A single-server waiting line system has an arrival pattern characterized by a Poisson distribution with 3 customers per hour. The average service time is 12 minutes. The service times are distributed according to the negative exponential distribution.
-The average time a customer can expect to wait in line is:
A) 18 minutes
B) 36 minutes
C) 30 minutes
D) 60 minutes

Question

Quizplus · Accepted Answer

The average time a customer waits in line in a single-server queue, where arrivals follow a Poisson distribution and service times follow a negative exponential distribution, can be calculated using the formula $W_q = \frac{\lambda}{2\mu(\mu - \lambda)}$, where $\lambda$ is the arrival rate (3 customers per hour) and $\mu$ is the service rate. Given the average service time is 12 minutes (or 5 services per hour), substituting these values gives a waiting time of 18 minutes.

A Single-Server Waiting Line System Has an Arrival Pattern Characterized