Arrival variability and connection success

Connectivity is the biggest determinant of public transport travel time for most trips involving a transfer. It can make all the difference between an efficient journey that’s only twice as slow as driving and one that takes three or four times as long. Missed connections also add a variability to public transport travel time that is absent from most suburban walking, cycling or driving trips. Strengthening connectivity is one of the cheapest and best ways to improve public transport.

Train arrival and departure times are logged at railway signal boxes and switched in panels at stations. Arrival times at intermediate stations can be estimated from times recorded at the nearest signal box. Such data is key to planning connectivity based on actual rather than timetabled travel times, especially if recorded over several months or more.

A cumulative graph of train arrivals can show the proportion of trains that have arrived within a specified time relative to schedule. Punctuality varies by time of day so separate graphs could exist for each half hourly or hourly block at major stations on each line along with yearly or monthly summary graphs.

The punctuality curves below are estimates only. However we know that their basic shape is about right. Arrivals more than two minutes early are rare. The time at TT +5 for each line can be obtained from Track Record and compared to the 88% performance standard. And we know the other end tends towards 100% less cancellations (normally 1 – 2 per cent).

The blue line represents an above average performer (where 90% of trains arrive on time – say on the Burnley group) while the red is a below average line (where maybe 70% of trains arrive on time – eg the Caulfield group). Long-term data would provide more robust figures unaffected by individual incidents.

Implications for bus connectivity scheduling

There is always a trade-off between waiting times and robust connections when deciding how many minutes buses should be scheduled to leave after trains are scheduled to arrive. Effective service co-ordination tends to be hardest at stations where train reliability and bus frequency are both low – the exact circumstances that make it most important to try for.

The punctuality curves show the relationship between train reliability, the probability of a connection being successful and the connection time to allow. Such data, collected for each line, would be most useful to the bus service planner who is responsible for making the abovementioned trade-offs. It would quantify popular lore as to train reliability (the extremes of ‘always on time’ and ‘never on time’ are rarely correct) and provide a better basis for bus scheduling than published train timetables.

An 80% reliability (ie a missed train – bus connection one day per week for a commuter) requires the bus to depart at least three minutes after the train arrives on the more punctual blue line and perhaps seven minutes on the less punctual red line.

For 90% reliability (ie a missed connection once a fortnight) these allowances increase to five and ten minutes respectively. At 95% reliability (ie a monthly missed connection) buses need to leave at least seven and twelve minutes after the train arrives. For suburban trips, a twelve minute connection becomes significant relative to the total journey time and a disincentive to use buses, especially during inclement weather. It is also worse than the average wait for a bus operating every 20 minutes that has not been specially co-ordinated to meet trains.

Punctuality time variability

The graph illustrate the effect of train reliability on passengers catching buses. Low train punctuality probably hurts feeder bus patronage more than train patronage due to the former’s typically lower frequencies and greater consequences of a missed connection. And where buses are scheduled to achieve more robust connections (such as aiming for 95% success) this must be paid for by longer bus waiting times most days (when trains are on or near time).

It’s a bit like insurance – pay a little now to save yourself future longer waits. The May 2011 train timetable changes that added extra running time to the underperforming Caulfield group appear to have lowered variability and probably improved connection reliability with buses.

Access time variability

Train delays aren’t the only reason for missed connections. The graphs above neglect the time to exit the station and reach the bus stop. Ideally this is under a minute where the bus stop is right at the station. Otherwise access time increases to five minutes or more where platform exits are poorly placed and/or busy roads or railways need to be crossed.

The variability of walking time is equally critical when scheduling connecting buses. High variability of access times can combine with train delays to increase overall variability and thus the difficulty of scheduling connecting buses. A greater range of possible arrival times at the bus stop either means that more connections are missed (for a given connection time allowance) or connection time needs to be lengthened (to achieve a target connection success rate). The latter lengthens waits at times when trains do arrive on time and walking conditions are favourable.

Busy unsignalised roads, roundabouts, level crossings, long-cycle traffic lights all have high access time variability. Variability for the first two is infinite, mitigated only by luck or the risk the pedestrian is willing to take.

Once traffic volumes pass a certain level, traffic lights are beneficial because they limit variability (determined by their cycle – typically 90 to 120 seconds). Traffic islands reduce variability on unsignalised roads, and may also do so on signalised roads, provided that walk cycles are sufficient to cross all lanes in both directions in the one go. No such conditions apply to simple zebra crossings, which as the highest and best form of pedestrian access, reduce access time variability to almost zero.

Active transfer management

So far I have assumed fixed train and bus timetables, with the latter’s departures timed to connect. On paper this approach would work perfectly. However in practice train delays and access impediments increase bus stop arrival time variability and reduce the success rate of scheduled connections. The remedy suggested, that of lengthening the interval between train arrivals and bus departures, improves connection reliability but slows travel on those days when trains are running to time.

One possible solution could be to schedule a tighter connection time (say 5 minutes instead of 12) but routinely hold buses if trains are delayed. This provides the fastest journey time for passengers changing from train to bus while reducing the number of missed connections.

For passengers coming off the train this is the best of both worlds. If holding buses avoids one or two ‘near misses’ per week (and their consequent 20 – 40 minute waits) the gains are large and definitely worthwhile. Note though that some bus routes intersect several train lines and holding may not be possible at all stations. Reference to train punctuality curves and surveyed passenger needs should assist bus planners decide which interchanges justify enforced connections.

One shortcoming of holding buses for trains is that it introduces variability for those bus passengers who did not come off the train. Those changing to other buses may also be affected. And holding buses for late trains reduces the efficiency and robustness of the bus network as timetables may need padding to lessen knock-on delays.

For these reasons there is a limit to the time that buses ought to wait for late trains. A holding time limit of five minutes might be reasonable for regular suburban buses; more for long-distance or less frequent routes. A longer holding time is also justifiable for the last departure for the night on each route.

The difference possible is dramatic. Even a five minute holding limit can more than halve the number of missed connections. Using the less punctual red line as an example, switching from a regularly scheduled four minute connection to a four minute connection with a five minute permissible hold time increases the proportion of successful connections from 60 to 85 per cent. Or in commuter terms, a reduction of broken connections from eight to three per month (measuring homebound trips only). Even higher gains would be possible if combined with other efforts that lessen arrival variability (eg improved train punctality and better pedestrian access).

Communication and staffing

Bus drivers will sometimes wait for running passengers from the station, thus informally achieving some of the above. But it’s a bit hit and miss. And at busy stations they may not be clear whether the train arriving is the late arrival they should be waiting for or another service. Therefore bus drivers need real-time train arrival information and a clear holding policy (which should also be well-communicated to passengers).

An even more refined method of ‘active transfer management’ for larger interchanges dominated by a single operator is to provide a despatcher (especially during afternoon peak times such as 3 to 8pm). They could be an experienced bus company employees equipped with a microphone to inform drivers and passengers of any delays and where buses need to be held. Use could also be made of web and phone applications to provide alerts to passengers still at work, on the train or waiting at stops away from the interchange.

While the staffing overheads for (say) twenty major interchanges would need to be considered the likely gains in improved travel times would probably be a greater overall passenger benefit than other possible staffing initiatives such as a similar number of tram conductors or more staffed stations.