Question

The hematology lab manager has received complaints that the turnaround time for blood tests is too long. Data from the past month show that the arrival rate of blood samples to one technician in the lab is five per hour and the service rate is six per hour. Using queuing theory, and assuming that (a) both rates are exponentially distributed and (b) the lab is at steady state, determine the following measures:

1. Capacity utilization of the lab

2• Average number of blood samples in the lab

3• Average time that a sample waits in the queue

4• Average number of blood samples waiting for testing

5• Average time that a blood sample spends in the lab

Answer 1

Using queuing theory, we can determine various measures related to the blood test turnaround time in the hematology lab. These measures include capacity utilization, average number of blood samples in the lab, average time that a sample waits in the queue, average number of blood samples waiting for testing, and average time that a blood sample spends in the lab.

Step-by-step explanation:

Using queuing theory, we can determine various measures related to the blood test turnaround time in the hematology lab. Let's go through each measure:

1. Capacity utilization: Capacity utilization is defined as the ratio of the arrival rate to the service rate. In this case, the arrival rate is 5 blood samples per hour and the service rate is 6 blood samples per hour. Therefore, the capacity utilization is 5/6 or 0.8333 (83.33%).
2. Average number of blood samples in the lab: The average number of blood samples in the lab can be calculated using the formula: Average number = Arrival rate / (Service rate - Arrival rate). In this case, the average number is 5 / (6 - 5) or 5 samples.
3. Average time that a sample waits in the queue: The average time a sample waits in the queue can be calculated using the formula: Average wait time = 1 / (Service rate - Arrival rate). In this case, the average wait time is 1 / (6 - 5) or 1 hour.
4. Average number of blood samples waiting for testing: The average number of blood samples waiting for testing can be calculated using the formula: Average number waiting = Arrival rate * (Average wait time / Service rate). In this case, the average number waiting is 5 * (1 / 6) or 0.8333 samples.
5. Average time that a blood sample spends in the lab: The average time a blood sample spends in the lab can be calculated using the formula: Average time in lab = 1 / Service rate. In this case, the average time in lab is 1 / 6 or 0.1667 (10 minutes).