Question

Customers enter the waiting line at a cafeteria on a first-come, first-served basis. The arrival rate follows a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is four per minute and the average service rate of a single server is seven per minute, what is the average number of customers in the system?

A.0.43
B. 1.67
C. 0.57
D. 1.33
E. none of the above

Answer 1

The average number of customers in the system is 1.33 customers (option D).

Explanation:

This is a problem of queing theory (single-server waiting line).

We have that the arrival rate is
`\lambda=4` and the service rate is
`\mu=7`.

The formula for the average number of customers in the system is:

`L=(\lambda)/(\mu-\lambda)=(4)/(7-4)=(4)/(3)=1.33`