Assignment- Wait Lines and Queuing Theory Models

Scenario One: Automobiles arrive at the drive-through window of the Elm Street branch of the local bank at the rate of 1 every ten minutes. The average service time is 8 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.

Question 1: What is the average number of customers in the system (in line plus being served)?
Question 2: What is the average time a customer spends in the system?
Question 3: What is the average number of customers in line "behind" the customer receiving service (queue)?
Question 4: What is the average time customers spend waiting to receive service?
Question 5: What is the probability the customer service person is busy?
Question 6: What is the percent of time (or the probability) that there are zero customers at the serving window?
Question 7: What is the probability that there are more than two customers in the system?
Question 8: What is the probability that there are exactly two customers in the system?
Question 9: What is the probability that there are two or less customers in the system?
Question 10: What is the probability that there are less than two customers in the system?

Scenario Two: The salary and benefits for a bank teller at the Elm Street branch is $16.50 per hour. If it has been estimated that the waiting time cost per hour is $65.00 per hour in line. Assume the bank is open 8 hours each day.

Question 11: How many customers would enter the bank's drive-in system on a typical day?
Question 12: How much total time would the customers spend waiting in line (system) during the entire day if one lane were open?
Question 13: If only one lane is open, what is the total daily waiting time cost of the system?
Question 14: If only one lane is open what is the total wait and service cost of the system?
Question 15: How much total time would the customers spend in line waiting to be serviced (queue) during the entire day if one lane were open?
Question 16: If only one lane is open, what is the daily total cost of thequeuingwait time?
Question 17: If only one lane is open what are the total service and queuing wait time costs?

Scenario Three: On Friday's the Elm Street branch opensa secondlane (window)during its 8 hours of operation in order to accommodate employees from a local manufacturing plant who want to deposit their paychecks. When a customer in the single line reaches the front of the line, it would go to the next available lane (window)for service. On Friday's customers arrive at the rate of about10 every hour according to a Poisson distribution and, on average,eachcustomer service person can process a transaction every 3 minutes, following an exponential distribution. The salary and benefits for a bank teller at the Elm Street branch is $16.50 per hour. If it has been estimated that the waiting time cost per hour is $65.00 per hour in line.

Question 18: What is the average number of customers in the system?
Question 19: What is the average number of customers in line "behind" the customer(s) receiving service?
Question 20: What is the average waiting time a customer spends in the system?
Question 21: What is the average time a customer is in the queue waiting to be serviced?
Question 22: What is the probability that there are no customers in line or being serviced?
Question 23: What percentage of the time are the customer service persons busy?
Question 24: How much total time would customers spend waiting in line to be serviced (queue) on a typical day?
Question 25: What is the total daily cost of customers waiting in line to be serviced (queue) on a typical day?
Question 26: What is the total daily cost of customers waiting in the system on a typical day?
Question 27: What is the total daily cost of customers waiting in the system plus the cost of service on a typical day?