Patients arrive to a small hospital emergency room according to a Poisson process with anaverage rate of 1.5 per hour. Because service times for these patients vary considerably, theservice times are accurately described by an exponential distribution. Suppose that the averageservice time is 26 minutes. If there is only a single doctor working at any point in time, find thefollowing measures of service for this emergency room:The expected total time in the system.b. The expected time each customer has to wait.c. The expected number of patients waiting for service.d. If the emergency room has a triage nurse who gives priority to more serious conditions,explain qualitatively how that would change your results to parts a, b, and c. Whatadditional information would one need to know to analyze a system like this?

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Answered: The expected total time in the system.…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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Patients arrive at your emergency room at a rate of 2 per hour. The average service time per patient is 20 minutes. In other words, you treat an average of 3 patients per hour if patients come in that fast. 1. To proceed with your analysis, what do you assume about the distributions of arrivals and service times? 2. What is the average number of patients in the ER (waiting or being served?) (Use formulae on p.21-22) 3. What is the average length of time that patients spend from the time they enter the ER to the time they leave?
Give and explain briefly that in what kinds of situations is queuing analysis is most appropriate.
Describe a situation in your daily life that could be improved by waiting line analysis. Explain how the design of a waiting system can negatively affect customers. Visit your local bank and observe the waiting line system. Describe the system in terms of number of lines, number of facilities, and number of phases.
Explain what are the most common measures of system performance in a queuing analysis ?
Patients arrive to a small hospital emergency room according to a Poisson process with an average rate of 1.5 per hour. Because service times for these patients vary considerably, the service times are accurately described by an exponential distribution. Suppose that the average service time is 26 minutes. If there is only a single doctor working at any point in time, find the following measures of service for this emergency room:a. The expected total time in the system.b. The expected time each customer has to wait.c. The expected number of patients waiting for service.d. If the emergency room has a triage nurse who gives priority to more serious conditions, explain qualitatively how that would change your results to parts a, b, and c. What additional information would one need to know to analyze a system like this?
A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup andis constant. Customers arrive at a mean rate of 80 per hour, and this rate is Poissondistributed.A) Identify the Queuing Model and sketch the system.B) What is the arrival rate?C) What is the service rate?
6. The Garrett-Tompkins Company provides three copy machines in its copying room for the use of its employees. However, due to recent complaints about considerable time being wasted waiting for a copier to become free, management is considering adding one or more additional copy machines. During the 2,000 working hours per year, employees arrive at the copying room according to a Poisson process at a mean rate of 40 per hour. The time each employee needs with a copy machine is believed to have an exponential distribution with a mean of 4 minutes. The lost productivity due to an employee spending time in the copying room is estimated to cost the company an average of $40 per hour. Each copy machine is leased for $4,000 per year. Find the following values for this system: λ, μ, Cs, Cw. Then use the Excel template to determine how many copy machines the company should have to minimize its expected total cost per hour. List your result in the following table. : S 3 4 5 P E(TC) = E(SC) + E…

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The expected total time in the system. b. The expected time each customer has to wait. c. The expected number of patients waiting for service. а. с.