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.

1. What is the expected number of patients that are either being seen or waiting to be seen by the triage nurse on weekdays?
2. What is the expected amount of time that a patient will spend waiting before being seen by the triage nurse on weekdays?

Consider the scenario presented in problem 1.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.

1. What is the expected number of patients that are either being seen or waiting to be seen by the triage nurse on weekends?
2. What is the expected amount of time that a patient will spend waiting before being seen by the triage nurse on weekends?

The urgent care facility adds a second triage nurse on the weekends to help with the increased rate of arriving patients.

1. What is the expected number of patients that are either being seen or waiting to be seen by the triage nurses on weekends?
2. What is the expected amount of time that a patient will spend waiting before being seen by the triage nurses on weekends?

Labs that are drawn by providers in a certain hospital are sent to a centralized laboratory through a vacuum system for analysis.Upon arriving to the laboratory, the specimens wait in a collection area until they picked up by a technician for processing.Assume all laboratory specimens have the same priority and are taken from the collection area one at a time by a technician.Further, assume that there is only one technician.From historical data, it is known that the arrival of laboratory specimens follows a Poisson distribution with a mean of 37.6 labs per hour.From the same data, the distribution of the time between the retrieval of specimens from the collection area was not able to be determined, but the sample mean time was calculated to be1.5 min (i.e. 0.025 hrs) and the standard deviation to be0.6 min (i.e. 0.01 hrs).Note that the collection area represents a queue, and the act of being processed represents time in the server.

• What is the expected utilization of the lab collection area?
• How many laboratory specimens would you expect to be in the collection area at any one time?
• How long (in minutes) would you expect a laboratory specimen to wait in the collection area before begin retrieved?
• Suppose that it was incorrectly assumed that time between the retrieval of specimens is Exponentially distributed with a mean of 1.5 min(i.e. modeled as an M/M/1 instead of M/G/1 queue).How long would you expect a laboratory specimen to wait in the collection area before being retrieved under this assumption?Compare this answer to that found in part (c)
• The hospital is considering implementing a process improvement program for the laboratory.If the program decreases the standard deviation of processing time from .6 min to .3 min (but leaves the mean unchanged), how long would you expect a laboratory specimen to wait in the collection area before being retrieved?Compare this answer to that found in part (c).Did the utilization of the laboratory technician change following this process improvement program?
• The hospital is considering implementing a process improvement program for the laboratory.If the program decreases the mean processing time from 1.5min to 1.25min (but leaves the standard deviation unchanged), how long would you expect a laboratory specimen to wait in the collection area before being retrieved?Compare this answer to that found in part (c).Did the utilization of the laboratory technician change following this process improvement program?