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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

Respuesta :

Answer:

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

Step-by-step explanation:

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

We have that the arrival rate is [tex]\lambda=4[/tex] and the service rate is [tex]\mu=7[/tex].

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

[tex]L=\frac{\lambda}{\mu-\lambda}=\frac{4}{7-4}=\frac{4}{3}=1.33[/tex]

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