1 / 31

Queuing Theory Models

Queuing Theory Models . By Nancy Hutchins. Agenda. What is queuing Why is queuing important How can this help our company Explanation How it works Summary Reading list. What is Queuing?. A queue is a line of waiting people, vehicles, products, etc.

nikki
Download Presentation

Queuing Theory Models

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Queuing Theory Models By Nancy Hutchins

  2. Agenda • What is queuing • Why is queuing important • How can this help our company • Explanation • How it works • Summary • Reading list

  3. What is Queuing? • A queue is a line of waiting people, vehicles, products, etc. • Queuing theory models use a mathematical approach to study queues and make them as efficient as possible

  4. Video Clip Office Space Grid Lock

  5. Why is this important? Inadequate queue management may lead to • Customers leaving before completing their transaction • Decrease in customer satisfaction • Reduction in number of return customers

  6. Why is this important? • Retaining customers much more cost effective than finding new customers • Many businesses depend on revenue from repeat customers

  7. How can this help your company? • Decrease average customer wait time • Increase customer satisfaction • Increase number of return customers • Increase revenue • Increase positive word-of-mouth customer advertising

  8. Basic Ways to Manage Queues • Train employees to be friendly • Segment customers by needs • Ensure customers know what to expect • Divert the customer’s attention during wait times • Encourage customers to come during slack times **Jacobs, F. Robert, and Richard B. Chase. "5." Operations and Supply Management The Core. New York: Irwin Professional Pub, 2006. 112. Print.

  9. The Queuing System

  10. Source Population Finite Infinite Large size Probabilities not affected by an increase/decrease in the population • Limited size • Probabilities affected by an increase/decrease in the population

  11. Distribution of Arrivals • Arrival Rate: is the number of units per period • Constant • Variable

  12. Exponential Distribution λe ^ (-λt) **Jacobs, F. Robert, and Richard B. Chase. "5." Operations and Supply Management The Core. New York: Irwin Professional Pub, 2006. 114. Print.

  13. Customer Arrivals in Queues • Arrival Characteristics • Distribution • Pattern • Size of Arrival • Degree of Patience

  14. Poisson Distribution PT(n) = Mean = = 3 Variance = = 3 **Jacobs, F. Robert, and Richard B. Chase. "5." Operations and Supply Management The Core. New York: Irwin Professional Pub, 2006. 115. Print.

  15. Pattern of Arrivals

  16. Size of Arrival Units

  17. Degree of Patience

  18. Queuing System Factors • Length • Infinite potential length • Limited capacity • Number of Lines • Single • Multiple • Queue Discipline

  19. Queue Discipline

  20. Service Time Distribution • Service rate: the capacity of the server in number of units per time period and not as service time. **Jacobs, F. Robert, and Richard B. Chase. "5." Operations and Supply Management The Core. New York: Irwin Professional Pub, 2006. 118. Print.

  21. Line Structures • Single Channel, Single Phase • Single Channel, Multiphase • Multichannel, Single phase • Multichannel, multiphase • Mixed

  22. Exiting the Queuing System

  23. Properties of Some Specific Line Models **Jacobs, F. Robert, and Richard B. Chase. "5." Operations and Supply Management The Core. New York: Irwin Professional Pub, 2006. 121. Print.

  24. Infinite Queuing Notation: Models 1-3 • λ = arrival rate • µ = service rate • 1/µ = average service time • 1/λ = average time between arrivals • ρ = ratio of total arrival rate to service rate for a single server (λ/µ) • Lq= average number waiting in line • Ls= average number in system (including and being served) **Jacobs, F. Robert, and Richard B. Chase. "5." Operations and Supply Management The Core. New York: Irwin Professional Pub, 2006. 121. Print.

  25. Infinite Queuing Notation: Models 1-3 • Wq= average time waiting in line • Ws= average total time in system (including time to be served) • n = number of units in the system • S = number of identical service channels • Pn= Probability of exactly n units in system • Pw = Probability of waiting in line

  26. Equations for Model 1 • Lq= • Ls= • Wq= • Ws= • Pn= • ρ = • Po =

  27. Equations for Model 2 and 3 Model 2 Model 3 Ls= Lq Wq = Ws = Pw = Lq • Lq= • Ls= Lq • Wq= • Ws=

  28. Brainstorming Exercise What are inexpensive ways our company can reduce customer wait times?

  29. Summary • Effective queue management may lead to improved customer satisfaction and increased revenue • Many queue management methods require little money to implement • Software is available to help with queue analysis

  30. Reading List • An Introduction to Queuing Theory: Modeling and Analysis in Applications (Statistics for Industry and Technology) by U. Narayan Bhat • Introduction to Queuing Networks by ErolGelenbe and Guy Pujolle • Optimal Design of Queuing Systems by ShalerStidham • Fundamentals of Queuing Theory by Donald Gross and Carl M. Harris • Operations and Supply Management The Core by Jacobs, F. Robert, and Richard B. Chase

  31. Reference ** Jacobs, F. Robert, and Richard B. Chase. "5." Operations and Supply Management The Core. New York: Irwin Professional Pub, 2006. 111-127. Print.

More Related