Dean Smith is dissatisfied with the time it takes to get a new faculty ID made and believes more servers will speed up service and reduce costs thanks to shorter lines. Prof. Karen is tasked to study the situation. Prof. Karen observes an average of 20 customers/hr arriving and each technician (service window) serves 5 customers/hr, on average. There are a total of 4 servers. Assume an M/M/s queue system. Dean Smith suggests that the average time in the QUEUE should be 4 minutes or less. How fast must each service worker work to achieve 4 minutes on average in the Queue? That is, what is the service rate necessary to get to this goal? Please provide an answer to 2 decimal places.

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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Dean Smith is dissatisfied with the time it takes to get a new faculty ID made and believes more servers will speed up service and reduce costs thanks to shorter lines. Prof. Karen is tasked to study the situation. Prof. Karen observes an average of 20 customers/hr arriving and each technician (service window) serves 5 customers/hr, on average. There are a total of 4 servers. Assume an M/M/s queue system.

Dean Smith suggests that the average time in the QUEUE should be 4 minutes or less. How fast must each service worker work to achieve 4 minutes on average in the Queue? That is, what is the service rate necessary to get to this goal? Please provide an answer to 2 decimal places.

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