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h) If a second drive-through window, with its own server, were added, the average time a car is in the system = minutes (round your response to two decimal places).

h) If a second drive-through window, with its own server, were added, the average time a car is in the system = minutes (round your response to two decimal places).

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Please answer part h.

### Drive-Through Post Office Analysis Automobiles arrive at the drive-through window at the downtown Baton Rouge, Louisiana, post office at a rate of 2 every 10 minutes. The average service time is 1.0 minute. A Poisson distribution is used to model the arrival rate and service times as they are negatively exponentially distributed. #### Key Metrics: a) **Average Time in System:** - Each car spends an average of **1.25 minutes** in the system. b) **Average Number of Cars in System:** - On average, there are **0.25 cars** in the system at any given time. c) **Average Number of Cars Waiting:** - The average number of cars waiting for service is **0.00 cars**. d) **Average Time in Queue:** - Each car spends an average of **0.25 minutes** in the queue. e) **Probability of No Cars at Window:** - There is an **80% probability** that no cars are at the window. f) **Clerk Busyness:** - The postal clerk is busy **20%** of the time. g) **Probability of Exactly 2 Cars in System:** - There is a **3.2% probability** of having exactly 2 cars in the system. h) **Impact of Adding a Second Window:** - If a second drive-through window with its own server was added, determine the average time a car would spend in the system. These metrics are crucial for optimizing operations and ensuring efficient service at the post office drive-through.
Transcribed Image Text:### Drive-Through Post Office Analysis Automobiles arrive at the drive-through window at the downtown Baton Rouge, Louisiana, post office at a rate of 2 every 10 minutes. The average service time is 1.0 minute. A Poisson distribution is used to model the arrival rate and service times as they are negatively exponentially distributed. #### Key Metrics: a) **Average Time in System:** - Each car spends an average of **1.25 minutes** in the system. b) **Average Number of Cars in System:** - On average, there are **0.25 cars** in the system at any given time. c) **Average Number of Cars Waiting:** - The average number of cars waiting for service is **0.00 cars**. d) **Average Time in Queue:** - Each car spends an average of **0.25 minutes** in the queue. e) **Probability of No Cars at Window:** - There is an **80% probability** that no cars are at the window. f) **Clerk Busyness:** - The postal clerk is busy **20%** of the time. g) **Probability of Exactly 2 Cars in System:** - There is a **3.2% probability** of having exactly 2 cars in the system. h) **Impact of Adding a Second Window:** - If a second drive-through window with its own server was added, determine the average time a car would spend in the system. These metrics are crucial for optimizing operations and ensuring efficient service at the post office drive-through.
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