Does system complexity lessen reliability?

It's been a rough week on parts of Melbourne's train network. Power failures, equipment faults, errant prams and unruly passengers all contributed to delays and line suspensions. And during peak periods replacement buses aren't necessarily available either.

This leads one to ask whether there is a relationship between a transit system's complexity and its reliability, as measured by cancellation statistics.

First let's look at the relative complexity of buses, trams and trains.

Buses are the simplest. The driver must be rostered and present, the bus must be available and serviceable and there must be a road with flowing traffic. True, buses do get delayed when roads are blocked due to an accident. But replacement buses can be sent out from the depot (during off-peak periods, subject to driver availability) are can overtake defective buses. Also buses are self-powered, and being trackless, do not rely on points and signals to run.

Trams are a bit more complex. Rather than being self-powered they require power from an overhead. They can also derail and a stuck tram can block the line. However they do not have the sorts of complex centralised signalling systems we have with rail.

Trains are the most complex of the lot. A train is useless by itself. Not only does it need overhead power, but it also needs a track and a signal. The route a train takes is determined by the way the points are set, and this is interlocked with the signals to provide seperation between trains through a safeworking system. Signals can be manual (controlled by the city-based Metrol or suburban signal boxes) or automatic, controlled by the presence of trains, as detected by track circuitry.

Unlike trams, trains can be a mixture of stopping and express, with some lines shared with country freight and passenger trains. Similar to trams, delays can cause knock-on delays to later trains, but with magnified effects.

For a train to proceed so many more things need to be 'just right' than with trams or buses. And because any spare trains/drivers are often not where needed, one train taken out of service can result in two services not running.

What do the reliability statistics from Track Record say?

These indeed confirm that trains are cancelled more often than trams which in turn are cancelled more often than buses.

For the 2008-2009 year, 0.1 percent of buses did not run. The figure for trams is 0.3 percent. 1.3 percent metropolitan trains did not run. Regional trains were cancelled 1.7 percent of the time, though replacement coaches are more commonly run for country services. Note that these are overall system-wide figures; performance varies by time of day and line group.

Longer-term, trams always ran more of their timetabled services than trains, with the difference widening from small to large as train performance declined since its 2000-2003 peak.

Trains however come into their own when it comes to on-time running. Once a train runs you are more likely to arrive on time than if you took a tram. This is because they have their own right of way, unlike trams and buses, which mostly operate in mixed traffic.

The cancellation (but not punctuality) figures do seem to confirm that the more complex systems have signifantly more difficulties than the simpler modes. Metro trams versus buses is a 3:1 difference, while metro trains verus buses is a 13:1 difference.

However the above by itself does not constitute evidence that there is a causal relationship between complexity and (un)reliability.

It is possible to conceive of a situation where a more complex system comprising of three reliable processes produces better outcomes than a simpler one with one less reliable process.

As an example, supposing the simple process required only one thing to work properly, and this happened 90 percent of the time. A more complex system might require three sequential processes to happen. However the probability of each working was 99 percent.

In this case despite its greater complexity the second system was more reliable; its failure rate was near enough to 3% versus 10% for the simpler one-stage system. Its higher reliability appears to be because each process was more reliable and this contributed to overall better system performance. But add a lot of extra steps (each at 99 percent reliability) to the second system and the overall result could deteriorate to be worse than 90 percent. The solution is to either to simplify the process (fewer steps to go wrong) or improve the reliability of each process to say 99.9 percent (ie reducing failure rates to one-tenth the previous level).

Nevertheless research in other fields eg Alexandrov's paper do find such increasing system complexity does risk reliability. While he writes about computer systems, his conclusion could well hold true for transit systems (noting that computer systems are involved here too).

This seems to support the idea that instead of a massive interconnected system, high-reliabity railways should operate as several independent lines or sectors, each with their own tracks and points. Problems are thus isolated rather than risk bringing down the whole network. Crucially, connectedness must still be provided in the eyes of the passenger, and this requires very careful station and interchange design due to the possible increased need to transfer.