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.
-A system has 5 servers. Customers arrive at a rate of 6 per hour and service time is 20 minutes. What is the system utilization?
A) .83
B) .40
C) .50
D) 20

Question

Quizplus · Accepted Answer

For the first system:

The arrival rate (λ) = 3 customers per hour
The average service time (μ) = 12 minutes per customer which equals to 0.2 hours per customer

The utilization rate of the system can be calculated as:
Utilization rate = λ/ (μ * c)

Where c is the number of servers.

In this case, c = 1 server

Utilization = (3/ (0.2 * 1)) = 1.5

For the second system:
The arrival rate (λ) = 6 customers per hour
The average service time (μ) = 20 minutes per customer which equals to 0.33 hours per customer.

The number of servers (c) = 5 servers

Utilization rate of the system can be calculated as:
Utilization rate = λ/ (μ * c)

Utilization = (6/(0.33*5)) = 0.36 which is very close to 0.40 from the choices. Therefore, the answer is B.

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