A local café has a single cash register, with a single assistant to work it, and three servers working to fill the customer orders. Customers arrive with exponential interarrivaltime an average of one every 2 minutes. The time to place their order and pay at theregister is normally distributed with mean 90 seconds and standard deviation 20 seconds. Each customer’s order is then passed to one of the servers who take on average5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order.c. What is the probability a customer is delayed at the register?
A local café has a single cash register, with a single assistant to work it, and three servers working to fill the customer orders. Customers arrive with exponential interarrivaltime an average of one every 2 minutes. The time to place their order and pay at theregister is normally distributed with mean 90 seconds and standard deviation 20 seconds. Each customer’s order is then passed to one of the servers who take on average5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order.c. What is the probability a customer is delayed at the register?
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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A local café has a single cash register, with a single assistant to work it, and three servers working to fill the customer orders. Customers arrive with exponential interarrival
time an average of one every 2 minutes. The time to place their order and pay at the
register is
5 minutes with standard deviation 1.5 minutes, also normally distributed, to fill the order.
c. What is the probability a customer is delayed at the register?
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