For a single server, single queue system with an arrival rate of 12 customers per hour and a service rate of 20 customers per hour, what is the probability of zero customers in the system (to two decimal places)?
A) 1.67
B) 0.60
C) 0.40
D) Cannot be determined from the information given

Question

Quizplus · Accepted Answer

This is a M/M/1 system, where arrivals and service times follow an exponential distribution. The probability of zero customers in the system can be calculated using the formula:
P(0) = [(µ/λ)^0 * e^(-µ/λ)] / 0! 
where µ is the service rate and λ is the arrival rate.

Substituting the given values, 
P(0) = [(20/12)^0 * e^(-20/12)] / 0! 
P(0) = 0.40 (rounded to two decimal places)

Therefore, the best choice is C.

For a Single Server, Single Queue System with an Arrival