Formulate develop and solve a queuing problem for your busin

Formulate, develop, and solve a queuing problem for your business unit. For example, the phone calls coming to the receptionist, or work arriving by mail, phone, or in person. List and explain the assumptions that you had to make to enable the problem to be solved, but caused the model to be unrealistic.

Solution

In my business unit of clinic, has a doctor examining every patient brought in for a general check-up. The doctor everages four minutes on each phase of the check-up although the distribution of time spent on each phase is approximately (assumption) exponential. If each patient goes through four phases in the check-up (assumption) and if the patients to the doctor\'s unit are approximately Poissin at the average rate of three per hour, what is the average time spent by a patient waiting in the doctor\'s clinic ? What is the average time spent in the examination ? What is the most probable time spent in the examination ?

I am required to make assumptions about the availability of the doctor. Assumptions are also made with respect to arrival of the patients and patients should not leave without the examinations. Assumptions are also made about the time taken by the doctor for conducting examinations.

Arrival rate is assumed to have mean = 3 patients per hour , denoted by m

Service rate, as per the assumption that there are four phases and each phase takes 4 minutes, is calculated as to have average (mean) of 3.75 (60/16) patients per hour , denoted by n

Number of phases denoted by k

Therefore we have formula for Average waiting waiting time = ((k+1)/2k) * (m/n(n-m))

=(5/8)(3/2.8125)=2/3 hours or 40 minutes

Average time spent in the examination = 4*4=16 minutes

Most probable time spent in the examination = (k-1)/kn = 3/15 hours or 12 minutes.

In real life the assumptions made about the discipline to be followed by the doctor and patients may not hold good and thus model may turn out to be unrealistic.