Asked by Pradeep Patil on May 08, 2024
Verified
A dental clinic at which only one dentist works is open only two days a week. During those two days, the traffic is uniformly busy with patients arriving at the rate of three per hour. The doctor serves patients at the rate of one every 15 minutes.
a. What is the probability that the clinic is empty (except for the dentist)?
b. What percentage of the time is the dentist busy?
c. What is the average number of patients in the waiting room?
d. What is the average time a patient spends in the office (wait plus service)?
e. What is the average time a patient waits for service?
Dental Clinic
A healthcare facility specializing in the diagnosis, prevention, and treatment of oral health issues, offering services such as dental check-ups, treatments, and surgeries.
Patients Arriving
The occurrence or process of patients coming to a healthcare facility for treatment or consultation.
- Analyze service systems to calculate probabilities related to service availability and busyness.
- Utilize the M/M/1 queuing model to calculate system utilization, waiting times, and numbers in system and queue.
Verified Answer
GH
Gloria HigueraMay 15, 2024
Final Answer :
(a) Po = 1 - 3/4 = 0.25; (b) The dentist is busy when the clinic is not empty, or 1 - .25 = 0.75 or 75% of the time; (c) Lq = 3∗3 / 4∗(4 - 3) = 2.25; (d) Ws = 1 / (4 - 3) = 1 hour; (e) Wq = 3 / 4 ∗ (4 - 3) = 0.75 hours.
Learning Objectives
- Analyze service systems to calculate probabilities related to service availability and busyness.
- Utilize the M/M/1 queuing model to calculate system utilization, waiting times, and numbers in system and queue.