For a single server, single queue system with an arrival rate of 6 customers per hour and a service rate of 15 customers per hour, what is the probability of zero customers in the system (to two decimal places)?
A) 0.60
B) 0.40
C) 0.90
D) Cannot be determined from the information given

Question

Quizplus · Accepted Answer

This system can be modeled as an M/M/1 queue. The formula for the probability of zero customers in the system is:
P(0) = (1 - (λ/μ))
where λ is the arrival rate and μ is the service rate. 
Plugging in the given values:
P(0) = (1 - (6/15))
P(0) = 0.60
Therefore, the answer is A) 0.60.

For a Single Server, Single Queue System with an Arrival