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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.

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Presentation on theme: "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."— 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, Print.

9 The Queuing System Source Population & Arrival Rate Servicing System Condition of Exiting Customers

10 Source Population Finite Limited size Probabilities affected by an increase/decrease in the population Infinite Large size Probabilities not 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 t (minutes) Probability that the next arrival will occur in t minutes or more Probability that the next arrival will occur in t minutes or less **Jacobs, F. Robert, and Richard B. Chase. "5." Operations and Supply Management The Core. New York: Irwin Professional Pub, Print.

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

14 Poisson Distribution **Jacobs, F. Robert, and Richard B. Chase. "5." Operations and Supply Management The Core. New York: Irwin Professional Pub, Print.

15 Pattern of Arrivals PatternControllableUncontrollable

16 Size of Arrival Units SingleBatch

17 Degree of Patience Patient (in line and stay) Impatient Arrive, View, and Leave Arrive, Wait Awhile, then Leave

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

19 First Come, First Served (FCFS) Shortest Processing Time Reservations First Emergencies First Limited Needs Other

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, Print.

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

22 Exiting the Queuing System Exit Low Probability of Re-service Return to Source Population

23 Properties of Some Specific Line Models Model Layout Service Phase Source Population Arrival Pattern Queue Discipline Service Pattern Permissible Queue Length Example 1Single Channel SingleInfinitePoissonFCFSExponentialUnlimitedOne-lane toll bridge 2Single Channel SingleInfinitePoissonFCFSConstantUnlimitedRoller coaster rides in amusement park 3Multi- channel SingleInfinitePoissonFCFSExponentialUnlimitedParts counter in auto agency **Jacobs, F. Robert, and Richard B. Chase. "5." Operations and Supply Management The Core. New York: Irwin Professional Pub, 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) L q = average number waiting in line L s = 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, Print.

25 Infinite Queuing Notation: Models 1-3 W q = average time waiting in line W s = average total time in system (including time to be served) n = number of units in the system S = number of identical service channels P n = Probability of exactly n units in system P w = Probability of waiting in line

26 Equations for Model 1

27 Equations for Model 2 and 3 Model 2Model 3

28 Brainstorming Exercise

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 Erol Gelenbe and Guy Pujolle Optimal Design of Queuing Systems by Shaler Stidham 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, Print.


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