Review It!


Questions

  1. Identify ten real-life examples of queuing systems with which you are familiar.
  2. Why must the utilization factor in a single-server model be less than 1?
  3. Give five examples of real-world queuing systems with finite calling populations.
  4. List the elements that define a queuing system.
  5. How can the results of queuing analysis be used by a decision maker for making decisions?
  6. What is the mean effective service rate in a multiple-server model, and what must be its relationship to the arrival rate?
  7. For each of the following queuing systems, indicate if it is a single- or multiple-server model, the queue discipline, and if its calling population is infinite or finite:
    1. Hair salon
    2. Bank
    3. Laundromat
    4. Doctor's office
    5. Adviser's office
    6. Airport runway
    7. Service station
    8. Copy center
    9. Team trainer
    10. Mainframe computer
  8. In Example 16.2 in this chapter, the second alternative was to add a new checkout counter at the market. This alternative was analyzed using the single-server model. Why was the multiple-server model not used?
  9. Discuss briefly the relationship between waiting line analysis and quality improvement.
  10. Define the four basic waiting line structures and give an example of each.
  11. Describe the traditional cost relationship in waiting line analysis.
    1. Is the following statement true or false? The single-phase, single-channel model with Poisson arrivals and undefined service times will always have larger (i.e., greater) operating characteristic values (i.e., W, Wq, L, Lq) than the same model with exponentially distributed service times. Explain your answer.
    2. Is the following statement true or false? The single-phase, single-channel model with Poisson arrivals and constant service times will always have smaller (i.e., lower) operating characteristic values (i.e., W, Wq, L, Lq) than the same model with exponentially distributed service times. Explain your answer.
  12. Under what conditions can the basic single-server and multiple-server models be used to analyze a multiple-phase waiting line system?
  13. Why do waiting lines form at a service facility even though there may be more than enough service capacity to meet normal demand in the long run?
  14. Provide an example of when a first-in, first-out (FIFO) rule for queue discipline would not be appropriate.
  15. Under what conditions will the single-channel, single-phase queuing model with Poisson arrivals and undefined service times provide the same operating characteristics as the basic model with exponentially distributed service times?
  16. What types of waiting line systems have constant service times?


Drag & Drop Exercise

With your mouse, drag the equations to the proper location on the chart.

    Launch Exercise 16.1


Solved Problems

1. Single-Server Model

The new-accounts officer at the Citizens Northern Savings Bank enrolls all new customers in checking accounts. During the 3-week period in August encompassing the beginning of the new school year at State University, the bank opens a lot of new accounts for students. The bank estimates that the arrival rate during this period will be Poisson distributed with an average of 4 customers per hour. The service time is exponentially distributed with an average of 12 minutes per customer to set up a new account. The bank wants to determine the operating characteristics for this system to determine if the current person is sufficient to handle the increased traffic.

Solution:

Determine operating characteristics for the single-server system:

The average waiting time of 48 minutes and the average time in the system are excessive, and the bank needs to add an extra employee during the busy period.

2. Multiple-Server Model

The Citizens Northern Bank wants to compute the operating characteristics if an extra employee was added to assist with new-accounts enrollments.

Solution:

Determine the operating characteristics for the multiple-server system:

The waiting time with the multiple-server model is 2.3 minutes, which is a significant improvement over the previous system; thus the bank should add the second new-accounts officer.