Scenario B.1
A single ticket taker can tear tickets and direct movie patrons to their seats at a rate of 90 per hour.Customers arrive every minute 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.
-Use the information in Scenario B.1.What is the average combined time a customer waits in line and spends being seated by the ticket taker?
A)1.00 minute
B)1.50 minutes
C)2.00 minutes
D)3.00 minutes

Question

Quizplus · Accepted Answer

We can use Little's Law to find the average combined time a customer waits in line and spends being seated by the ticket taker.
Average number of customers in system = arrival rate * average time in system
The arrival rate is given by the Poisson distribution with an average rate of 1 customer per minute.
The average time in system is the sum of the average waiting time in line and the average service time.
The average service time is the inverse of the service rate, which is 90 customers per hour, or 0.015 hours per customer.
The average waiting time in line is the average number of customers waiting in line times the average time per customer in line. The average number of customers waiting in line can be found using Little's Law:
Average number of customers in line = arrival rate * average time in line
We can assume that the system is in steady state, so the average number of customers in line is equal to the average number of customers in system:
Average number of customers in line = average number of customers in system = arrival rate * average time in system
Therefore, the average time in line is:
Average time in line = Average number of customers in line / arrival rate = average time in system - average service time = 5 - 0.015 = 4.985 minutes
Adding the average service time, we get:
Average combined time = average time in line + average service time = 4.985 + 0.015 = 5 minutes
Therefore, the average combined time a customer waits in line and spends being seated by the ticket taker is 2 minutes.

Scenario B.1 A Single Ticket Taker Can Tear Tickets and Direct Movie