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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.

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Queuing Theory Models

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  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.

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