In a single-server queuing system, if 12 customers arrive per hour and 30 customers are served per hour, what is the probability that there are no customers in the system?
A) 0.75
B) 0.60
C) 0.40
D) 0.2 5

Question

Quizplus · Accepted Answer

We can use the M/M/1 queuing model, where arrivals follow a Poisson distribution with a rate of λ=12 customers per hour, service times follow an exponential distribution with a rate of μ=30 customers per hour, and there is one server (hence M/M/1). 
The probability that there are no customers in the system (i.e., the server is idle) can be calculated as:
P(0 customers in the system) = P(server idle) = P(arrival rate < service rate) = 1 - λ/μ
Substituting the values, we get:
P(0 customers in the system) = 1 - 12/30 = 0.6
Thus, the answer is B.

In a Single-Server Queuing System, If 12 Customers Arrive Per