Service frequencies, trip combinations and triangular numbers

Consider a village (A) that has two round bus services a day to the next town (B).

The timetable might look like this:

Depart A 7:00am
Arrive B 7:30am
Depart B 7:30am
Arrive A 8:00am

Depart A 7:00pm
Arrive B 7:30pm
Depart B 7:30pm
Arrive A 8:00pm

Assuming that no overnight stays are desired, the number of trip choices from either place to the other is one. Thus the service is inflexible and would only cater for the minority of travellers for whom the timetable was suitable, or those who had to make the trip and had no other alternative.

Now supposing an extra trip was added so it departed A at 1:00pm, called at B at 1:30pm and returned to A at 2:00pm.

The level of service has increased by 50% (3 services instead of 2) but what has happened to the travel choices possible?

The answer is that instead of one choice only, there are now three combinations available for visitors to B from A (leave 7:00am, return 2:00pm, leave 7:00am, return 8:00pm, or leave 1:00pm, return 8:00pm).

Adding a fourth trip (at say 9:00am) increases choice dramatically. Double in fact, so that instead of three possible combinations there are now six.

Similarly five trips allows ten choices and six trips gives fifteen choices.

Maths boffins will see a pattern in this. Each extra service increases the number of combinations added by one. Hence the pattern (1), (1+2 = 3), (1+2+3 = 6), (1+2+3+4 = 10) and so on. As a point of trivia note that all answers are 'triangular numbers' due to the pattern formed (below).

O Total = 1
OO Total = 3
OOO Total = 6
OOOO Total = 10
OOOOO Total = 15

At this level a relatively small service increase (say two extra services) dramatically increases travel choices and the practicality of using public transport for many trips. This is something to bear in mind when planning services, particularly in areas that may currently get only one or two a day.

Merry Christmas, and good luck catching the bus!

If you need to catch public transport in Perth on a public holiday or over the December - January period, it's simple. With few exceptions trains and buses run Sunday timetables on public holidays, so services connect as they would on a normal Sunday.

Transperth has consistent service arrangements between trains and buses, and across all bus companies. This is a key advantage of having a consciously-planned integrated network, with co-ordinated routes and timetables.

Melbourne's system has a degree of integration through thanks to the unified Metcard ticketing and (now) Metlink signage, advertising and websites. However beneath the gloss, it is still correct that is 'the system' is still best described as a loose grouping of seperate self-contained fiefdoms, each of which do their own thing.

Since the departure of National Express, the biggest fiefdom is the partially reintegrated train network. This is followed by our world-reknowned tram system. Then there are the bus companies, large and small.

A consequence of this seperation is that timetables generally make sense from an individual operator perspective but not a network point of view. Hence it is not uncommon for buses every 20 minutes 'connecting' with trains every 15 minutes. Any connection achieved owes more to good luck than good planning. At other times duplication may cost-effectiveness and service quality may both suffer.

Never is this mess more obvious on public holidays and the Christmas-New Year period, where all combinations of service arrangements coexist.

There is a measure of conistency with on public holiday timetables for trains and buses as Saturday schedules are usually used. However differences reappear with the reduced summer weekday timetables, with trams resuming full services a week before the trains.

Buses are an even bigger dogs' breakfast. For instance, some bus routes operate on Sundays and not public holidays. Yet others run public holidays and not Sundays. To make it even more complex, some bus operators are like the trains and trams and run public holiday services to a more frequent Saturday timetable. Reduced summer timetables may apply on some routes, but again the dates for these vary. The consequence of this is that journey times may increase by up to 30 minutes or more, due to a lack of co-ordination. In extreme cases some areas may have be left with no public transport at all for several days.

The variations are so numerous that transport enthusiasts have made a sport of keeping up with it as this Bus Australia thread attests. This is full for those who enjoy that sort of thing, but is likely to be confusing for the ordinary person who wishes to get between A and B.

Given the complexity of modern travel travels and that many trips involve at least one and sometimes two connections, it makes more sense to keep the number of variations to a minimum. For instance there may only be weekday, Saturday and Sunday/Public holiday timetables. One of those timetables should apply on public holidays, with conistency across the network. This can be further simplified by having common 7-day timetables as is largely the case for trains in Perth and Melbourne's western suburbs.

Keeping variations down requires reaching a common agreement on public holiday timetables amongst all operators, be it a Saturday or Sunday service. It is also important to harmonise the dates starting and finishing date for any reduced summer timetable, so that this is uniform for all modes.

Exceptions may still be needed, on some services, but should be route rather than operator-based. A sound reason for an exception may be if a specific route has a particular travel needs. For instance routes that serve a university might operate weekday service on a public holiday if it is still a teaching day. The use of a harmonised network-wide service frequency hierachy (eg 15/30/60 minutes for all routes) can actually increase flexibility here as individual routes can be varied without throwing out major connections while minimising travel time increases.

Standardising holiday services is a small but important step towards establishing a connected transport network. To succeed, this needs to be done well in advance for staffing and leave planning reasons. Thus it is desirable that the Department and operators agree that unity is desirable and start planning now to harmonise schedules for 2006-7 and beyond.

Merry Christmas everyone, and good luck catching the bus/train/tram this festive season!

Good news on V/Line-Metlink fare integration

The changes, to come into effect next year, are described at Viclink.

Fare integration means an end to the extra cost and inconvenience of buying multiple tickets for the one journey.

It will almost eliminate the problems that visiting country bumpkins have with ticket machines on trams, as they won't need to use them for 99% of trips. Similarly local regional city buses are a mystery to nearly all tourists. Now there's incentive to use them and patronage should increase greatly if propery co-ordinated and advertised.

In any system there will be anomalies and unfinished business. For example it is desirable that private bus routes like 788 (which are integrated for 60+ but not for everyone else) are brought into line given their proximity to Melbourne and the commuter/tourist potential. Ditto for Skybus getting full Met fares (even if Zone 3).

But overall it's a major advance that will make transport cheaper and more usable to more destinations. In fact you'd need to go back to the 1980s to find a fare reform that was more significant.

Webcam of Flinders Street Station

Located at Eureka Tower, Southbank.

view images

Supply vs Demand-led service provision

The public transport version of the chicken and the egg dilemma seems to be the debate about which comes first; supply or demand.

Transport operators and governments may take the view that as existing services are not overcrowded at the moment, providing more services would produce few returns for the cost. Cost-effective patronage growth would have to come from better marketing, such as 'Travelsmart' programs or increasing charges for motorists.

Consumer and passenger groups counter by saying that people cannot use services that do not exist. Hence service increases must precede patronage growth; marketing alone isn't enough and could be counter-productive.

In anticipating future demand, others such as shopping centre builders and road engineers are also big fans of supply-side planning. Just the act of initial supply helps shape consumption. Provided the product isn't completely to the customer's disliking, the total market for it will probably be bigger than if a more timid demand-side scarcity-based approach was taken. The slogan 'build it and they will come' explains the supply-side planning assumption well.

That these debates apply in areas other than passenger transport was brought home when listening to today's Hindsight program on Radio National (downloads available). The program profiled Gordon Barton, who got his start by challenging (then) government-controlled railway monopolies on freight by forming a trucking company in the 1950s. IPEC grew and became a dominant company in its field.

In 1979 he moved to Europe and successfully established IPEC there. The Hindsight report mentioned that established transport companies waited they could fill a truck before despatching it. Hence it took many weeks to send items a few hundred kilometres. Though not pointed out, this is a good example of a demand-driven approach, ie not running a truck unless the load was sufficient.

Barton's genius was that he sent off trucks on a regular schedule, regardless of whether they were full or empty. Regular departure times allowed connections with other trucks, forming a co-ordinated network. In the early years running nearly-empty trucks around the countryside was expensive. However IPEC Europe provided a superior service, and as the loads increased, it thrived. In this example, Barton showed that his agressive supply-driven approach not only worked but took business from his more complacent rivals.

Public transport more important than coffee bars: 'Creative Class'

I'm currently reading The Flight of the Creative Class by Richard Florida. This book argues that human creativity has become a key driver of economic growth and cities that attract people of the increasingly-mobile 'creative class' will prosper in the future. Though the United States has historically been a magnet for talented migrants, Florida argues that socially tolerant cities in Canada, Australia, Asia and northern Europe are of increasing appeal to the 'creative class', with implications for the US's economic competitiveness.

One finding was that public transport, particularly fixed rail, is very important to the 'Creative Class'.

A common feature of leading creative centers around the world is efficient and heavily-trafficked subway and light-rail systems. The availability of subway and rail transportation was a key factor cited by creative people in the interviews and focus groups for The Rise of the Creative Class, trumping amenities like bike trails, coffee bars, and music venues. (page 201)

Florida mentions that though public transport exists in the US's larger and more creative cities it is sorely lacking in too many others. He goes on to say that:

On this critical dimension (public transport), large cities and regions outside the United States have another powerful advantage in the growing global competition for global talent. (ibid)

In other words, if cities are to attract world-class talent, they also need world-class public transport.

All this is consistent with research by Peter Newman & Jeff Kenworthy (Cities and Automobile Dependence, etc) which highlights the key role of public transport in enhancing a city's liveablity and prosperity.