A single-server waiting line system has an arrival pattern characterized by a Poisson distribution with 3 customers per hour. The average service time is 12 minutes. The service times are distributed according to the negative exponential distribution.
-The probability that the system is idle is:
A) 0
B) .20
C) .40
D).60

Question

Quizplus · Accepted Answer

The system's idle probability can be calculated using the formula P₀ = 1 - ρ, where ρ (rho) is the traffic intensity. Given the arrival rate (λ) is 3 customers per hour and the service rate (μ) is 5 customers per hour (since 60 minutes / 12 minutes per customer = 5), ρ = λ/μ = 3/5 = 0.6. Therefore, P₀ = 1 - 0.6 = 0.4.

A Single-Server Waiting Line System Has an Arrival Pattern Characterized