Why Island Platforms Rule

Many words have been used to describe the myriad reasons why island platforms are best, and why express train traffic should be on the outside pair of tracks.  To amplify those points, here is a picture of what a Caltrain station could be.

In a true public transit system, trains and buses should connect seamlessly.  Anyone who has transferred between Caltrain and buses knows that the transfer is rarely direct; it usually involves a circuitous path on foot, occasionally requiring an umbrella, followed by a slow bus ride around a bunch of convoluted islands that are often configured opposite to the bus' main direction of travel.  Combine that with irregular timetables that are poorly adhered to, and what you've got is a time-wasting, ridership-killing mess of a connection.

It doesn't have to be this way, and the addition of passing tracks for the blended system is a perfect opportunity to rectify the situation with seamless transfer stations that:

• provide the shortest route from one vehicle to another
• allow each vehicle to pick up or drop off passengers without going out of its way
• provide shelter from the elements
• provide permeable access to pedestrian, bike, bus, and other road traffic
• enable coordinated clock-face schedules

Transbay Update

Early mockup of Transbay layout

Since our previous coverage of Transbay, a gigantic hole has been dug where the old Transbay Terminal used to be.  That's the part you can see.  Behind the scenes, design of the yet-to-be-funded DTX (Downtown Extension) from 4th & King to Transbay continues.  Millions have been spent to bring the design up to "30% engineering" where the details of tracks, stations, and tunnels have been sufficiently defined, down to the inch, to support construction bids and final design.

The TJPA was kind enough to share the latest overview engineering drawing (PDF file) with Friends of Caltrain.  This drawing is marked 'preliminary'.  Sadly, it does not reveal any substantive changes since 2009, and the DTX remains the same slow, 35 mph conflict-ridden mess that it was then.  Where previously it might have earned an overall grade of D, we'll give it a C-minus.  Some improvements were made around the margins, but certainly nowhere near what it could be.  Let's take a closer look.

1. Analysis of an ideal Transbay station interlocking

In the TJPA drawing, the Mission Bay station (built underground and alongside the existing 4th & King terminal) is laid out as in the diagram below.  Inbound traffic comes from MT2 (Main Track 2) and exits on MT5 or MT2, and outbound traffic comes from MT4 or MT2 and exits on MT4.

If we assume that MT4, MT2 and MT5 from a three-track tunnel that feeds the six-track Transbay Transit Center (TTC), we have 3 x 6 = 18 possible routes from the DTX tunnel to the TTC platform tracks numbered T21 through T26 from south to north.  Each of these 18 routes through the interlocking (also known as the "throat" of the station) is labeled by a single letter at the entrance and the exit. In this context, a route is one particular alignment of the tracks, established in the anticipation of a train using it to traverse the interlocking from one track to reach another.

Without getting into expensive simulations, a complex interlocking can be analyzed using a route locking table.  All table elements representing routes that lock each other (converge, diverge, or cross--i.e. conflict, and cannot be simultaneously set without risking a collision) are marked with an 'X'.

To evaluate the performance of the DTX track layout as proposed, we need to compare it to the ideal case, a track layout that cannot be improved upon because it has the fewest possible route conflicts.  If we assume that the entire facility must remain on one level (with no tracks passing over or under each other) then conflicts necessarily occur between any route that crosses over another, for example routes f and m in the diagram above, or routes that share a portion of track, such as m and n.  By inspection of the diagram, we can construct the ideal route locking table below.

Ideal route locking table for Transbay

This is the most conflict-free this interlocking design can ever be, and illustrates why stub terminals are avoided whenever possible.  234 out of 324 possible routes (72%) conflict with each other at best, so we would like a Transbay design that doesn't make an already bad situation even worse.

The route locking table can be improved (representing the pros and cons of various layouts more realistically) by weighting each route combination by the number of trains it carries, because we don't care if seldom-used routes happen to conflict.  Instead of filling each cell of route locking table with an 'X', we compute a weight that represents the relative frequency of route combination a,b as n_a * n_b / N^2, where n_a is the number of trains using route a, n_b using route b, and N the total number of trains.

The weights for the current Transbay design are computed by recalling that all Caltrain traffic is routed to/from platform tracks T25 and T26, while all HSR traffic is routed to/from platform tracks T21 through T24.  Furthermore, MT5 is intended for inbound traffic, and MT4 for outbound traffic.  MT2 is used more rarely to relieve congestion.  For the "blended" system planned for 2029, let's assume the following traffic levels in trains per hour:

• 6 inbound Caltrains, 4 of which use MT5 and 2 use MT2 to get out of the way of HSR
• 6 outbound Caltrains, all of which must use MT4 to serve Mission Bay
• 6 inbound HSR (of which 2 are dead-head moves with no passengers), using MT5
• 6 outbound HSR (again with 2 dead-head moves), 4 of which use MT4 and 2 use MT2 to overtake Caltrain at Mission Bay.

Out of those 6 x 4 = 24 movements per peak hour, ten use MT5, four use MT2, and ten use MT4.  Distributing that traffic to the corresponding platforms, we obtain the traffic-weighted route locking table for the "ideal" interlocking, subject to non-ideal platform segregation per TTC plans.  Because of this segregation between HSR and Caltrain platforms, each route is used exclusively by HSR (shaded in blue) or exclusively by Caltrain (shaded in yellow).

Ideal route locking table, weighted by traffic

The sum of each row or column is a measure of how conflict-prone each route is.  It comes as no surprise that the worst actors are routes q and r (because of high outbound Caltrain traffic) as well as e and f (because Caltrains inbound on MT5 must cut across the entire interlocking to reach their assigned platforms).  The 0.70 route locking rate means that two typical routes through the interlocking will conflict 70% of the time.

This implies the best Transbay track layout that can ever be designed will allow two trains to simultaneously move into or out of the station without regard to each other only 30% of the time.  Timetable planners and dispatchers will have their work cut out for them even on a good day.

2. Analysis of the Transbay station interlocking as designed

Inspection of the latest DTX track layout shows that it is configured like so:

The dotted lines show two curved 'emergency' crossovers, known as XO-201 and XO-202, that were provided in response to Caltrain's request for emergency operational capacity.  They will be used only when a failure occurs, and not during normal operations.  Without those crossovers, Caltrain was one failure away from total shutdown.

What immediately jumps out to a casual observer is that each pair of platform tracks (T21-22, T23-24, T25-26) necks down to a single turnout, preventing simultaneous routes from being established on both sides of the same platform.

By inspection of the DTX layout, one can draw up the traffic-weighted route locking table below.

As-designed route locking table, weighted by traffic

The cells highlighted in orange are those that differ from the ideal layout discussed previously.  The route locking rate has increased, to 0.75.  The unused emergency crossover XO-202 single-handedly accounts for 0.03, the lion's share of the increase.  The free-route rate of 0.25 is down from 0.30 in the ideal case; in other words, the probability of a conflict-free route is 17% lower than for the ideal layout.

For an already constrained and inherently conflict-prone stub terminal, it is unacceptable to make traffic jams even worse than they need to be, and yet that is precisely what the proposed DTX track layout will do.

The simplest improvement to be made is to add crossovers in the curved throat where the DTX enters the train box, to enable simultaneous and conflict free movements to/from opposite sides of the same platform.  This achieves the lowest-possible route locking rate.  The Caltrain curved crossover, XO-202 connecting tracks T25 to T24, is the most important one of these and needs to become part of normal operations.  Two more curved crossovers need to be added to allow simultaneous movements to reach HSR platforms.  The three missing crossovers are shown below.

DTX track layout with three crossovers added to achieve "ideal" route locking rate

Better yet, the Caltrain and HSR platforms should be desegregated to give dispatchers the flexibility to avoid conflicts when they do threaten to arise.  The route locking table gives the likelihood that any two randomly selected routes will conflict, but if a dispatcher can send a train to any platform or track, such conflicts can be avoided completely.

3. Another problem entirely: interlocking length

Route conflicts are one problem, but not the only problem with the DTX design.

When a train occupies the station "throat" interlocking, the duration of that occupancy must be minimized so that those conflicts that do inevitably arise (especially during off-timetable situations) are as short-lived as possible.  This conflict duration depends on the signaling system (through such parameters as route setting time, signal watching time, approach time, clearing time, and release time), and also on the time when the train physically occupies the interlocking.  This we can do something about; it is related to the length of the train, its speed, and the length of the interlocking.

As currently designed, the throat interlocking extends over a considerable distance from the TTC train box all the way down to Bryant Street. The November 2012 plans show the interlocking stretching from STA 148 to STA 173, a length of 2500 ft or 750 meters.  The speed is constrained at both ends, 35 mph at the south end and 22 mph into the train box.  We can take 29 mph or a nice round 13 m/s as a realistic average speed through the interlocking.

The physical occupancy time for one train is equal to (train length + interlocking length) divided by speed.  To this we can add 30 seconds of route clearing/setting time, and 30 seconds of approach time after the route has been set but before the train enters the interlocking.  For example, a 400 meter train moving at 13 m/s through a 750 meter interlocking will tie up a route for (400 + 750) / 13 + 30 + 30 = 148 seconds.

Using the assumed traffic levels as well as train length parameters below, we can run a simple randomized trial to quantify the relationship between throat length and the cumulative duration of route conflicts.  For each trial, the timing of train arrivals / departures is randomized over one hour (admittedly a worse assumption than reality, where conflicts are avoided by adhering to a timetable) and the total duration of conflict between routes is computed, after applying the route locking factor to account for routes that are mutually compatible.

Here are some realistic parameters for the "blended" scenario planned for 2029:

• Caltrain train length: 180 m
• HSR train length: 400 m
• Speed through interlocking: 13 m/s
• Caltrain movements: 12 per hour
• HSR movements: 12 per hour (including 4 dead-head movements to/from yard)

Effect of interlocking length
on average route conflict duration,
over the span of one hour

As can readily be observed in the graph at left, the relationship between the typical cumulative duration of conflicts and the length of the interlocking is strong, which implies that making the interlocking as short as possible will (a) facilitate the construction of a workable blended timetable by allowing closer spacing between train movements, and (b) facilitate timetable recovery after something goes wrong by reducing the cascading effect of delays in the station throat.

Note that things will get exponentially worse if traffic increases, as it may in the long-term horizon beyond the blended system.

As currently designed, the layout of the Transbay interlocking betrays little or no attempt to minimize overall length.  The resulting length of 750 meters is grossly excessive; it can and should be reduced to less than 400 meters.  A shorter layout for the interlocking would dramatically reduce route conflict duration--by fully one third compared to the current design--even if it requires the use of #10 turnouts and more turnouts and crossovers in the curved portion of the station throat, where the design speed limit is just 22 mph.  Why not take advantage of this tight speed restriction to do the dirty business of routing trains to the correct track?

This solution isn't obvious to American designers because it requires the use of non-standard track elements that may be considered exotic under typical U.S. freight rail AREMA standards, such as slip switches, curved turnouts and curved crossovers.  Indeed, this prejudice explains why the curved crossovers in the DTX design are usable only in emergencies. While designing "by the book" is always a safe option, it is unfortunately not feasible to engineer a compact throat layout for Transbay using standard turnouts.  Unlike the 100-ton coal hoppers with worn wheels anticipated by AREMA standards, this facility will only ever serve trains with very light axle loads, and maintained to the most exacting specifications.  Much of the conservatism and design margin built into AREMA standards is completely unwarranted for Transbay, and inevitably leads to a mediocre layout.

4. Conclusion

Transbay will be a special station, probably the most valuable piece of rail real estate west of the Mississippi.  As an inherently constrained stub terminal, it demands excellence in design to achieve the highest possible capacity. While the current track layout may be deemed adequate for the blended Caltrain / HSR scenario planned for 2029, the twin failings of unnecessary route conflicts and excessive length will rapidly reveal themselves as fatal weaknesses when traffic demand increases or minor incidents throw timetables into disarray.  Such entirely avoidable self-inflicted delays will cause excess traffic to be diverted to 4th & King, a terrible outcome for passengers as well as the economic vitality of the TTC and the city of San Francisco.  Minor changes to the DTX track layout can address these failings.

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!

CBO$$

Today another $40 million was pumped into Caltrain's CBOSS project, a unique reinvention of the wheel that is nearly certain to fail based on the past track record of similar projects in the Bay Area.

The cheerful press release contains the following gem:

The system, which costs $231 million, is fully interoperable with freight traffic using the Caltrain corridor and future High Speed Rail trains.

This one sentence could easily make one choke twice on the same pretzel.  First, the astronomical cost of more than $4 million per route mile is more than triple the world standard for similar projects.  Second, the claim of interoperability with HSR is an outright lie according to Caltrain's own contracting documents.

Interoperability, in this context, means spending additional millions to outfit each and every high-speed train in California (in a fleet that will dwarf Caltrain's) with CBOSS on-board signaling equipment.  Under this definition, CBOSS is no more interoperable with future "High Speed Rail trains" than it is interoperable with the red rail-cycle pictured above.

HSR and Grade Crossings

The Palo Alto Daily Post, bastion of journalistic integrity, has on several occasions reported as fact that the blended HSR system on the peninsula would require 100% grade separation in order to share tracks with Caltrain, resulting in dozens of seized residential properties.

Not so.

When sharing tracks with other trains, high-speed trains can and do use grade crossings on a daily basis, with all their attendant risks.  Examples of this practice abound in Europe, where new HSR networks have been patched into existing rail networks.  High-speed trains are limited to the same speeds as other trains when using grade crossings, and are exposed to the same collision risk.  The trains are built to take it (the relevant standard is EN 15227) and have been involved in dozens if not hundreds of grade crossing accidents over the past three decades.  When a train collides with a car, damage to the train is usually only cosmetic.  But high-speed trains have also collided with trucks and farm tractors, with more dire results, but only one known passenger fatality in 1988.  A small sample of those horrors is provided at right.

On a mostly grade-separated corridor like the peninsula, new grade separations are desirable primarily because they reduce gate down-time and speed the flow of road traffic, and secondarily because they reduce the risk of collision with pedestrians, cars and trucks.  They are not inherently required to operate high-speed trains in a blended system, any more than they are required to operate Caltrain.  Suggesting otherwise amounts to baseless fear-mongering that is best confined to the editorial page.