Great Western Coffee Shop

Whoa, there! You can't just add probabilities together to get a result, you know.

Just so that we're clear, these calculations are intended to calculate the probability that you are delayed: I've assumed that this means delayed at your final destination, rather than arbitrarily delayed at some point in the journey.

With a train journey consisting of a single train, there are two possible states:

• The train is on time
• The train is late

With one journey consisting of two separate trains - and assuming that the connection is made - there are four possible states:

• Both trains on time
• First train on time, second train late
• First train late, second train on time
• Both trains late

Now for the grey area: let's assume that there's a 50% chance that a train is late (a bit like it was before Andrew Haines, say ;)) This means that each of the above will occur with a 25% probability, and makes the sums easy!

With one train the calculation is easy, there's a 50% chance you are late.

With two trains it's also easy: you get to your destination on time two times out of four, so you still have a 50% chance of being on time. It makes no difference - in absolute terms - whether you change or not.

There is a difference if you take account of the possibility of missing your connection. First, another assumption: if the first train is late, you'll miss the second 50% of the time. There are now eight possible states (I've included the probability of each occurence this time):

• Both trains on time and you make the connection - 25%
• Both trains on time and you miss the connection - 0% (you don't miss a connection when your train is on time)
• First train on time, you make the connection, second train late - 25%
• First train on time, you miss the connection, second train late - 0%
• First train late, you make the connection and the second train is on time - 12.5%
• First train late, you miss the connection and the second train is on time - 12.5% (although you will be late!)
• Both trains late but you make the connection -12.5%
• Both trains late and you miss the connection -12.5%

Now you will be on time 37.5% of the time, and late 62.5% (remember, I'm not trying to work out how late, just whether you are late).

Remember, this is based on on a worst-case scenario of:

• each train having a 50% probability of being late
• missing the connection half the time

Even on their worst days, FGW aren't that bad.

In the real world^TM, having to catch a connecting train does not double the chance of being late.

You are correct, but we need to use a better figure for the lateness (is it 1 train out of 10?). We then need to try and work out what the average connection time is, and the average lateness of a train,  to work out the probabilities of making the connection.

Does anyone know these values so we can do a more accurate calculation - as I for one would be very interested in the result. What effect does changing have on getting to your destination on time? We could then expand it with two changes etc.

Then present the mathematical findings to FGW and other companies.

I'd suggest a third state, which is becoming more and more common - especially at Birmingham New Street to help massage CrossCountry's performance figures - and that is to find your delayed through train from Newcastle>Bournemouth teminates prematurely at Brum ("Pined" is the railway jargon for this I believe!) and a substitute train left there on time for the South Coast without you on it! It's like missing a connection you never intended to make and is bloody annoying!

That just complicates things unnecessarily ;)

[note to moderator - perhaps this thread ought to be split off and given a new heading!]

Actually there's a further complication, which occasionally works in your favour.

That's where the first train is on time and the train before the second train is late, so that you make what would otherwise be an impossible connection.

An example. A couple of months ago I travelled back from Bradford Interchange to Worcester. Left Bradford 17:05. Expected to be back at Shrub Hill at 21:41.

The 17:05 from Bradford gets me into Leeds at 17:28, where I expect to wait and catch the 18:10 southbound CrossCountry. But ... the 17:10 is running 28 late and I'm able to catch it, get to New St ahead of my expected time and end up into Shrub Hill at 21:08 - some 33 minutes early.

Same thing happens in a slightly different way at Reading. Coming in from Guildford, the timetable has the usual padding on it. But the train arrives 4 early, so that an impossible connection (arrive 16:23 depart 16:23) works, and I'm back into Shrub Hill an hour early.

I think that the moral of this story, certainly as far as the previous posts are concerned, is that the statistical analysis of train reliability is not straightforward.

But the other issue is the whole business of connections. Nowadays, with many services running every hour, the timetable planners don't bother about connections.

I came back from Lincoln in April. Leaving at 17:29, the timetable had me changing at Leicester and Birmingham and got me back into Worcester at 21:41. An elapsed time of 4:12, which is pretty awful.

Out of interest, I look up in the Bradshaw reprint how long it would have taken back in 1910. I could've left at 17:35, changed at Nottingham and Derby, and been back at 22:00 - elapsed time 4:25. The average speed of the trains was lower, but the connections were well-organised - 5 minutes at Nottingham and 7 at Derby.

The 2008 timings have you going round a slow way via Leicester, with a 16-minute connection there and a 22-minute one in Birmingham.

Is this progress, I ask. 13 minutes faster per century.

I have (as suggested above) split this topi off from "Brighton to Plymouth" in th ecampaign board as it has far more general interest.  Original thread is at

http://www.firstgreatwestern.info/coffeeshop/index.php?topic=3573.0

Ok, ok, I said it probably wasn't exactly double the chance..... ;D so it's increasing the chance by 25%.... I think.... ???

Anyway, the number of times my first train has been on time and the second one late or cancelled suggests to me that in the real world, there is a higher chance of the second train being late than the first one!

Another drawback when changing is that if you do miss your connection, you could be waiting 30 minutes, 1 hour, 2 hours or even 12 hours for the next one, so changing trains can risk a much more substantial delay than a through train is likely to.

Yet another disadvantage of changing is when you reach Plymouth and find a whole HST load of passengers is expected to squeeze onto a two car DMU.  ;D

And of course there is the fact that connections are often rubbish these days, as Worcester Passenger points out. I've planned my journeys around unauthorised connections many times..... I appreciate they have to have a cutoff point, but in the real world, whether it's a 9 minute or a 10 minute connection isn't going to make any difference on most occasions. It's not as if the "authorised" connections are going to be held for you anyway.

I think you've hit the nail on the head when you say "find a whole HST load of passengers is expected to squeeze onto a two car DMU." and 
"It's not as if the "authorised" connections are going to be held for you anyway."

I believe it was John Watts MP for Slough who famously said during the privatisation debate "Connections will not be held".

My view is that wherever possible through trains should be provided between principle centres of population or "between railheads" from whence connections can be made. Perhaps as a yardstick and excepting London and South East where the network is too complicated. The aim perhaps should be that you should be able to travel between any two stations in England Wales and Scotland (not via London) with only 2 changes at Railhead 1 and Railhead 2 with the connecting journies to the railheads being as short as possible. For travel to London, all stations on a mainline should have at least one through service a day.

Implicit in this should be that connections will be held up to certain time depending on how frequent the ongoing service is.

Even with franchising and privitisation the bulk of services are still mostly based on the pre 1922 pattern of services as Worcester passenger pointed out in his post above.
Where it has changed some places have got a worse service e.g.  Melksham or you get Warminister - Great Malvern trains which might give good stock working but doesn't seem to have much point. Southampton to Birmingham via Bristol/Worcester might be a possibility.

If more through trains are instituted how long will they last? We had the Bristol Oxfords which as discussed in another post enabled people to change jobs to travel by these trains only to have them withdrawn. Not in FGW territory but the recast of services East and West of the MML has cause a lot of upset with passengers losing through trains on which they commuted to work and a change imposed with increased journey times. 

Don't forget we are also faced with the withdrawl of the Brighton Scotland XCs in December.

However to  achieve a nationwide sevice of through trains  would require a degree of planning and forecasting well beyond the capability of the D(a)fT.
 

Remember that the whole train doesn't always have to run through for a service to be direct, just a portion.  Spliting and joining trains ought to be simple nowadays with automatic couplers and you would think that the pressures to maximise rolling stock utilisation and the increasing scarsity of paths would make spliting and joining more attractive, but it is done less now than it used to be.

Splitting and joining trains works fine on the continent where it is generally very common, but of course in Britain, too often you would have one half of a service waiting around for the delayed other half to reach the joining point. And if a train is late then splits, maybe it would count as two late trains and depress the statistics.

When I first saw the little Voyagers I imagined they would be joining and splitting trains at Birmingham New St to provide a network of through services, but it's probably just as well they didn't.

Tim and bemmy are both right. Although I wonder whether auto couplers make the task easier.
See article in October Modern Railways over the mess we are in with incompatible couplers.

Splitting and joining is an excellent idea Southern Electric thrived on it for years, every half hour at places like Staines and Ascot. But bemmy is also right we would get the trains joining at the right time.

Along with loco changes we seem to lost the art of running a railway properly. It's like most things these days we seem to fall down on attention to detail or fall prey to imaginary health and safety concerns or polictical correctness.

Tale from Gerry Fiennes "I Tried to Run a Railway" Pre war LNER, Doncster Division bottom of the league for timekeeping a new manager was appointed and gradually they climbed out bottom place and up the league. When asked by God (General Manager) how he done it "Personal Supervision Sir". What he didn't say was this supervision comprised standing in the Buffet doorway on Doncaster Station with a pint in his hand just watching.

Or as Tom Peters the American management guru put it MBWA:  Mangement by Walking About.