Probability of queuing

0liver

New Member
We are students and we developing the project of a music festival that takes place in 3 venues. We have identified some risks; one of those is related to the capacity of the venues, the tickets sold and how people will behave during the festival.
The total capacity of the venues is 6000, however we just sell 5800 tickets to have some spare capacity (200). The tickets allow the audience to access the three venues if there is free space on them.
Venue A Venue B Venue C
Capacity (people) 3000 2000 1000

In order to reduce people queuing outside because the venues are full the following measures have been taking:
The concerts in the three venues start at the same time; this is 18.00h, 19.00h and so forth and last 45minutes each.
The line up has been done in such way that bands playing at the same time have a similar fan-base on the social media.
The venues are located in the same area but walking time between them takes approx 5 minutes between venues is required.

The question are:
What is the probability at any given moment of time to have people queuing outside the venues A, B, C?
Probability of having queues in more than one venues simultaneously (e.g A and C)
It is possible to know an estimate, using statistics, of the queuing time? What time of data would be required to carry such analysis?

We appreciate your time and help.
Best,
Oliver

BGM

TS Contributor
Your problems seems quite interesting but there are quite a number of follow-up questions need to be asked.

1. Do you mean there are a total of 5800 people (inside the venue + queuing outside) at any given moment of time?

2. If yes, "have a similar fan-base on the social media" means that you want to model the number of people supporting the band in three different venues follows

$$\text{Trinomial}\left(5800; \frac {1} {3}, \frac {1} {3}, \frac {1} {3}\right)$$

3. Why do people queuing outside? Do you mean the people buying the ticket will only watch their most supported band without considering the other two?

4. You have mentioned the show started on time 1800 1900 etc. Do you mean there are different people in each hour? Or people enter freely at anytime? Also do you mean the band will rotate the venue at each time?

5. Not sure how the walking time between each venue will be related to the estimates (unless you are taking somehow complicated model considerations that the people are moved freely between the venues based on several factors). So that's why I am not very sure how "queuing time" plays the role here. As mentioned above unless you consider the people to be very dynamic, can moving around freely throughout the 45 minutes show time; but this backs to the question 3 why do people queue outside? why do not they just go to the empty seat?