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# For Dave's Carwash, the arrival rate is 8 / hour and the service rate is 15 / hour. The arrival and service distributions are not known so we can't...

For Dave's Carwash, the arrival rate is 8 / hour and the service rate is 15 / hour. The arrival and service distributions are not known so we can't use the M/M/1 formulas. If the average waiting time in the line is 23 minutes, then what is the length of the line?

For Dave's Carwash, the arrival rate is 9 / hour and the service rate is 14 / hour. The arrival and service distributions are not known so we can't use the M/M/1 formulas. If the average waiting time in the line is 22 minutes, then how many customers (waiting and being served) are at the Carwash?

There is only one copying machine in the student lounge of the business school. Students arrive at the rate of = 40 per hour (according to a Poisson distribution). Copying takes an average of 40 seconds (according to an exponential distribution). What is the probability that there will be 2 students in the system?

Dave's is a take-out yogurt shop. Customers arrive at a rate of 25 per hour. Dave serves a customer, on the average, in 1.5 minutes. Assume that the arrivals and the service times are Poisson distributed and exponentially distributed, respectively. What is the probability that a customer will wait between 3 to 6 minutes?

Dave's is a take-out yogurt shop. Customers arrive at a rate of 30 per hour. Dave doesn't want a customer to be more than 3 minutes in the shop. What should be the service rate / hour which will make it possible?

The Atlanta International Airport currently operates with one runway. Airplanes arrive at a rate of 19 per hour and the average landing time is 2.8 minutes. The estimated average fuel consumption for an aircraft stacking in the air is 18 liters per minute, and a liter of fuel costs $7. What is the average cost of fuel burned by an aircraft waiting to land?

The Atlanta International Airport currently operates with one runway. Airplanes arrive at a rate of 17 per hour and the average landing time is 2.8 minutes. The estimated average fuel consumption for an aircraft stacking in the air is 19 liters per minute, and a liter of fuel costs $11. What is the chance of finding 1 or less airplanes in the airport area including those that are in the waiting line and the one that is landing?