Problems
1. Melanie is the manager of the Clean Machine car wash and has gathered the following information. Customers arrive at a rate of eight per hour according to a Poisson distribution.
The car washer can service an average of ten cars per hour with service times described by an exponential distribution. Melanie is concerned about the number of customers waiting in line. She has asked you to calculate the following system characteristics:
(a) Average system utilization
(b) Average number of customers in the system
(c) Average number of customers waiting in line
2. Melanie realizes that how long the customer must wait is also very important. She is also concerned about customers balking when the waiting line is too long. Using the arrival and service rates in Problem 1, she wants you to calculate the following system characteristics:
(a) The average time a customer spends in the system
(b) The average time a customer spends waiting in line
(c) The probability of having more than three customers in the system
(d) The probability of having more than four customers in the system
3. If Melanie adds an additional server at Clean Machine car wash, the service rate changes to an average of 16 cars per hour. The customer arrival rate is 10 cars per hour. Melanie has asked you to calculate the following system characteristics:
(a) Average system utilization
(b) Average number of customers in the system
(c) Average number of customers waiting in line
4. Melanie is curious to see the ...
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