QUEUING MODELS Queuing Exercise Lab Exercise (25 Points) SCM 300 The purpose of this exercise is to discuss the situation facing a manager and help her determine how many servers to use and what the characteristics of the system will be. Endeavor Communications, a long distance provider, is reevaluating its account management department for handling customer service questions and requests. During the 2:00 pm to 10:00pm time period, past data show that calls to the account management department occur at an average rate of one call every 7.1 minutes. A study of past service tin indicate that the average time to process a call question/request is 5.1 minutes. Like other phone systems, when a call comes in and all the servers are busy, the caller hears a message telling them to hold until the next server is available. Top management at Endeavor Communications understands that the staffing decision involves the analysis of trade-offs. Increasing the number of servers will reduce the waiting times and increase the probability of immediate service at a higher cost with more idle time for the servers. Management has decided that the GOAL of the account management department is to immediately answer and service at least 90% of the incoming calls during the busiest time period of 2:00pm to 10:00pm. They have asked you to determine the staffing level that will help them meet this goal. Also, they'd like you to provide your own recommendations. For questions 1-5 it is recommended you draw a picture of the underlined section of each question. Then draw a number line that will help you represent the entire statement. Hopefully, that will help you more easily get the correct answer. An example of how to do this is provided at the bottom of this page. 1. What is the probability there are exactly 2 customers in line in a two-server model? 2. What is the probability there are fewer than 2 customers in the system in a two server model? 3. What is the probability there are fewer than 1 single customer in the line in a three-server model? 4. What is the probability there are more than three customers in the system in a two-server model? 5. What is the probability there is more than one in line in a one-server model? 6. What is the probability of being served immediately in a three-server model? 7. What percentage of the time is the server busy in a two-server model? 8. On average, how much time does a customer spend in line in a single-server model? 9. On average, how many customers are on hold in a two-server model? 10. How many employees are required to meet the account management department's goal? QUEUING MODELS Queuing Exercise Lab Exercise (25 Points) SCM 300 The purpose of this exercise is to discuss the situation facing a manager and help her determine how many servers to use and what the characteristics of the system will be. Endeavor Communications, a long distance provider, is reevaluating its account management department for handling customer service questions and requests. During the 2:00 pm to 10:00pm time period, past data show that calls to the account management department occur at an average rate of one call every 7.1 minutes. A study of past service tin indicate that the average time to process a call question/request is 5.1 minutes. Like other phone systems, when a call comes in and all the servers are busy, the caller hears a message telling them to hold until the next server is available. Top management at Endeavor Communications understands that the staffing decision involves the analysis of trade-offs. Increasing the number of servers will reduce the waiting times and increase the probability of immediate service at a higher cost with more idle time for the servers. Management has decided that the GOAL of the account management department is to immediately answer and service at least 90% of the incoming calls during the busiest time period of 2:00pm to 10:00pm. They have asked you to determine the staffing level that will help them meet this goal. Also, they'd like you to provide your own recommendations. For questions 1-5 it is recommended you draw a picture of the underlined section of each question. Then draw a number line that will help you represent the entire statement. Hopefully, that will help you more easily get the correct answer. An example of how to do this is provided at the bottom of this page. 1. What is the probability there are exactly 2 customers in line in a two-server model? 2. What is the probability there are fewer than 2 customers in the system in a two server model? 3. What is the probability there are fewer than 1 single customer in the line in a three-server model? 4. What is the probability there are more than three customers in the system in a two-server model? 5. What is the probability there is more than one in line in a one-server model? 6. What is the probability of being served immediately in a three-server model? 7. What percentage of the time is the server busy in a two-server model? 8. On average, how much time does a customer spend in line in a single-server model? 9. On average, how many customers are on hold in a two-server model? 10. How many employees are required to meet the account management department's goal