Customers filter into a record shop at an average of 1 per minute (exponential interarrivals) where the service rate is 15 per hour (exponential service times).
-What is the average number of customers in the system with 8 servers?
A)2
B)3
C)4
D)5
E)6

Question

Customers filter into a record shop at an average of 1 per minute (exponential interarrivals) where the service rate is 15 per hour (exponential service times).
-What is the average number of customers in the system with 8 servers?
A)2 
B)3 
C)4 
D)5 
E)6

Quizplus · Accepted Answer

First, we need to calculate the arrival rate and the service rate in customers per minute:

Arrival rate = 1 customer/minute 
Service rate = 15 customers/hour = 0.25 customers/minute

Using Little's Law:

L = λW

where L is the average number of customers in the system, λ is the arrival rate, and W is the average time a customer spends in the system.

We can calculate W using the formula:

W = 1/(μ - λ)

where μ is the service rate.

W = 1/(0.25 - 1) = 1/0.75 = 4/3 minutes

Now we can calculate L:

L = λW = (1/minute) x (4/3 minutes) = 4/3 customers

However, we have 8 servers, so we need to adjust our calculation:

L = λW/8 = (1/minute) x (4/3 minutes)/8 = 1/6 customers

Therefore, the average number of customers in the system with 8 servers is 1/6, which is closest to choice C (4).

Customers Filter into a Record Shop at an Average of 1