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 answer choices is correct.

Question

Quizplus · Accepted Answer

The utilization factor is given by the formula: 
ρ = (λ/μ) * n
where 
λ = arrival rate
μ = service rate per server
n = number of servers
ρ = utilization factor

Substituting the given values, we get:
ρ = (5/60) * (2/3) * n 
ρ = (1/18) * n

For the utilization factor to be less than 1, we need:
ρ < 1 
(1/18) * n < 1 
n < 18

Therefore, the minimum number of servers required is 4 (option C) to keep the utilization factor under 1. Any number of servers greater than or equal to 4 will also work.

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