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 from Scenario B.1 are either waiting in line to be seated or being seated by the volunteer octogenarian usher?
A) four
B) five
C) six
D) seven

Question

Quizplus · Accepted Answer

Given the arrival rate ($\lambda$) is 25 customers per hour and the service rate ($\mu$) is 30 customers per hour, we can use the formula for the average number of customers in the system (L) in an M/M/1 queue: $L = \frac{\lambda}{\mu - \lambda}$. Plugging in the given values, $L = \frac{25}{30 - 25} = \frac{25}{5} = 5$. This means, on average, there are five patrons either waiting in line or being seated.

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