Question

To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for the week. Previous experience indicates that, on average, 10 persons per hour request a test. Assume arrivals are Poisson distributed from an infinite population. Blood pressure measurements can be made at a constant time of five minutes each. Assume the queue length can be infinite with FCFS discipline. Hint: Use model 2. Use the MS Excel template provided in Blackboord to compute the answers and state your answer for each part clearly indicating the unit of measurement ie. Minutes or persons etc. a. What average number in line can be expected? b. What is the average amount of time that a person can expect to spend in line? c. What average number of persons can be expected to be in the system? d. On the average, how much time will it take to measure a person's blood pressure, including waiting time? e. On weekends, the arrival rate can be expected to increase to over 12 per hour. What effect will this have on the number in the waiting line?

Answer 1

Queue metrics can be calculated using the characteristics of Poisson processes and the exponential distribution, which allows determining the probability of arrivals and waiting times in different scenarios.

Step-by-step explanation:

Based on the provided information, we can calculate various metrics in a queueing system. Particularly, if we take the example where 30 customers per hour arrive, meaning one customer arrives every two minutes on average, we can dive into the scenario for the blood pressure testing booth at El Con Mall described in the student's question. In Poisson processes, arrivals are random yet with a known average rate, and the time between arrivals is exponentially distributed.

For instance, if we know the average rate for a process like the urgent care facility, where one patient arrives every seven minutes, we can calculate the probability of getting a patient in less than two minutes or waiting more than fifteen minutes using the exponential distribution's properties.

With a higher rate of arrivals, such as on weekends at the blood pressure booth, the waiting line would typically increase because the capacity to serve customers (in this case, to test blood pressure) remains constant. Therefore, a higher arrival rate would lead to longer queue lengths and increased waiting times.