A fast-food restaurant has one drive-in window. It is estimated that cars arrive according to a Poisson distribution at the rate of 3 every 6 minutes and that there is enough space to accommodate a line of 12 cars. Other arriving cars can wait outside this space, if necessary. It takes 2.5 minutes on the average to fill an order, but the service time actually varies according to an exponential distribution. Determine the following: The probability that the facility is not idle; The expected number of customers waiting but currently not being served; The expected waiting time until a customer can place his order at the window;
A fast-food restaurant has one drive-in window. It is estimated that cars arrive according to a Poisson distribution at the rate of 3 every 6 minutes and that there is enough space to accommodate a line of 12 cars. Other arriving cars can wait outside this space, if necessary. It takes 2.5 minutes on the average to fill an order, but the service time actually varies according to an exponential distribution. Determine the following: The probability that the facility is not idle; The expected number of customers waiting but currently not being served; The expected waiting time until a customer can place his order at the window;
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 fast-food restaurant has one drive-in window. It is estimated that cars arrive according to a Poisson distribution at the rate of 3 every 6 minutes and that there is enough space to accommodate a line of 12 cars. Other arriving cars can wait outside this space, if necessary. It takes 2.5 minutes on the average to fill an order, but the service time actually varies according to an exponential distribution. Determine the following:
The probability that the facility is not idle;
The expected number of customers waiting but currently not being served;
The expected waiting time until a customer can place his order at the window;
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