I have already talked about the word schedule, but let’s refresh your memory and add a few more things.

Schedule – noun: ˈʃedjuːl, ˈske- $ ˈskedʒʊl, – dʒəl 

1 a plan of what someone is going to do and when they are going to do it:

a production schedule 

hectic/tight (= very busy) schedule

How can he fit everything into this busy schedule?

2 a list of the times when events are planned to happen, for example, the times when classes happen or when buses, etc. leave and arrive (UK timetable):

The class schedule is available on the website.

a bus schedule

a schedule of talks at the convention

3 a formal list of something, for example prices

a schedule of postal charges

a schedule of business expenses

Now, things can happen:

on schedule

at the expected or planned time/at the right time, not early or late:

The bus arrived on schedule.

We are on schedule to meet our targets.

Her first baby arrived right on schedule.

according to schedule

at the time or in the way that was planned:

If everything goes according to schedule, work will be complete in December.

Everything went according to schedule.

ahead of schedule

early, before the planned time:

The meeting finished ahead of schedule.

If things continue to run ahead of schedule, construction could be finished two months early.

behind schedule

to do less work than you planned to do by a particular point in time:

We are already two months behind schedule.

The project started six months late and continued to fall behind schedule.

run behind schedule

1 to arrive and/or leave later than the time that is expected, after the planned time:

The trains are running behind schedule.

2  to do something or happen later than planned or expected or to take longer than planned or expected: 

The doctor’s appointments are running behind schedule today.

 The doctor is running behind schedule today.

The project is running behind schedule.

https://dictionary.cambridge.org/dictionary/english/schedule

https://www.ldoceonline.com/dictionary/schedule

https://www.merriam-webster.com/dictionary/run%20behind%20schedule