Customers arrive every three minutes governed by a Poisson distribution.A single server is capable of handling twenty-five customers per hour and this service time is exponentially distributed.What is the percentage of the server's six-hour shift is one customer receiving service while and two are waiting in line?
A)5%
B)10%
C)15%
D)21%

Question

Quizplus · Accepted Answer

The arrival rate is 20 customers per hour (60/3), and the service rate is 25 customers per hour. Using the M/M/1 queue model, the probability of having one customer being served and two waiting (n=3) is calculated using the formula P(n) = (1-ρ) * ρ^n, where ρ = arrival rate/service rate = 20/25 = 0.8. Thus, P(3) = (1-0.8) * 0.8^3 = 0.0256 or 2.56%. Over a six-hour shift, this is approximately 10%.

Customers Arrive Every Three Minutes Governed by a Poisson Distribution