Waiting Line Theory

1. DAVIS AQUILANO CHASE PowerPointPresentation by Charlie Cook Waiting Line Theory F O U R T H E D I T I O N supplement 11 © The McGraw-Hill Companies, Inc., 2003

2. Supplement Objectives • Introduce the major characteristics that exist in waiting lines and describe how they can impact a customer’s waiting time. • Identify the various constraints and/or conditions that waiting line theory and its associated equations require for the results to be valid. • Present waiting line theory in the form of a set of equations that represent various types of waiting line configurations that can be encountered. Fundamentals of Operations Management 4e

3. Waiting Line Characteristics • Major Components • The source population • The way customers arrive at the service facility • The physical line itself • The way customers are selected from the line • The characteristics of the service facility itself • The condition of the customers when they exit the system Fundamentals of Operations Management 4e

4. Framework for Viewing Waiting Line Structures Exhibit S11.1 Fundamentals of Operations Management 4e

5. Population Source • Finite Population • Limited size of the customer pool • Each customer leaving or returning to the pool changes the probability of a customer requiring service. • Infinite Population • A customer pool so large that subtractions or additions to the pool do not significantly affect system probabilities. Fundamentals of Operations Management 4e

6. Arrival Characteristics • Pattern of Arrivals • Controllable or uncontrollable • Size of Arrival Units • One at a time or in batches • Distribution Pattern • Constant or statistically distributed rates of arrivals • Degree of Patience • Whether the arrival stays in line or leaves • Balking or reneging Fundamentals of Operations Management 4e

7. Arrival Characteristics in Queues Exhibit S11.2 Fundamentals of Operations Management 4e

8. Physical Features of Lines • Length • Infinite potential length • limited line capacity • Number of Lines • Single or multiple lines Fundamentals of Operations Management 4e

9. Customer Selection • Factors in a Queuing Discipline Exhibit S11.3 Fundamentals of Operations Management 4e

10. Service Facility Structure Exhibit S11.4 Fundamentals of Operations Management 4e

11. Arrival Characteristics (cont’d) • Service Rate • The capacity of a service station, usually expressed in terms of customers per hour. • The reciprocal of the service rate is the average time to serve a customer. • Capacity Utilization • The percentage of time a service station is busy serving a customer. • Exit • Customer returns to the waiting population. • Customer does not return to the population. Fundamentals of Operations Management 4e

12. Waiting Line Equations Average total waiting time in the system is equal to the average waiting time in the system plus the average service time: Little’s Formula—the average total number of customers in the system is directly related to the total time in the system: Fundamentals of Operations Management 4e

13. Properties of Specific Waiting Line Models Exhibit S11 .5 Fundamentals of Operations Management 4e

14. Equations for Solving Six Model Problems Exhibit S11.6a Fundamentals of Operations Management 4e

15. Equations for Solving Six Model Problems(cont’d) Exhibit S11.6b Fundamentals of Operations Management 4e

16. Notations for Equations (Exhibit S11.6) Exhibit S11.7 Fundamentals of Operations Management 4e

17. Calculating the Relationship between Capacity Utilization and Waiting Time Exhibit S11.8 Fundamentals of Operations Management 4e

18. The Relationship between Capacity Utilization and Waiting Time Exhibit S11.9 Fundamentals of Operations Management 4e

19. The Trade-off between Balking and Reneging Exhibit S11.10 Fundamentals of Operations Management 4e