Herewith a Bald Rick essay.
Engineering Allowance (Box time) [x] is there to cater for temporary speed restrictions imposed following engineering work, usually track renewal. In theory, these allowances could be inserted into the timetable wherever the work is, but as the speed restrictions typically last for 1-3 weeks, this would mean a lot of timetabling work. Therefore, they are typically inserted into the timetable over a longer section of the journey, because on average there is likely to be a temporary speed restriction on that stretch at any one time. If a service travels on a section of line where engineering allowance is applied, it must be included in the schedule. (The ex Southern region did things differently, and even now with the exception of some services to Waterloo, none have any engineering allowances applied). Engineering allowances are set by Network Rail.
Pathing Allowance (Circle time) (x) is there to make the timetable function, and is one of the key tools for timetable planners when trying to get all the services to fit together. It can be applied anywhere, but most often on the approaches to conflicting junctions. If, say, two trains are scheduled to arrive at a junction conflict too close to each other such that the first service would not be clear of the junction by the time the second is due to arrive, AND neither of them can be altered to depart its previous station earlier or later to make it work, then pathing allowance is inserted to the schedule of the second train on the approach to the junction conflict such that it will cross the junction when it is clear. (Obviously the signalling system is the method for actually keepin the trains a safe distance apart). Pathing allowance is also used where faster trains are scheduled to catch up slower trains on a given stretch of track. The West Anglia Main Line between Bishops Stortford and Tottenham Hale is a great example of that. Pathing allowances can be proposed by either Network Rail or a TOC, but ultimately NR has the final say on making the whole timetable work. The passenger experiences this as slow running, red signals, ‘waiting for an available platform’ or ‘congestion’, but yet still arriving on time.
Performance allowance (Diamond time) <x> is applied where a train operator determines that a given service (or group of services) is likely to be delayed compared to its base schedule for unspecified reasons. This can be applied anywhere, and is within the gift of the train operator. It is more often used by long distance operators. Application of performance allowance is often a good indicator of where a timetable doesn’t quite ‘work’, but no one is quite sure why.
Passenger differential is simply where the published time of arrival of a service in the public timetable is later than in the working timetable. Again this can be anywhere, but is usually at the service destination or at a key station. This is entirely in the gift of the train operators.
The first two categories are essential to make the timetable work reliably, ie in theory if there were no unplanned incidents that cause a train to be delayed you would still need these categories to ensure all trains ran punctually.
The last two categories are there to deal with the principle that there are unplanned incidents, every day, and thus helps the service run closer to the advertised time. These are what are colloquially known on this forum as ’padding’ and (to bring this post back on topic
) is what airlines use in their schedules.