Question

The hematology lab manager has been receiving 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. To answer the following questions, use queuing theory and assume that both rates are distributed exponentially and that the lab is at a steady state.

6. What is the average time a blood sample spends in the lab? (Hint: Average time in the system (Ws)) The answer should be in the form: # hr or ## min

The hospital has instituted a new flu shot process. Rather than flu shots being given throughout the hospital and clinics, management has decided to centralize all flu shots in one place. There is keen interest in examining how this change has affected capacity and demand. Data have been collected and it has been determined that patients arrive at the hospital's vaccination station at a rate of five per hour. Arrivals can be described by a Poisson distribution. Patients are seen by the care provider on a FCFS basis. The time to obtain consent, prepare the supplies and administer the shot averages 6 minutes. Use the following questions to evaluate the performance of this system.

7. Because all performance measures require knowledge of λ and μ, it is always good practice to state them first. λ = patients/hour μ = shots/hour

8. What is the percentage of time that the provider is busy? [Capacity utilization (p)] The answer may be submitted as either a decimal or a percentage.

9. On average, how long does a patient spend waiting in line to receive his shot? [Average waiting time in queue (Wq] The answer may be submitted in either of the following formats: # minutes or .## hour

10. On average, what is the total time a patient spends at the vaccination station? [Average time in the system (Ws)] The answer may be submitted in either of the following formats: ## minutes or .# hour

11. On average, how many patients are waiting in line to be served at any one time? [Average length of queue (Lq)] The answer should be submitted in the following format: #.# patient

12.These questions are based on The Vaccination Station scenario above. Assume the following changes: * It is flu season and the arrival rate is now 10 patients per hour. The arrival rate has doubled from the scenario above. * Efficiencies have been implemented. It now takes only 5 minutes to obtain consent, prepare the supplies and administer the shot. To answer this question, fill out the following matrix with the correct answers. Use leading zeros, round to 1 decimal point Prior to Flu Season Flu Season Average Number of Patients in the Queue (Lq) Average Time Patients Will Spend in the Clinic Waiting and Getting Their Shots (Ws) Minutes Minutes

Answer 1

6. Here arrival rate lambda = 5 per hour

Service rate mu = 6 per hour

Avg time spent in the system = 1/mu-lambda = 1/6-5 =1 hour.

7.

Lambda = 5 per hour

mu = 60/6 =10 per hour

8. Utilisation rho = lambda /mu = 5/10 =0.5

Hence the provider is busy 50% of the time.

9. Avg waiting time in line = Wq = lambda / mu*(mu-lambda) = 5/10*(10-5) = 0.1 hour = 6 minutes.

10 Avg time in system = 1/ mu-lambda = 1/10-5 = 1/5 hours = 12 minutes.

Note: As per policies, I can answer first 4 parts of a question. Inconvenience is regretted.