Question

An urgent care facility has the policy that all arriving patients be seen by a triage nurse before being admitted for care by a provider. There is one triage nurse at this facility and based on data that has been collected over the past several years, it is discovered that the arrival of patients on weekdays follows a Poisson Distribution with a mean of 5.5 per hour. It is further discovered from the data that the time the triage nurse spends with each patient is Exponentially distributed with a mean of 7.5 minutes.

On weekend, the mean arrival of patients to the urgent care facility is greater than on weekdays, with the average being 6.75 patients per hour.

a. What is the expected number of patients that are either being seen or waiting to be seen by the triage nurse on weekends?

b. What is the expected amount of time that a patient will spend waiting before being seen by the triage nurse on weekends?

Answer 1

a.

Arrival rate, = 6.75 patients per hour

Service rate = 1 patient per 7.5 minutes = (60/7.5) patients per hour = 8 patients per hour

Using M/M/1 model,

Expected number of patients that are either being seen or waiting to be seen by the triage nurse on weekends

= / ( - )

= 6.75 / (8 - 6.75)

= 5.4 patients

b.

Expected amount of time that a patient will spend waiting before being seen by the triage nurse on weekends

= / ( - )

= 6.75 /(8 * (8 - 6.75))

= 0.675 hour

= 40.5 minutes