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?

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
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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?

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