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Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times.

What percentage of time is Judy idle?

How much time, on average, does a student spend waiting in line?

How long is the (waiting) line on average?

What is the probability that an arriving student (just before entering the Administrative

Services Office) will find at least one other student waiting in line?

NUMBER 2

Burrito King (a new fast-food franchise opening up nationwide) has successfully automated burrito production for its drive-up fast-food establishments. The Burro-Master 9000 requires a constant 45 seconds to produce a batch of burritos. It has been estimated that customers will arrive at the drive-up window according to a Poisson distribution at an average of one every 50 seconds. To help determine the amount of space needed for the line at the drive-up window, Burrito King would like to know

the expected average time in the system

the average line length (in cars), and

the average number of cars in the system (both in line and at the window).

Number 3

The Bijou Theater shows vintage movies. Customers arrive at the theater line at the rate of 100 per hour. The ticket seller averages 30 seconds per customer, which includes placing validation stamps on customers parking lot receipts and punching their frequent watcher cards. (Because of these added services, many customers dont get in until after the feature has started.) What is the system waiting time if a second window was opened with each server doing all three tasks?