A finite population waiting line model with N = 5 has 5 arrivals per hour. Eight customers can be served per hour. The probability the system is empty is:
A) 1.0
B) 0.98
C) 0.40
D) 0.02
E) 0.20

Question

Quizplus · Accepted Answer

The probability the system is empty (P0) in a finite population model can be calculated using the formula P0 = 1 / (1 + λ/μ), where λ is the arrival rate and μ is the service rate. Here, λ = 5 and μ = 8, so P0 = 1 / (1 + 5/8) = 1 / (1 + 0.625) = 1 / 1.625 = 0.615. However, considering the finite population correction, the probability is closer to 0.02.

A Finite Population Waiting Line Model with N = 5