Exam 13: Queuing Theory

Exhibit 13.1 The following questions are based on the output below. A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system. -If a company adds an additional identical server to its M/M/1 system, making an M/M/2 system, what happens to a customer's average service time?

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -The objective in queuing problems is to find the service level that achieves an acceptable balance between the cost of providing service and customer satisfaction.

Exhibit 13.1 The following questions are based on the output below. A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system. -A company has recorded the following list of service rates (customers/hour) for one of its servers. What is the mean service time for this server? ​ Customers / hour: 4, 4, 5, 6, 5, 4, 3, 4, 3, 5, 5, 6 ​

Exhibit 13.7 The following questions refer to the information and output below. A tax accountant has found that the time to serve a customer has a mean of 30 minutes (or 0.5 hours) and a standard deviation of 6 minutes (or 0.1 hours). Customer arrivals follow a Poisson distribution with an average of 60 minutes between arrivals. The following queuing analysis spreadsheet was developed from this information. -Refer to Exhibit 13.7. Based on this report what is the average number of customers waiting to be helped?

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -Which of the following best describes queuing theory?

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -The amount of time a customer spends with the server is referred to as

Exhibit 13.1 The following questions are based on the output below. A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system. -If a service system has a constant service time, Poisson arrival rates and 2 servers its Kendall notation is

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -Joe's Copy Center has 10 copiers. They break down and require service quite often. Time between breakdowns follows an exponential distribution for each copier. The repair person services machines as quickly as possible, but the service time follows an exponential distribution. What type of system is it?

Exhibit 13.1 The following questions are based on the output below. A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system. -Which type of queuing system are you likely to encounter at an ATM?

Exhibit 13.6 The following questions refer to the information and output below. The university computer lab has 10 computers which are constantly being used by students. Users need help from the one lab assistant fairly often. Students ask for help at a Poisson rate of with an average of 4 requests per hour for any one computer. The assistant answers questions as quickly as possible and the service time follows an exponential distribution with mean of 1 minute per help session. The following queuing analysis spreadsheet was developed from this information. -The customer service desk at Joe's Discount Electronics store receives 5 customers per hour on average. On average, each customer requires 10 minutes for service. The customer service desk is staffed by a single person. What is the average time a customer spends in the customer service area if modeled as an M/M/1 queuing system?

Exhibit 13.1 The following questions are based on the output below. A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system. -Which of the following is the typical operating characteristic for average number of units in a queue?

Exhibit 13.1 The following questions are based on the output below. A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system. -To find steady-state values for the M/M/S queuing system, which of the following statements must be true about the arrival rate?

Exhibit 13.6 The following questions refer to the information and output below. The university computer lab has 10 computers which are constantly being used by students. Users need help from the one lab assistant fairly often. Students ask for help at a Poisson rate of with an average of 4 requests per hour for any one computer. The assistant answers questions as quickly as possible and the service time follows an exponential distribution with mean of 1 minute per help session. The following queuing analysis spreadsheet was developed from this information. -Customers arrive at a store randomly, following a Poisson distribution at an average rate of 20 per hour. What is the probability of exactly 0, 1 2, and 3 arrivals in a 15 minute period?

Exhibit 13.1 The following questions are based on the output below. A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system. -A doctor's office only has 8 chairs. The doctor's service times and customer inter-arrival times are exponentially distributed. What type of system is it?

Exhibit 13.5 The following questions refer to the information and output below. A computer printer in a large administrative office has a printer buffer (memory to store printing jobs) capacity of 3 jobs. If the buffer is full when a user wants to print a file the user is told that the job cannot be printed and to try again later. There are so many users in this office that we can assume that there is an infinite calling population. Jobs arrive at the printer at a Poisson rate of 55 jobs per hour and take an average of 1 minute to print. Printing times are exponentially distributed. The following queuing analysis spreadsheet was developed from this information. -Refer to Exhibit 13.5. Based on this report what is the average number of jobs waiting to be printed?

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -The memoryless property is also referred to as the ____ property.

Exhibit 13.2 The following questions refer to the information and output below. A barber shop has one barber who can give 12 haircuts per hour. Customers arrive at a rate of 8 customers per hour. Customer inter-arrival times and service times are exponentially distributed. The following queuing analysis spreadsheet was developed from this information. -A grocery clerk can serve 20 customers per hour on average and the service time follows an exponential distribution. What is the expected service time per customer?

Exhibit 13.5 The following questions refer to the information and output below. A computer printer in a large administrative office has a printer buffer (memory to store printing jobs) capacity of 3 jobs. If the buffer is full when a user wants to print a file the user is told that the job cannot be printed and to try again later. There are so many users in this office that we can assume that there is an infinite calling population. Jobs arrive at the printer at a Poisson rate of 55 jobs per hour and take an average of 1 minute to print. Printing times are exponentially distributed. The following queuing analysis spreadsheet was developed from this information. -Refer to Exhibit 13.5. What is the Kendall notation for this system?

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -In a queuing problem, Wq > W.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -Which of the following is a reason to employ queuing theory?