Calculation of time position in queue?

Question

Message Queues

You have come to see the doctor. He starts taking at 10.00. You came at 9.30, there was already a queue. The people in the queue made a list, you signed up for the list at number 100. You need the best option for calculating the time when your turn comes, so as not to stand and wait. Options like cheat - negotiate with people (so that they call you), go out of line, etc. - unsuitable. What options do you have for solving this problem? Does it make sense to look towards the theory of queuing?