Tuesday, March 17, 2009

Expresses versus frequency

Those who have ever sat on an evening or weekend train stopping all stations to Pakenham or Frankston have no doubt wondered whether the trip should be sped by running express services to these areas.

In Melbourne, with few exceptions, off-peak suburban trains stop at all stations. With stations almost every kilometre and a City Loop that reduces directness, this slows in-train travel speeds. In Melbourne a 40 km trip takes about an hour compared to about half that on Perth's Joondalup line (with widely spaced stations and no City Loop).

Running off-peak trains express, as is done widely in Sydney, can speed in-train travel and is worth considering here. Compared to adding peak services it's easy to do; there are few rolling stock, signalling or infrastructure constraints. All that is needed is money for more drivers, maintenance staff and services if even the skipped stations are to retain existing service frequencies.

As the diagram below shows, stopping patterns can be a choice of 1. all trains stopping all stations, 2. Local/Express - a 'local' train terminating half way along the line to service areas nearer the city and an express going the whole way but skipping the closer-in stations, or 3. a pattern where all trains go the full distance but run express on differing portions of the trip.

Apart for a few inner-suburban stations skipped on lines such as Frankston and Hurstbridge, Melbourne off-peak services generally stop all stations. The main virtue of this is that all but outer stations receive the full line frequency - ie three or four trains per hour. This compares to express-rich Sydney whose smaller stations have only two trains per hour (but larger stations get 4 or more per hour).

The two express options have their strengths and weaknesses. For us the local/express pattern seems to provide the best possible frequency with economical use of trains (as the locals can be sent back into the city to commence their next run sooner). The third pattern is only desirable where the terminus needs every single train due to its large capture area and the stations nearest to it are fairly quiet. To some extent this applies on the Frankston line, but off-peak patronage is insufficient to make it a better option than local/express running.

This brings us to the main point - the trade-off between frequency and express services. Sydney and Melbourne have handled this differently; Melbourne has gone for more stoppers and better frequency while Sydney has favoured express running but poorer frequency at less favoured stations. From a resourcing perspective it's a juggle between the two; both would be best but are unlikely to be delivered.

Which approach is best?

This is best evaluated in terms of passenger waiting time and travel time, which will be discussed in turn.

Waiting time

In considering waiting time, it's best to assume the highest standard of service, which is 'I want it now', and assumes 'turn up and go' or 'random arrival' behaviour. While there is nothing to stop someone turning up on spec to an houly train service, the other part of this is predictable travel times, which depend on frequency and reliability. In-vehicle travel time is largely dependent on express running and does not convey the full picture. End to End travel time includes in-vehicle travel time but adds access, transfer, and waiting time. This makes it a better measure more useful to service planners.

The service frequency that choice passengers start rocking up to a stop or station without a timetable will vary depending on trip length, purpose, time requirements and quality of alternative modes. A lunchtime tram in the city obviously has a different threshold to a rail service serving a commuter-belt satellite town 50 to 100 kilometres out. Somewhere in between would be suburbs in the 8 - 40km belt, which is the mainstay of the suburban rail system.

For the latter (which is the concern of this article) most in-train trip lengths would vary between about 10 and 60 minutes, with many off-peak trips in the bottom half of this range (ie up to 30 minutes). To lessen travel time variability (another concept of 'reliability' different from the usual discussion about cancellations/delays) maximum waiting times need to be a fraction of total travel times in a high-service 'turn up and go' system. I will not seek to quantify the minimum service frquency needed, suffice to say that it will likely be much nearer to 10-15 minutes than 30 minutes.

Travel time

As well as the benefit of frequency in cutting waiting time, there is a benefit of express running in cutting travel time. A suburban express train typically saves about one minute per station skipped. A 'super-express' pattern may involve removing 10 stations from a suburban train trip. In Melbourne this may be about the maximum possible without removing service from the City Loop, junction and major suburban stations while and maintaining safe train seperation.

Doing this will make the trip about 10 minutes quicker, or a 17% saving on an hour journey, which is not insignificant. However this 10 minutes is the maximum saving applying only for passengers travelling the length of the line or nearly so. Many local off-peak trips will involve no expressing and no reductions in travel time. Hence the average time saving per passenger is probably nearer to 5 minutes and could be even less.

The trade-off

The travel time savings possible by running services express can conflict with the increased waiting times of a reduced frequency service if the new expresses are merely existing services that now skip some stations. The service planner will need to compare the two in case express running ends up being counter-productive.

Average waiting time is half the service frequency. For example, for 30 minutes it's 15 minutes, 20 minutes gives 10 minutes, 15 minutes makes 7.5 minutes, 10 minutes is 5 minutes et cetera.

If an off-peak express proposal saved passengers 5 minutes (average) but resulted in a frequency drop from 15 to 30 minutes at some stations, then the value of this five minutes saved must be compared against the 7.5 minutes extra average waiting time. For those subject to that extra waiting time it does not look a good bargain.

While the 7.5 minutes extra does not apply at all stations, so should probably also be averaged down, it should be remembered that waiting minutes are perceived longer than 'in-vehicle' time, so the former could just as easily be weighted up! Plus the risk of waiting 29 minutes instead of 14 minutes if a train has just been missed is a major disadvantage of the express pattern. It is not a bad principle to design transport systems for the risk-averse who crave end-to-end reliabilty, and for them a few minutes extra moving is preferable to infrequent timetables that force longer waits, particularly in the heat, wet or cold.

The above difference is less if it's a trade-off between 15 and 20 minute headways. In this case the maximum wait is 5 minutes longer, or 2.5 minutes average. This compares with the 10 minutes saved by the express running for the maximum length trip. Those making this specific trip are probably better off with the less frequent express, though they must accept the risk of longer waits (and hence poorer reliability) if services are cancelled.


I could give many examples to compare the merits of frequency versus express running for a 'basket' of randomly timed off-peak trips of varying lengths, some with bus connections. Results will no doubt vary, but I'm confident enough to give some rules of thumb for a Melbourne-sized suburban system.

My first conclusion is that where basic off-peak suburban frequencies are inferior to 10 - 15 minutes the overall end-to-end travel time and reliability benefits of adding express running is inferior to boosting frequency. Should this be considered too harsh, the supporters of express services are reminded that the travel time savings of expresses are relatively small (even for those who go the whole way), many passengers would be disadvantaged if a trade-off involved reduced frequency and waiting time is perceived longer than in-train time.

My second conclusion is that once frequency reaches 10-15 minutes, the time savings of express running become competitive with falls in average waiting times that an even more frequent service would provide. It is at this point, particuarly for long lines where there is significant off-peak CBD-oriented travel from outer suburbs, that express running can be be recommended.

Differences between the lines

The above conclusions are not one-size-fits-all since there are some important differences between the major lines. Some have high weekend patronage but low off-peak weekday usage. Lengths vary along with the need for express services. Other have high patronage demand but lower than justified service levels, so need off-peak frequency increases before any express running.

On lines like the Frankston line, where there is low off-peak weekday patronage, but high weekend patronage, a two-tier weekend express pattern of local and express services, each running every 15 minutes, is probably ideal.

The other high patronage lines on the network have different needs. Dandenong and Ringwood are both long lines with consistently high patronage - weekday off-peak, weekend and evening. For these lines a two-tier pattern of off-peak expresses and locals such as mentioned above (but running 7 days per week) appears desirable.

Sydenham and Craigieburn are shorter so off-peak expresses offer less time savings. Both these lines' catchment areas (especially the Sydneham line, which has a huge low-income belt from Footscray to St Albans) include high off-peak train users. many of whom would be making local trips to Sunshine or Footscray. For this patronage pattern off-peak frequency is more important than express running and an improvement from 20 minutes to 15 minutes would be highly valued.

Werribee line is only included here as it is proposed for an off-peak frequency upgrade to 10 minutes later this year. While such an upgrade is commendable, there is a risk of it being squandered on a line with low off-peak patronage, a low catchment population and no significant intermediate trip generators. Such resources may be better used upgrading other lines in the west, such as Craigieburn and Sydenham, to 15 minute running.

Nevertheless being a growth area, Werribee needs some service improvement and some off-peak express running wouldn't go astray. A Sydney-style pattern of four non-loop trains per hour, with two operating direct and two via Altona may give the best 'bang for the buck', albeit with the risk of reduced services to six quiet stations (in Altona and possibly Williamstown). Although controversial, a greater-good argument for the network could readily be mounted given the high benefits elsewhere.

The remaining lines have lower off-peak patronages than those discussed above. However for other reasons, such as optimal use of capital, spreading the peaks, harmonised headways and service standards, upgrading where necessary to a Perth-style 15 minutes 'minimum standard' (with a few exceptions on 30 minutes) would aid service legibility and network utility.

1 comment:

Anonymous said...

Peter, good post. If you wanted to quantify wait times better, research indicates that the total accepted maximum trip time is proportional to total time spent at destination (A rough rule would be
max(time(trip)) ~= 2*sqrt(time(dest))).
This works relatively well whether you are flying three hours for the weekend, or traveling ten minutes to the shop.

These proportions also seem to affect the components of the trip, so people are willing to park further away if they are staying somewhere longer, willing to walk further to the station, and willing to wait longer at the station. The point being that, for people traveling by express, it is reasonable to assume that their extended traveling time translates to an extended destination time and higher tolerance for small waits. That is, you don't have to regain every minute lost on an express on the equivalent local.

I'm not sure about your saved time either. It will be a function of the spatial configuration you are applying the express to. With double track, the maximum saved time depends on the trains the express is squeezed between. If the local traisn run at 5 minute intervals, the maximum saved time might only be 3 minutes. Add passing loops and that can be extended indefinitely, but you need to hold the local trains periodically, which will impact on short trip passengers with the lowest time tolerance. With quadruple track, the express will gain more than one minute per stop, because it can (at least theoretically) run at higher speeds, saving on acceleration and braking.

Which brings up a different issue. There are 26 stops to Frankston, so a single local/express changeover (say to Cheltenham), will save significant time for anyone traveling to the CBD from outside Cheltenham, but will still take time to go all the way to Frankston, and will require some intermediate train switching for some passengers. With quadruple lines (or even a train/local bus), you can easily create several local/express combinations on the same line, (for Frankston, South Yarra/Caulfield, Caulfield/Bentleigh, Bentleigh/Southland, Southland/Mordialloc, Mordialloc/Frankston). At this point, however, the local/express and the zoned express are functionally equivalent. Both are essentially two-tiered services, one for long distance commuters, and one for short trips, separating out the two different time preferences.

The advantages of this type of system are three-fold. The short trippers, with their short wait time preference and small ped-zones can stop more frequently than they do now. The commuters will have to get to an express station, which may take longer than before if there are more frequent stops, but will save significant amounts of time on the express train (for a Frankston traveler stopping as above, I'd estimate 20-30 minutes). And country lines can share an express line without being held up by a commuter train, since they would, in general, be stopping at the express stops as well.

The difficulty with implementing this type of operation is spatial and political though, not technical. Spatial because there aren't four lines of track end to end, on any line in Melbourne, and there isn't room for four lines in many places. And political, because apart from the cost of conversion, if there isn't space for extra lines, it essentially means closing stations in exchange for improved local bus/trams.