1. Kevin Ross, UCSC, September 2005 1 Service Network Engineering Resource Allocation and Optimization Kevin Ross Information Systems & Technology Management University of California, Santa Cruz September 2005

2. Kevin Ross, UCSC, September 2005 2 Service Networks X1X1 X2X2 XqXq XQXQ … …

3. Kevin Ross, UCSC, September 2005 3 Service Networks Source: www.capital.lv/ pics/news/data.jpg Autonomous Computing (Utility Computing / Data Center Management /Grid Commputing) Call Center Management Utility Providers

4. Kevin Ross, UCSC, September 2005 4 Example: Human Resource Optimization Queues correspond to various jobs/requests A large pool of people with –Varying skill levels (speed of service) –Different costs (distance from job, rate of pay) Each configuration of people corresponds to a unique service mode We consider selecting the service mode, given –Constraints on resources –Current backlog of tasks to complete

5. Kevin Ross, UCSC, September 2005 5 Typical Scenarios … thousands of jobs / employees … interacting service requirements … deadlines … different costs for service … jobs of different priorities … we could hire more support … all the numbers are uncertain Service Network Engineering

6. Kevin Ross, UCSC, September 2005 6 Summary of Research Issues Allocating resources when there are –Large number of job types (classes) –Large number of service configurations –Dynamic demand levels –Interactive service constraints –Priority jobs –Variable costs

7. Kevin Ross, UCSC, September 2005 7 Key Findings Proved –a large class of scheduling algorithms are throughput-maximizing for service networks under very general conditions –we can optimize for quality of service performance –these algorithms scale well –we can implement the control in a distributed way Work in progress –Tradeoff analysis: quality of service / load balancing / costs / throughput –Pricing schemes and value of resources

8. Kevin Ross, UCSC, September 2005 8 Base Case: Parallel Queue networks X = workload vector S = service rate vector S S = set of all possible service mode vectors Dynamically select service mode S from S - based on workload X X1X1 X2X2 XqXq XQXQ … … SqSq S2S2 S1S1 SQSQ … … ……

9. Kevin Ross, UCSC, September 2005 9 Service Networks X1X1 X2X2 XqXq XQXQ … …

10. Kevin Ross, UCSC, September 2005 10 Service Networks X1X1 X2X2 XqXq XQXQ … … 14221422

11. Kevin Ross, UCSC, September 2005 11 Service Networks X1X1 X2X2 XqXq XQXQ … … 14221422

12. Kevin Ross, UCSC, September 2005 12 Service Networks X1X1 X2X2 XqXq XQXQ … …

13. Kevin Ross, UCSC, September 2005 13 Service Networks X1X1 X2X2 XqXq XQXQ … … 42114211

14. Kevin Ross, UCSC, September 2005 14 What about networks? 12534 2 Serving one queue creates work in another Known as feedback and forwarding

15. Kevin Ross, UCSC, September 2005 15 Network of Queues 12345 2 Feedback and forwarding can be modeled with a similar framework

16. Kevin Ross, UCSC, September 2005 16 Network of Queues 12345 2 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 1 0 0 Transfer matrix T 1234512345 1 2 3 4 5

17. Kevin Ross, UCSC, September 2005 17 Network of Queues 12345 2 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 2 2 1121111211 Arrivals = Departures

18. Kevin Ross, UCSC, September 2005 18 Network of Queues 12345 2 1 Service = Departures - Arrivals 0012200122 1121111211 = -

19. Kevin Ross, UCSC, September 2005 19 Core Model: Example X = backlog vector S = service rate vector X1X1 X2X2 X3X3 X5X5 X4X4 1 1 1 S Q=5 (# queues) 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 1 0 0

20. Kevin Ross, UCSC, September 2005 20 Core Model: Example X = backlog vector S = service rate vector X1X1 X2X2 X3X3 X5X5 X4X4 1 1 1 S Q=5 (# queues) 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 1 0 0

21. Kevin Ross, UCSC, September 2005 21 Analytical and Practical Issues Performance –Throughput –Quality of service –Load balancing –Cost minimization Robustness –Assumptions required –Unreliable information –Adaptive to variation –Switching times Complexity –Huge number of configurations

22. Kevin Ross, UCSC, September 2005 22 System Dynamics AIM: Rate Stability: Notation: Q-vectors X1X1 X2X2 X(t-1) A(t) - S(t) X(t)

23. Kevin Ross, UCSC, September 2005 23 R What arrival rates can we consider? 11 22 S1S1 Stability Region R :  vectors which could be served S2S2 S3S3 S4S4 R = {  :  0 with   m = 1 } S6S6 S5S5

24. Kevin Ross, UCSC, September 2005 24 Some Types of Algorithms Offline Know the arrival rates in advance Randomized / Round Robin Online Arrival rate is not known Adapt to Arrivals and Buffer backlog Two main classes: –Batch Schedules –Projective Cone Schedules

25. Kevin Ross, UCSC, September 2005 25 Projective Cone Scheduling (PCS) Algorithms PCS: When the workload vector is X, choose the service configuration S that maximizes S max over S in S For a fixed matrix B that is positive diagonal

26. Kevin Ross, UCSC, September 2005 26 PCS Algorithm: Example X1X1 X2X2 X3X3 X5X5 X4X4 6 0 0 0 1 3 2 0 3 1 0 3 5 0 0 0 0 1 1 6 S1S1 S2S2 S3S3 S4S4 5 6 3 2 4 X = = 64 62 63 35 10 6 9 2 4 BX 2 0 0 0 0 0 1 0 0 0 0 0 3 0 0 0 0 0 1 0 0 0 0 0 1 B = max

27. Kevin Ross, UCSC, September 2005 27 When X is in cone C, choose S = S(C) corresponding to that cone The set of workload vectors X for which S* maximizes is a convex cone X1X1 X2X2 S4S4 S3S3 S2S2 S1S1 X PCS as a Cone Algorithm

28. Kevin Ross, UCSC, September 2005 28 Workload Drift in Cones Workload drifts between cones over time X1X1 X2X2 S4S4 S3S3 S2S2 S1S1

29. Kevin Ross, UCSC, September 2005 29 What are the Cones? S1S1 S2S2 S1S1 S2S2 S3S3

30. Kevin Ross, UCSC, September 2005 30 Cone Boundaries: Varying B S1S1 S2S2 S3S3

31. Kevin Ross, UCSC, September 2005 31 In Higher Dimensions S3S3 S2S2 S1S1 S4S4

32. Kevin Ross, UCSC, September 2005 32 Performance Comparison on Simple Network

33. Kevin Ross, UCSC, September 2005 33 Performance: Varying Parameters in B

34. Kevin Ross, UCSC, September 2005 34 Key Observation: Neighborhood Structure If arrivals are bounded, workload can only jump to “neighboring cones” X1X1 X1X1 S4S4 S3S3 S2S2 S1S1 X(t)

35. Kevin Ross, UCSC, September 2005 35 Local PCS: When the workload vector is X and previous service was S -, choose the service configuration S that maximizes max over S in N(S - ) X1X1 X1X1 S4S4 S3S3 S2S2 S1S1 Local PCS X

36. Kevin Ross, UCSC, September 2005 36 S6S6 S2S2 S3S3 S4S4 S5S5 S7S7 S1S1 S8S8 S6S6 S5S5 S4S4 S3S3 S8S8 S2S2 S7S7 S1S1 Local PCS: Graph Representation

37. Kevin Ross, UCSC, September 2005 37 Local PCS S = Permutation Vectors For crossbar switch

38. Kevin Ross, UCSC, September 2005 38 Pricing and Resource Valuation Pricing scenarios: 1.We could add a new mode to the set of modes for a price 2.Each service mode has a different price associated with it 3.It costs to shift modes When should we pay and how much?

39. Kevin Ross, UCSC, September 2005 39 Sketch: Adding new modes A new mode creates a new stability region R 11 S1S1 S2S2 S3S3 S4S4 S6S6 S5S5 S new

40. Kevin Ross, UCSC, September 2005 40 Sketch: Differential pricing We have price-based stability frontiers R 11 S1S1 S2S2 S3S3 S4S4 S6S6 S5S5 R2R2

41. Kevin Ross, UCSC, September 2005 41 Sketch: shifting costs Boundaries of Cones become flexible X1X1 X2X2 S4S4 S3S3 S2S2 S1S1 X

42. Kevin Ross, UCSC, September 2005 42 Summary: Service Network Engineering Resource Management in –Dynamically changing complex networks –Call centers, Utility Computing, Networks, Workforce, etc. Challenges –Analytical Concepts of throughput, QoS, scalability, distributed control –Resource Valuation and Pricing