Snoring is a sleep study center that specializes in the diagnosis and treatment

Question

Snoring is a sleep study center that specializes in the diagnosis and treatment of sleep disorders such as sleep apnea. Its state-of-the art facility is conveniently located in xxx. The facility operates only with appointments and for that reason variability is not an issue. The following process describes the different stages that a patient typically undergoes in a single visit (assume steady state). Specifically, upon arrival patients wait at the reception. The reception accepts new patients only during 6pm-12:00am. Typically, there are 5 patients per hour arriving from Virginia, 2 patients per hour arriving from DC and 3 patients per hour arriving from Maryland. The receptionist leaves when the last person has been called into the main facility. Patients are called on a first-come-first served basis. Once in the main facility, medical staff help prepare the patient for the sleep study. This involves placing a large number of electrodes on the patient’s scalp, face, chest, limbs, and fingers, which is a time consuming activity. The staff can prepare 15 patients per hour. Each patient sleeps for 12 minutes. After that, the patient remains in the room until he is called from the doctor of the facility to go over the data from the sleep study. The diagnosis based on the data is rather straightforward. The doctor checks the values of only certain indices (e.g., the Apnea Hypopnea Index-AHI) and based on these prescribes the use of a Continuous Positive Airway Pressure (CPAP) machine with certain pressure settings. There is only one doctor in the facility who always completes the review of the results and the consultation with each patient in exactly 15 minutes. Based on the information given above please calculate the following: a. (3 points) What is the maximum number of patients that will have to wait in the lobby? b. (1 point) What is the average number of patients that the receptionist will see waiting? c. (5 points) How long does it take a patient to go through the entire process? d. (2 points) If NiteNiteSnoring (reception and main facility) opens at 6pm and the last person sneaks in the reception at midnight, at what time will the entire system (reception and main facility) be empty of patients?

Explanation / Answer

In case of reception arrival rate = 10 patients per hour

Service rate =15 patients per hour

a) Maximum no. of patients that will have to wait = 5 because 15 patient will be served and ina single time max. 20 patients can arrive . therfore difference is 5

b) Using Waiting line Model method

Average number of patients that the receptionist will see waiting = 10 *10/15*(15-10)

= 1.33 patients per hour

c)

Average waiting time in reception = 10 /15*(15-10)

= 8 minute

Patient preparation by staff =60/15 = 4 minute

Patient sleep =12 minute

Consultation =15 minute

Therfore Entire process will take =8+4+12+15 = 39 minutes

d) If last patient enter at midnight than it will take around 39 minute for the whole process to complete. therefore at 12: 40 a.m. entire system will be empty of patients.

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