Scenario B.4
Customers arrive at an airline ticket counter at the rate of 50 customers per hour, according to a Poisson distribution. There are three ticket agents. Customers select the first available agent from one line. Each agent can process 20 customers per hour with exponential service times.
-Use the information in Scenario B.4. What is the average number of customers waiting in line for service?
A) fewer than or equal to 4.0
B) greater than 4.0 but fewer than or equal to 4.5
C) greater than 4.5 but fewer than or equal to 5.0
D) greater than 5.0

Question

Quizplus · Accepted Answer

The system can be modeled as an M/M/3 queue (Poisson arrivals, exponential service times, 3 servers). The arrival rate ($\lambda$) is 50 customers per hour, and the service rate ($\mu$) for each agent is 20 customers per hour. The traffic intensity ($\rho$) is $\lambda / (s\mu) = 50 / (3*20) = 5/6$. Using the formula for the average number of customers in the queue ($L_q$) for an M/M/s queue, we find that $L_q$ is less than or equal to 4.0 for this scenario, considering the system's capacity to handle the given arrival rate efficiently.

Scenario B.4 Customers Arrive at an Airline Ticket Counter at the Rate