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

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

5. Disney World 1. 2. 3.

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

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. Servers 1. 2. – A. – B. Example of a multi-phase, multi-server system: CCCCC DepartArrivals 1 2 36 5 4 Phase 1Phase 2

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 L q = The average number of customers waiting in queue L = The average number of customers in the system W q = The average waiting time in queue W = The average time in the system  = 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 Students in the System, and in Line

23. Average Time in the System & in Line

24. Probability of n Students 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 P 0 from 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 P 0  = 45/(3*18) = 0.83 P 0 ≈ 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: 5. Change priority rules – Ex: 6. Change the number of lines – Ex: