A fast-food restaurant has one drive-in window. Cars arrive according to a Poisson distribution at the...

 

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A fast-food restaurant has one drive-in window. Cars arrive according to a Poisson distribution at the rate of 2 cars every 5 minutes. The space in front of the window can accommodate at most 10 cars, including the one being served. Other cars can wait outside this space if necessary. The service time per customer is exponential, with a mean of 1.5 minutes. Determine the following: a. The probability that the facility is idle. b. The expected number of customers waiting to be served. c. The expected waiting time until a customer reaches the window to place an order. d. The probability that the waiting line will exceed the 10 space capacity. A fast-food restaurant has one drive-in window. Cars arrive according to a Poisson distribution at the rate of 2 cars every 5 minutes. The space in front of the window can accommodate at most 10 cars, including the one being served. Other cars can wait outside this space if necessary. The service time per customer is exponential, with a mean of 1.5 minutes. Determine the following: a. The probability that the facility is idle. b. The expected number of customers waiting to be served. c. The expected waiting time until a customer reaches the window to place an order. d. The probability that the waiting line will exceed the 10 space capacity.

Answer rating: 100% (QA)

To solve this problem we can use the MM1 queueing model where M represents the Poisson arrival proce... View the full answer