- HW6 (BONUS) Computer Simulation Systems - Due Jan 6th, end of day. Calculate your factor...

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- HW6 (BONUS) Computer Simulation Systems - Due Jan 6th, end of day. Calculate your factor f as the very first thing in answering hw questions. f=max [0.15, (Average of the last two digits of your ids)/100]. Q1. A fast-food restaurant has one drive-through window. An average of 40+10f customers per hour arrive at the window. It takes an average of 1 minute to serve a customer. Assume that interarrival and service times are exponential. a On the average, how many customers are waiting in line? b On the average, how long does a customer spend at the restaurant (from time of arrival to time service is completed)? c What fraction of the time are more than 3 cars waiting for service (this includes the car (if any) at the window)? Q2. The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee's time is worth $15 per hour. The slow copier rents for $4 per hour and it takes an employee an average of 10+5f minutes to complete copying (exponentially distributed). The fast copier rents for $15 per hour and it takes an employee an average of 6+5f minutes to complete copying. An average of 4 employees per hour need to use the copying machine (interarrival times are exponential). Which machine should the department rent? Answer the same question with the following change: In the fast copier, Copying time does not follow exponential distribution and it takes an employee an average of 6+5f minutes to complete copying with a the standard deviation of copying time = 2.5 minutes. (M/G/1 correction needed) Q3. An average of 40-10f cars per hour (interarrival times are exponentially distributed) are tempted to use the drive-in window at the Hot Dog King Restaurant. If a total of more than 4 cars are in line (including the car at the window) a car will not enter the line. It takes an average of 4 minutes (exponentially distributed) to serve a car. a What is the average number of cars waiting for the drive-in window (not including a car at the window)? b On the average, how many cars will be served per hour? c I have just joined the line at the drive-in window. On the average, how long will it be before I have received my food? my ID number 202003214 last two digits is 14 - HW6 (BONUS) Computer Simulation Systems - Due Jan 6th, end of day. Calculate your factor f as the very first thing in answering hw questions. f=max [0.15, (Average of the last two digits of your ids)/100]. Q1. A fast-food restaurant has one drive-through window. An average of 40+10f customers per hour arrive at the window. It takes an average of 1 minute to serve a customer. Assume that interarrival and service times are exponential. a On the average, how many customers are waiting in line? b On the average, how long does a customer spend at the restaurant (from time of arrival to time service is completed)? c What fraction of the time are more than 3 cars waiting for service (this includes the car (if any) at the window)? Q2. The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee's time is worth $15 per hour. The slow copier rents for $4 per hour and it takes an employee an average of 10+5f minutes to complete copying (exponentially distributed). The fast copier rents for $15 per hour and it takes an employee an average of 6+5f minutes to complete copying. An average of 4 employees per hour need to use the copying machine (interarrival times are exponential). Which machine should the department rent? Answer the same question with the following change: In the fast copier, Copying time does not follow exponential distribution and it takes an employee an average of 6+5f minutes to complete copying with a the standard deviation of copying time = 2.5 minutes. (M/G/1 correction needed) Q3. An average of 40-10f cars per hour (interarrival times are exponentially distributed) are tempted to use the drive-in window at the Hot Dog King Restaurant. If a total of more than 4 cars are in line (including the car at the window) a car will not enter the line. It takes an average of 4 minutes (exponentially distributed) to serve a car. a What is the average number of cars waiting for the drive-in window (not including a car at the window)? b On the average, how many cars will be served per hour? c I have just joined the line at the drive-in window. On the average, how long will it be before I have received my food? my ID number 202003214 last two digits is 14