Scenario B.1
A single volunteer octogenarian usher can scan tickets with a handheld device and direct theater patrons to their seats at a rate of 30 per hour with an accuracy rate approaching 23%. On average, about twenty-five customers arrive every hour for assistance and always wait, regardless of how long the line gets. Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution.
-How many theater patrons are waiting for their favorite octogenarian usher in Scenario B.1?
A) two
B) three
C) four
D) five

Question

Quizplus · Accepted Answer

We can model this scenario using queuing theory, specifically an M/M/1 queue. Using the given arrival rate of 25 customers per hour and service rate of 30 customers per hour, we can calculate the utilization of the system:
Utilization = arrival rate/service rate = 25/30 = 0.83
Since the utilization is greater than 0.7, we can expect that there will be waiting in the system. The average number of customers waiting in the system can be calculated as:
Lq = (Utilization^2)/(1 - Utilization) = (0.83^2)/(1 - 0.83) = 4.89
Therefore, on average, there are about 5 theater patrons waiting for their favorite octogenarian usher. The closest answer choice is C (four).

Scenario B.1 a Single Volunteer Octogenarian Usher Can Scan Tickets with a with a Handheld