hour span during the morning peak.  One can then determine (in units of time):

1. The average trip time between A and B (Tmean_AB)
2. The fastest trip time between A and B (Tmin_AB)
3. The average wait between trips that connect A and B (Wmean_AB)
4. The longest wait between trips that connect A and B (Wmax_AB)

The first two metrics measure trip time on board the train, and the next two can be used as a proxy for measuring typical wait times on the platform.  The trip time and wait time figures are intrinsic to the timetable and can be extracted by a computer program.

Step 2: Compute an “effective” trip time from A to B by computing a weighted sum of the time components extracted above. This is where judgment calls start to be made. Taking into account the waiting times Wmean and Wmax is just as important as the actual trip times Tmin and Tmean, in order to properly account for the frequency of service. For example, the effective trip time could be defined as:

Teff_AB = (30% of Tmin_AB + 70% of Tmean_AB) + (20% of Wmean_AB + 15% of Wmax_AB)

The trip time term (30% of Tmin_AB + 70% of Tmean_AB) accounts for some trips being shortened by express service. The waiting time term (20% of Wmean_AB + 15% of Wmax_AB) properly penalizes long service gaps, but remains shorter than the waiting time incurred when the passenger shows up randomly, which is 50% of Wmean_AB.  This lower weighting reflects the fact that passengers don’t show up randomly, but usually time their arrival at origin A for a particular trip to destination B.  For example, when trips are available every 15 minutes, the waiting term works out to a quite reasonable 5 minutes. The effective trip time is a reasonably good measure of how long it will take you to get from A to B.

Step 3: Determine the “effective” speed between origin A and origin B. This is simply distance divided by time, or: V_AB = d_AB / Teff_AB where d_AB is the distance between A and B. This process is repeated for every origin and destination pair A-B, and describes not the speed of a train, but the average speed of a typical trip from A to B including waiting time, based only on the available service provided by the specific timetable being considered.

Step 4: Compute weighting by population and jobs.  This is where census data enters the calculation, as it must.  For the morning rush hour, since ridership consists primarily of people going from their home near A to their work near B, we calculate a potential ridership weight based on how many people live near A and how many people work near B.  This simply reflects that if a lot of people live near A and work near B, it is more important to provide fast service between A and B than between other station pairs where fewer people and jobs are located.

The “home weight” Whome_A of origin station A is a simple gravity sum (1/r squared law) of the residential population, taken from the 2010 census, as described previously in greater detail.  Each person is divided by the square of how far they live from station A, to reflect that people who live further away from the station are less likely to use it. To prevent over-counting people who live very close to the station (where the 1/r squared term diverges), anyone living closer than ¼ mile from the station is considered to live ¼ mile away.  The resulting weights are shown at left, in orange.

Similarly, the “work weight” Wwork_B of destination station B is a simple gravity sum of the number of jobs over $40k, again taken from census data. Each job is divided by the square of how far it is from station B, to reflect that people who work further away from the station are less likely to use it. Once again, to prevent over-counting jobs located very close to the station, any job closer than ¼ mile from the station is considered ¼ mile away.  The resulting weights are shown at right, in blue.

Step 5: Compute weighting by distance. Regardless of where people live and work, there are upper and lower limits to how far they will typically commute by rail. Extremely short trips are less likely because of the overhead of access and egress to and from the station at each end of the journey. Conversely, extremely long trips are less likely because of their sheer duration.  As it turns out, the typical rush hour trip on Caltrain turns out to be about 25 miles, or 40 km.

For our purposes, the distance weighting is constructed by drawing a curve with a peak at 40 km. This distance weight starts off at zero for a trip distance of less than 7 km (reflecting no demand for such short trips), peaks at a distance of 40 km, and decays slowly thereafter.  Converted to miles, it looks like the figure at left.  The underlying math to draw this curve is a Rayleigh distribution with a peak at (d-7) = 33, where d is the trip distance in km.

Step 6: Combine the population, jobs and distance weights to obtain a ridership potential matrix.  The ridership potential matrix R is a matrix of size N squared, where N is the number of stations.  Each element R_AB of this matrix represents the "potential" ridership (in arbitrary relative units) that can be tapped into during the morning commute from origin A to destination B.  This ridership potential matrix has an important property: it is independent of any timetable, and concisely describes the underlying demand that inherently exists out there--regardless of how or whether that demand is met by rail service.  Each element R_AB is given by the product:

R_AB = Whome_A * Wwork_B * Wdistance_AB

Note that the matrix R is not symmetric, because the number of residents and jobs near each station differs.  For example, far more people will want to commute to SF Transbay in the morning than from it, since the number of jobs within a half mile of that station is greater than all the jobs within a half mile of every other Caltrain station all the way to Gilroy combined.

Step 7: Compute the service quality matrix. The service quality matrix Q is again a matrix of size N squared, where N is the number of stations. Each element Q_AB of this matrix represents the quality of morning rush hour service from station A to station B, and is given by the following formula:

Q_AB = R_AB * V_AB

This combines R_AB, the timetable-independent ridership potential from origin A to destination B, with V_AB, the timetable-dependent effective speed from A to B.  If you have a preferred AM origin and destination (as most commuters do), then you can compare your Q_AB for various timetables to see how any given timetable will meet your own specific needs.

Step 8: Extract overall service quality scores. The service quality metrics must be bench marked against some reference, so they are simply normalized against the most current timetable.  That means today's timetable will score 100, by definition.  By adding the elements of Q over all possible origin and destination pairs, we can quantify the degree of service improvement and compute a score for the entire timetable as well as a score for each individual station. The overall timetable service quality score is S = ΣQ / Sref, i.e. the sum of all the elements of Q divided by the corresponding sum for today's timetable.

An entire timetable can now be distilled to its essence, a single service quality score.

We are now empowered to compare various timetables and understand quantitatively the pros and cons of each.  This method will tell you objectively whether timetable A provides better overall service than timetable B--and if you happened to disagree with the scoring outcome, then your argument would be with the scoring method and not any particular detail of this or that proposed timetable.  Beyond the mathematical minutiae of the rather simple scoring method presented here, the larger point is that there needs to be a defined scoring process and a framework for stakeholders to discuss what makes a good timetable.  This scoring process is absolutely essential for planning future blended service on the peninsula.  Caltrain's approach so far has been to prescribe a certain skip-stop pattern (see Tables 7 and 8) and restrict all analysis to that particular pattern, seemingly without regard to overall service quality!

Peninsula Rail Corridor Census

The U.S. Census Bureau provides an astonishing array of fine-grained statistics on population and jobs along the peninsula rail corridor.  When thinking about the future of peninsula rail service, and especially in deciding quantitatively how good a proposed timetable might be, or where stations should be placed, or how HSR should mesh with Caltrain in a 'blended' scenario, the basic consideration should be where people live and work.

Annual ridership counts provide one way of planning your timetable: simply add more service to the stops that get a lot of ridership.  This becomes a self-fulfilling prophecy with ridership patterns becoming distorted by the timetable, as observed with the Baby Bullet Effect.  Teasing apart the timetable-induced distortion from the underlying (and often untapped) ridership demand is impossible, so it is necessary to go back to the raw population and jobs data to build the full picture.  That is where the census really delivers.

Where People Live

Figure 1

The 2010 census provides the most recent snapshot of the population distribution on the peninsula, on a block-by-block basis that includes over 45,000 locations in the three Caltrain counties.  By tallying up how many people live within 1/4, 1/2, 1 and 2 miles of each Caltrain station location, you can build Figure 1.  This chart reveals where the population is densely concentrated around stations (e.g. San Mateo), or sprawled out (e.g. Sunnyvale).

Observations on the population numbers:

• The new Oakdale station long proposed by San Francisco (with little support from Caltrain) could tap into more residential population than just about any other stop along the peninsula, or even 22nd Street.
• The population density doesn't suddenly drop off at the southern end of the Caltrain-owned right of way in San Jose, where service suddenly drops off.  There are large concentrations of under-served population within a mile of the Tamien and Capitol stops, accounting for more than 3 times as many people as live within a mile of the San Jose Diridon station.
• A stop like Broadway (Burlingame) with zero weekday rail service has more people living near it than Millbrae, site of the all-important BART intermodal station.  Other stations with poor Caltrain service (San Antonio, Cal Ave, San Bruno, Burlingame, Belmont, Santa Clara) have more people living nearby than stops with the best service, such as Palo Alto.

Figure 2

To assign to each station location a single weighting factor that quantifies that station's accessibility for nearby residents, regardless of distance, one can sum up each person divided by the square of how far away they live.  This inverse-square relationship is empirical, but captures the fact that people who live far away from a station are less likely to use it; its use in ridership modeling is not unprecedented.  A 1/r law would fall off too slowly, with the same number of people using the station from 1/2 mile away as 2 miles away (assuming constant population density).  A 1/r cubed law would fall off too quickly, with only 1/16th as many riders from 2 miles away as from 1/2 mile away.  As it turns out, the precise value of the exponent--if not exactly two--doesn't really drive the relative weights that strongly.  Only one small tweak has been applied to prevent people who live very close to a station from skewing the results: anyone living closer than 1/4 mile is considered 1/4 mile away.  The resulting inverse-square population weights for each station location are shown in Figure 2.

Where People Work

Figure 3

The Census Bureau publishes extensive statistics on local employment dynamics, providing block-by-block data on the number and distribution of jobs, pay levels, and industries.  The latest data set as of this writing is from 2009 (based on geographical data from the 2000 census covering over 32,000 locations in the three Caltrain counties).  The analysis presented here is based on raw data files, but the data can also be analyzed interactively using the Census Bureau's On The Map application.   Figure 3 shows how many jobs are located within 1/4, 1/2, 1 and 2 miles of each Caltrain station location.  Only the jobs worth more than $40k a year are shown, since lower-income jobs are less likely to require commuting (only about 15% of Caltrain riders earn less than $40k, and the average household income of a weekday peak Caltrain rider is over $100k).

Observations on the jobs numbers:

• Not so surprisingly, there is a concentration of jobs in the vicinity of the future Transbay Transit Center, adjacent to the financial district.  What is more surprising is just how massive that concentration is: Transbay has more jobs within a half-mile radius (over 100,000) than all the other Caltrain stations combined, from 4th & King all the way down to Gilroy!
• Job sprawl shows up in Santa Clara and southern Palo Alto (and most of Silicon Valley, really) in the form of few jobs near stations but many jobs within a mile or two.  Mountain View, despite its status as a major Baby Bullet stop, and home of Google, is not a particularly large job center.

Figure 4

Again, assigning to each station a weighting factor that quantifies that station's accessibility to nearby jobs, we apply the same inverse square relationship to obtain the job weights for each station location shown in Figure 4.  Note that Transbay goes way off the chart.

The Ridership Potential Matrix

Since 86% of riders during the weekday peak are commuters, the distribution of population and jobs can be used to construct a relative weight for the ridership that could potentially be generated between any given origin and destination (O&D) pair.  This is the ridership potential matrix.  The eventual purpose of this matrix is to help derive a single figure of merit for timetables, on an apples-to-apples basis, for how much of the potential ridership is tapped based on the service metrics for each O&D pair.  When considering any given timetable, this weighting scheme ensures that O&D pairs that have a lot of population and jobs at each end (such as 4th & King and Palo Alto) are given more importance compared to O&D pairs with lower population and fewer jobs (such as Atherton and Bayshore).

It is important to note that this ridership potential matrix is completely independent of how each O&D pair is connected by rail service; it holds true for any timetable.  It is solely a product of census data and the geographic location of each station.  A timetable must then be designed to unlock the maximum potential ridership.

The ridership potential matrix works like this: take for example station 1 and station 2, with respective population and job weights P1, P2, J1 and J2.  The weight for morning peak trips from origin 1 to destination 2 is P1*J2 (for people living near station 1 and working near station 2).  Conversely, the weight for morning peak trips from origin 2 to destination 1 is P2*J1 (for people living near station 2 and working near station 1).  When you multiply all the population weights from Figure 2 by all the job weights from Figure 4, you get a basic ridership potential matrix.  But there's a bit more to it than just people and jobs.

Distance Considerations

Regardless of where people live and work, there are upper and lower limits to how far they will typically commute by rail.  Extremely short trips are less likely because of the overhead of access and egress to and from the station, at each end of the journey.  Conversely, extremely long trips are less likely because of their sheer duration; regional commute patterns are not just a factor of train service considered in isolation, but also driving times.  That's why we will make the assumption that the distance distribution of commutes, generally speaking, is independent of the quality of train service--and that no foreseeable rail service pattern could significantly alter it.  Good service might lead to greater market share for rail, but the underlying distance distribution will be assumed not to budge.  This allows us to apply a (timetable-independent) distance distribution to the ridership potential matrix.

Figure 5

Caltrain ridership surveys show that the average trip length on the peninsula rail corridor during the weekday peak is about 25 miles.  The distance weighting function will be modeled as a Rayleigh distribution with a value of 0 at 0 miles and a peak of 1 at 25 miles-- for no particular statistical reason other than it ends up looking about right, as shown in Figure 5.

Each element of the ridership potential matrix is now the product of three factors: the distance weight based on the distance between origin and destination; the population weight at the origin station; and the job weight at the destination station.  This simple formulation yields the morning peak values shown in Figure 6 as a bubble graph (numerical values are available as a tab-delimited text file).  The evening peak is described by the transpose of the matrix, i.e. origin and destination switch places.  The distance-weighted ridership potential matrix is now ready for use in the quantitative analysis of past, present and future timetables, a topic that will be covered in upcoming posts revisiting the topic of service metrics.

Figure 6

Figure 8

Figure 7

In the meantime, we can explore other interesting aspects of the ridership potential matrix.  For example, summing the nth row together with the nth column of the matrix allows us to build a single weighting factor for the potential ridership at each stop including both the morning and evening peaks, i.e. a measure of the ridership distribution that could exist if it were tapped with excellent service, shown in Figure 7.  These weights can then be compared to the actual Caltrain ridership realized in 2011, yielding the scatter plot in Figure 8.  This comparison provides another more fundamental way (much better than historical ridership patterns) to visualize which groupings of Caltrain stops are under-served, and is amazingly accurate considering that it was constructed without ever looking at a timetable.

Key conclusions:

• Access to Transbay would provide a step-change improvement in Caltrain service, with probable ridership gains of more than 25%.  Terminating any weekday peak train at 4th & King, as is inexplicably planned by Caltrain, is a huge mistake.  Agency turf battles with BART and the CHSRA regarding whether or how to pay for the downtown extension tunnel, and how to share platforms at Transbay, must be fought and won.
• Underlying ridership demand is not accurately reflected by realized ridership, which suffers from severe timetable distortion.  Future service planning, and in particular the timetables assumed for the ongoing 'blended' operations analysis, must be based less on realized ridership and more on fresh census data--even if not using the simplified approach described here.
• For the same reason that every Caltrain should serve Transbay (the huge concentration of jobs in San Francisco), HSR service that does not provide a one-seat ride into Transbay is a non-starter.