A multiple-server system has customers arriving at an average rate of five per hour and an average service time of forty minutes The minimum number of servers for this system to have a utilization factor under 1 is:
A)2
B)3
C)4
D)5
E)None of the above

Question

A multiple-server system has customers arriving at an average rate of five per hour and an average service time of forty minutes The minimum number of servers for this system to have a utilization factor under 1 is:
A)2 
B)3 
C)4 
D)5 
E)None of the above

Quizplus · Accepted Answer

The utilization factor is given by the formula:

Utilization factor = (average arrival rate) x (average service time)

To have a utilization factor under 1, we need:

(average arrival rate) x (average service time) < 1

Substituting the given values, we get:

(5 customers/hour) x (40 minutes/customer) / (60 minutes/hour) = 200/60 = 3.33

Therefore, we need at least 4 servers to keep the utilization factor under 1, as:

(5 customers/hour) x (40 minutes/customer) x 4 servers / (60 minutes/hour) = 13.33 < 1

A Multiple-Server System Has Customers Arriving at an Average Rate