Question

An orthopedic clinic takes appointments between 8:00 and 11:30 a.m. and between 1:00 and 3:30 p.m. and is operational 234 days per year. The clinic receives 24,903 visits annually. Because patient visits involve more than just a visit with the MD, the clinic flow is not a simple in-and-out process. Patients are subjected to a multiple-line queuing system. The first step is patient registration. Four registration clerks are able to register an average of 5.5 patients per hour. Registration includes co-pay collection, insurance and referral verification, and updating demographics in the computer information system. Although the clerical staff have other duties at the end of the day, their only responsibility for this six-hour span is to register patients. The second step is nurse check-in, in which six nurses spend an average of ten minutes with each patient. The average time a patient is with one of the seven MDs is twenty-four minutes. Arrivals follow a Poisson distribution, with a mean of 15 for all steps.

For each individual process (registration, nurse check-in, and MD visit), compute the following performance metrics using the Excel queuing template:

a. Arrival and service rates

b. Average number of patients in a queue

c. Average number of patients in the system

d. Probability of idle time

e. System utilization rate

Answer 1

To find the probabilities related to the time between patient visits at an urgent care facility, we use the exponential distribution. We can calculate the probabilities of various time intervals using the cumulative distribution function. The probabilities of interest include the probability that the time between two visits is less than two minutes, more than 15 minutes, and the conditional probability of the next arrival within five minutes. Finally, we can find the probability of more than eight patients arriving during a half-hour period using the Poisson distribution.

Step-by-step explanation:

To find the probability that the time between two successive visits to the urgent care facility is less than two minutes, we need to calculate the cumulative distribution function (CDF) of the exponential distribution with a mean of seven minutes and evaluate it at two minutes. This can be done using the formula:

P (T<2) = 1 - e^(-2/7)

To find the probability that the time between two successive visits is more than 15 minutes, we use the complementary CDF:

P (T>15) = 1 - P(T<15) = 1 - (1 - e^(-15/7))

To find the probability that the next person arrives within the next five minutes, we need to calculate the conditional probability:

P(T<5 | T>10) = P(T<5 and T>10) / P(T>10)

To find the probability that more than eight patients arrive during a half-hour period, we can use the Poisson distribution formula:

P(X > 8) = 1 - P(X <= 8)