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Service Systems & Queuing

Service Systems & Queuing. Chapter 12S OPS 370. Nature of Services. 1. 2. A. 3. 4. 5. 6. 7. . Service System Design Matrix. Degree of customer/server contact. Extensive. None. Some. (Buffered System). (Permeable System) . (Reactive System). High. (low). Face.

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Service Systems & Queuing

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  1. Service Systems &Queuing Chapter 12S OPS 370

  2. Nature of Services • 1. • 2. • A. • 3. • 4. • 5. • 6. • 7.

  3. Service System Design Matrix Degree of customer/server contact Extensive None Some (Buffered System) (Permeable System) (Reactive System) High (low) Face - to - face total customization Face - to - face Sales loose specs Opportunity? Face - to - face tight specs Phone Internet & Contact (Production on - site Efficiency?) technology Mail contact Low (high)

  4. Designs for On-Site Service • 1. • Ex: • 2. • Ex. • 3. • Ex.

  5. Disney World • 1. • 2. • 3.

  6. Implications of Waiting Lines • 1. • 2. • 3. • 4.

  7. Elements of Waiting Lines • 1. • 2. • A. • B. • 3. • 4.

  8. Customer Population Characteristics • 1. • A. • 2. • A. • 3. • A. • 4. Jockeying • A.

  9. Service System • 1. The service system is defined by: • A. • B. • C. • D. • E.

  10. Number of Lines • 1. Waiting lines systems can have single or multiple queues. • A. • B.

  11. 1 4 Arrivals Depart C C C C C 2 5 3 6 Phase 1 Phase 2 Servers • 1. • 2. • A. • B. Example of a multi-phase, multi-server system:

  12. Example Queuing Systems

  13. Arrival & Service Patterns • Arrival rate: • 1. The average number of customers arriving per time period • 2. Modeled using the Poisson distribution • 3. Arrival rate usually denoted by lambda () • 4. Example: =50 customers/hour; 1/=0.02 hours between customer arrivals (1.2 minutes between customers)

  14. Arrival & Service Patterns (Continued) • Service rate: • 1. The average number of customers that can be served during the period of time • 2. Service times are usually modeled using the exponential distribution • 3. Service rate usually denoted by mu (µ) • 4. Example: µ=70 customers/hour; 1/µ=0.014 hours per customer (0.857 minutes per customer). • Even if the service rate is larger than the arrival rate, waiting lines form! • 1. Reason is the variation in specific customer arrival and service times.

  15. Waiting Line Priority Rules • 1. First come, first served • 2. Best customers first (reward loyalty) • 3. Highest profit customers first • 4. Quickest service requirements first • 5. Largest service requirements first • 6. Earliest reservation first • 7. Emergencies first

  16. Waiting Line Performance Measures • Lq = The average number of customers waiting in queue • L = The average number of customers in the system • Wq = The average waiting time in queue • W = The average time in the system • r = The system utilization rate (% of time servers are busy)

  17. Single-Server Waiting Line • Assumptions • 1. Customers are patient (no balking, reneging, or jockeying) • 2. Arrivals follow a Poisson distribution with a mean arrival rate of . This means that the time between successive customer arrivals follows an exponential distribution with an average of 1/  • 3. The service rate is described by a Poisson distribution with a mean service rate of µ. This means that the service time for one customer follows an exponential distribution with an average of 1/µ • 4. The waiting line priority rule is first-come, first-served • 5. Infinite population

  18. Formulas: Single-Server Case

  19. Formulas: Single-Server Case con’t

  20. State Univ Computer Lab • A help desk in the computer lab serves students on a first-come, first served basis. On average, 15 students need help every hour. The help desk can serve an average of 20 students per hour. • Based on this description, we know: • 1. µ = 20 students/hour (average service time is 3 minutes) • 2. = 15 students/hour (average time between student arrivals is 4 minutes)

  21. Average Utilization

  22. Average Number of Studentsin the System, and in Line

  23. Average Time in the System & in Line

  24. Probability of nStudents in the Line

  25. Single Server: Probability of n Students in the System

  26. Multiple Server Case • Assumptions • 1. Same as Single-Server, except here we have multiple, parallel servers • 2. Single Line • 3. When server finishes with customer, first person in line goes to the idle server • 4. All servers are identical

  27. Multiple Server Formulas

  28. Multiple Server Formulas con’t

  29. Multiple Server Formulas (Continued) Find Value for P0from Chart Handout

  30. Example: Multiple Server • Computer Lab Help Desk • Now 45 students/hour need help. • 3 servers, each with service rate of 18 students/hour • Based on this, we know: • µ = 18 students/hour • s = 3 servers •  = 45 students/hour

  31. Finding P0 r = 45/(3*18) = 0.83 P0 ≈ 0.04

  32. Probability of n Students in the System

  33. Changing System Performance • 1. Customer Arrival Rates • Ex: • 2. Number and type of service facilities • Ex. • 3. Change Number of Phases • Ex.

  34. Changing System Performance • 4. Server efficiency • Ex: • Ex: • 5. Change priority rules • Ex: • 6. Change the number of lines • Ex: • Ex:

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