A multiple-channel system has customers arriving at an average rate of five per hour and an average service time of 40 minutes. The minimum number of servers for this system to be underloaded is
A)2.
B)3.
C)4.
D)5.
E)6.

Question

Quizplus · Accepted Answer

To find the minimum number of servers for the system to be underloaded, calculate the traffic intensity (ρ) using the formula ρ = λ / (μ * c), where λ is the arrival rate, μ is the service rate, and c is the number of servers. Here, λ = 5 customers/hour, and μ = 1.5 customers/hour (since 40 minutes = 2/3 hour, so 1/ (2/3) = 1.5). To be underloaded, ρ < 1. Solving 5 / (1.5 * c) < 1 gives c > 3.33. Therefore, at least 4 servers are needed.

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