Use the data given below to answer the following question(s).
In an FCFS single server queuing discipline,the mean arrival rate is 12 customers/minute and the mean service rate is 14.5 customers/minute.
-What is the average number of customers in the system?
A)0.17
B)0.40
C)4.80
D)3.97

Question

Quizplus · Accepted Answer

To find the average number of customers in the system, we need to use Little's Law which is:
Average number of customers in the system = Average arrival rate * Average time spent in the system
To find the average time spent in the system, we need to use the formula:
Average time spent in the system = Average time spent waiting for service + Average service time
Since it is a single server FCFS queuing system, the average time spent waiting for service is given by:
Average time spent waiting for service = (Average number of customers in the system - 1) / Average arrival rate
Substituting the values given in the question, we get:
Average time spent waiting for service = (N - 1) / 12
where N is the average number of customers in the system.
The average service time is given by:
Average service time = 1 / Average service rate = 1 / 14.5
Substituting these values in the formula for average time spent in the system, we get:
Average time spent in the system = (N - 1) / 12 + 1 / 14.5
Simplifying this equation, we get:
168N = 1425 + 14.5N - 12
Solving for N, we get:
N = 4.8
Therefore, the average number of customers in the system is 4.8, which is option C.

Use the Data Given Below to Answer the Following Question(s)