Question

Please complete all work in excel. Use excel to make the calculations (cells can be clicked on to view any formulas used) and be sure to identify your answer, including units.

1. Patrons arrive at a movie theater at an average of 4 per minute (Poisson) where the service rate is 50 per hour (Poisson).
   1. What is the average number of patrons in the system with 5 ticketing stations?

2. What is the minimum number of ticketing stations needed to keep the average time in the system under three minutes?

Answer 1

Arrival rate = 4 per minute

Service rate = 50 per hour = 50/60 = 0.8333 per minute

Formulate Excel model with formulas as shown below:

b)

Using 5 ticket stations (number of servers, s=5), calculations are following:

Average number of patrons in the system, L = 26.4408

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b)

Increase the number of servers in cell B6 to 6 and see the value in cell B12

Using 6 ticketing stations,

Average time in the system = 1.7178 minutes

We see that, with 6 ticketing stations, average time in system (W) is well under three minutes

Therefore, minimum number of ticketing stations needed to keep the average time in system under three minutes = 6 ticketing stations