# Predict parallel time intervals

I have the following problem. There is a service station that can provide service for a number of vehicles at the same time. The service data looks like this:

    Vehicle    ServicePlanStart      ServicePlanEnd    ServiceTrueStart      ServiceTrueEnd
0         A 2022-08-01 08:00:00 2022-08-01 13:00:00 2022-08-01 09:00:00 2022-08-01 14:00:00
1         B 2022-08-01 10:00:00 2022-08-01 15:00:00 2022-08-01 09:00:00 2022-08-01 14:00:00
2         C 2022-08-01 11:00:00 2022-08-01 13:00:00 2022-08-01 11:00:00 2022-08-01 13:00:00
3         D 2022-08-01 12:00:00 2022-08-01 17:00:00 2022-08-01 14:00:00 2022-08-01 18:00:00


We have plan times and true times that are often different, as not all vehicles come in time (too late/too early) for service, or some need to wait for a free slot (because others came too late, etc.). There may be a different number of vehicles at the service station simultaneously. My task is to predict the actual start and end times ('ServiceTrueStart' and 'ServiceTrueEnd') or the status (in service/not in service) of a vehicle at some time point in the future (in the next x hours). For example, let's say we have 9:30 now and want to predict true start/end values (or status in x hours) for all 4 vehicles: As we can see, vehicles A and B are already in service from 9:00 (so we already know their 'ServiceTrueStart' times). How can we predict the rest of the true values (or status in x hours) that we don't know at that time point? What kind of algorithm should I use? How can I transform my data, so it's possible to use classic machine/deep learning algorithms? Any ideas are highly appreciated. This example is simplified and in reality I have about 2000 vehicles and a few hundred service stations. The business problem I try to solve here is how many vehicles I have available at some time point in the future.

• This is the subject of queuing theory. I posted a detailed illustration at stats.stackexchange.com/a/129786/919. Analogous simulations can be used to understand your system and make short-term predictions.
– whuber
Aug 4, 2022 at 19:47
• Thank you for the hint. I think the difference is that I have planned times and other variables which I don't list here (kind of service) that influence real values. Aug 4, 2022 at 20:14
• It looks a lot like parking occupancy prediction, they use occupancy History and other data like weather, special-days... To predict incoming rate, and length of stay. The modelisation could look similar. Aug 9, 2022 at 17:24
• You could predict probability of vehicle to be late/early on one side (depending of Time of the day for expl) and then predict length of service (depending of service type, number of current vehicles...) And then run multiple simulation with those models Aug 9, 2022 at 17:29