This is just needlessly complicated. In your own example your 3tph has to be bent creating a 25-minute gap. When you mix a 30-minute cycle with a 20-minute cycle on a common section of railway, managing speed differential becomes nigh-on impossible, and you end up pathing out limited stop services, and your overall service interval becomes a mess. Such timetables rarely perform well.
Outside of Haslemere or Eastleigh don't need 6tph. There's no point in providing a Southampton via Andover service - London passengers aren't going to use that service beyond Salisbury - you'll be running a 10-car train carrying fresh air. Big trains carrying few passengers on cheap tickets = losses = subsidies.
With Crossrail 2, the 'first stop Surbiton' trains can be routed via the existing slow lines. You can run a peak pattern of 6tph Guildford via Cobham and 6tph Surbiton then all stops to Woking (need a Woking turnback + flyover solution).
With 24+ tph to play for the fast line peak pattern can be something like (all services first stop Woking or even some non-stop Woking)
- 6tph Portsmouth Direct Line (of which 2tph to Haslemere only)
- 6tph via Winchester
- 4tph via Andover
- 2tph Alton
- 6tph Woking then all stations to Basingstoke
Sorry service 3/3 should have read as xx:45, as whilst the indirect xx:40 did give a 25 minute gap after it, it also gave a 15 minute gap before it. Ah of forgotten that I'd shifted the 3tph forwards by 5 minutes and so it wasn't at 00, 20 and 40 minutes past the hour but rather at 05, 25, and 45 minutes past the hour.
Whilst your suggested service pattern looks neat there's a few problems.
Firstly, the good people of Aldershot and Farnham (even if you couldn't get a more frequent service beyond,v or even to Farnham) aren't going to be happy about only having 2tph when places like Hook and Winchfield (their combined passenger count pre COVID was circa 1.2 million) would be getting 6tph - a frequency which few other stations would be getting, so there would be a lot of other places wondering why they are getting such a good service.
The larger stations (Farnborough and Fleet) are already served by via Winchester services and so see 4toh and 3tph already, so would be seeing up to 10tph with your proposed uplift.
You're also going to struggle to be able to turn back 6tph at Basingstoke.
A more likely outcome would be 4tph to Aldershot with at least 2tph beyond there (assuming Farnham keeps its 1tph to Guildford they would benefit from the Aldershot uplift if they are willing to change trains, even if they only have 2tph direct to Waterloo) and 4tph all stations to Basingstoke (Farnborough and fleet would see up to 6tph under this option)
Having said that, there could be a good case for some of the new services through Andover to gain a stop at Farnborough Main and possibly Fleet, as currently to travel to stations within Hampshire either side of Basingstoke requires a chance at Basingstoke.
Secondly, given that XC could only ruin 1.5tph to/through Southampton, I'm not sure that you could run 6tph via Winchester and even if you can that's not much more than the 5tph which currently run in some hours.
I fully accept that you're not going to have a lot of people from Southampton using a via Andover service, however that doesn't mean that it won't increase capacity on the Southampton services via Winchester.
First up you can get some shift by having some less time sensitive but more money sensitive passengers go the other way. However the likely larger shift would be those from the line between Romsey and up towards Salisbury (although the further north you go the fewer people who would have been changing in Southampton) who would likely prefer to take a direct service rather head south and change at Southampton.
Would it justify 10/12 coach trains, probably not, however until such time as there sufficient passenger uplift to need to run everything as full length trains it's not unreasonable to run shorter services (for instance it's not uncommon for the to be 3 coach 159's off peak into Waterloo).
For peak hour services there's two options, pair it with another service at Andover so it's a full length, and/or accept it might be fairly empty until Basingstoke (although you'll likely get a fair amount of people going to or changing trains at Basingstoke) and then work out the best calling pattern to maximise the capacity of the train after that (potentially a fast service with no other stops just ahead of a train from Southampton with a couple of stops so those heading to Waterloo "save" a few minutes by getting the earlier train and are more likely to get a seat).
Finally, I'm not running trains on the show like which don't call at every stop onwards of Surbiton is going to do to the frequency which could be delivered. Anyway, you also don't want to make everyone who is going to places served by the Basingstoke and Alton trains currently have to change trains at Woking for a shower train into Waterloo for those stations.
In fact it may even be that (assuming 4tph to Aldershot and 4tph to Basingstoke) you might even run 2tph using the current Alton casing pattern onwards of Woking and 2tph using the Basingstoke casing pattern for each route, so that would be:
- 2tph Clapham Junction, Surbiton, Walton-on-Thames, Weybridge, Woking, Brookwood
- 2tph Clapham Junction, Surbiton (possible extra stop at Wimbledon), West Byfleet, Woking, Brookwood
The reason for the extra stop at Wimbledon is to balance the journey times between the service pairs but also to create a whole raft of station pairs which can be undertaken with just one change of train (be that London Underground or tram or Crossrail 2 - remembering that will see a those services too in the future).
Yes, there may need to be consideration at to how such calls happen as thought may need to be given to if it is acceptable to have the fast platforms fully open again due to the safety issues there have been there in the past. Although, something which may mitigate this concern (and/or permit the use of the slow line platforms anyway) is the fact that the Crossrail 2 platforms will be underground so there could be fewer passengers waiting in the existing platform.
One additional minor point, I'm not sure if the 8tph uplift would also need to cater for services like the Woking stoppers, this wouldn't necessarily be ideal to extend beyond Woking, but as with the Southampton Via Andover service, it's not without it's merits.
However it would need to have careful consideration as to service patterns so you don't in effect create a service pattern with a 15, 15 minute 30 minute fast service and the train in the 30 minute gap then ends up resulting in people either not using it to go to Waterloo or changing along the route to avoid being overtaken by the train they could have got it they waited another 15 minutes.
If we were to do that, we'd be better off with even my miss typed 3tph service pattern as then the largest gap would have been 25 minutes (although with the corrected time it's only 20 minutes).
Personally, running 4tph for the Woking stoppers (maybe extending them as an extra service to Basingstoke and/or Aldershot, but as a 1tph not to try and make it part of a 4tph frequency) with Basingstoke and Aldershot (and beyond) services seeing 3tph frequencies with at least 1tph of those calling at Wimbledon (any Woking Stoppers being extended would increase that). Even under this option Farnborough would see an uplift from 4tph to 5tph (maybe even 7tph of the Southern Approach to Heathrow is also built) and Fleet would be 4tph.
If there was a desperate need for a higher frequency between Woking and Basingstoke you could make one of the via Andover services call at those stations, although most likely only Farnborough Main and Fleet (giving them +1tph over the above).
If there was truely a need for more services to Hook and Winchfield, it would be better (assuming it's built) to have them served by Heathrow services using the Southern Approach to Heathrow scheme (would give them 5tph calling). As chances are that would generate more passengers using the railways than 6tph to Waterloo. Especially if those services were linked through at Heathrow to run onto Old Oak Common (HS2) and Paddington.
Of course the Southern Approach to Heathrow could be an issue in running 16tph between Woking and Basingstoke (6tph to Basingstoke, 6tph through Winchester and 4tph through Andover), especially with 8tph of those turning back at Basingstoke (6tph Waterloo and 2tph Heathrow/Paddington) with only a flat junction to do that.
Even increasing from 2tph to 5tph or even 6tph could be bad enough (although you could look at a turn back facility fully to the west of the station so platform 4 is used by these services heading towards Farnborough rather than platform 1).