Hysterical cruise vacationers besiege Tatiana, their excursion coordinator, and her fourteen assistants at the Port of Cozumel when they realize that all water excursions have been cancelled for no reason in particular. It takes them 4 minutes to find the customers an alternative excursion activity and customers cluster around them at the rate of 200 per hour. About how many customers are waiting in line to receive their valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

Question

Quizplus · Accepted Answer

We can use the M/M/1 queuing model to solve this problem. Since the arrivals follow a Poisson distribution and the service times are exponentially distributed, the utilization factor (ρ) is equal to λ/μ = (200/60)/(1/4) = 4/3. Using the formula for the expected number of customers in the system, Ls = ρ/(1-ρ), we get Ls = (4/3)/(1-4/3) = 4.52 customers. Therefore, the answer is C.

Hysterical Cruise Vacationers Besiege Tatiana, Their Excursion Coordinator, and Her