Optimal resource assignment to maximize multistate network reliability for a computer network Yi- Kuei Lin, Cheng-Ta Y

1. Optimal resource assignment to maximize multistate network reliability for a computer networkYi-Kuei Lin, Cheng-Ta Yeh Advisor : Professor Frank Y.S. Lin Presented by: Tuan-Chun Chen Presentation date: May 8, 2012

2. Agenda • Introduction • Problem formulation • Development of MSNRA-GA • Experimental results • Conclusions and further research

3. Agenda • Introduction • Problem formulation • Development of MSNRA-GA • Experimental results • Conclusions and further research

4. Introduction • How to evaluate and enhance network reliability is an important issue for organizations, especially to maximize network reliability. • search for the optimal resource assignment (RA) • The multistate network (MSN) reliability is the probability that the maximal flow of the MSN is no less than the demand

5. Introduction • The existed optimization problems of MSN reliability are categorized into two types: (1) Achieving the optimal MSN reliability subject to different constraints . (2) Minimizing the resources needed for providing a required reliability level.

6. Introduction • Many researches involve the issues of network structure, flow assignment, and commodity allocation. • This paper focuses on “searching for the optimal resource assignment with maximal MSN reliability”.(MSNRA problem) • Resources denote transmission lines of a computer network. • The MSNRA problem is solved at the design phase.

7. Introduction • Implicit enumeration method can be applied intuitively to solve the MSNRA problem, but it is very time-consuming. • This Study develops an optimization method named MSNRA-GA (genetic algorithm) based on the simple GA (SGA) architecture. • Chromosome  resource assignment. • Fitness value of a chromosome  MSN reliability. • Evaluated in terms of MPs.

8. Introduction • Higher MSN reliabilities have higher possibility to be preserved and to propagate their offspring. • Thus, MSNRA-GA can avoid searching for the worse solutions and the optimal solution can be found in a reasonable time.

9. Agenda • Introduction • Problem formulation • Development of MSNRA-GA • Experimental results • Conclusions and further research

10. Problem formulation • Multistate network

11. Problem formulation • Assumptions: 1. No resource is assigned to any node. 2. Flow in (N,E) must satisfy the flow-conservation law. 3. Each resource can be assigned to at most one edge and each edge must contain exact one resource. 4. The capacities of resources are statistically independent.

12. Problem formulation • MSNRA problem formulation (1)

13. Problem formulation (2)

14. Problem formulation (3) (4) • Assumption3: Each resource can be assigned to at most one edge and each edge must contain exact one resource.

15. Problem formulation • MSN reliability evaluation Any minimal state vector in the set is said to be a lower boundary point for d or d-MP. Suppose U1,U2,...,Ub are b d-MPs. (5)

16. Problem formulation • Flow vectors and state vectors • flow vectors: (6) (7)

17. Problem formulation • state vectors: (8) (9)

18. Problem formulation • Generate all d-MPs (10) (11)

19. Problem formulation • Check whether a d-MP candidate is a d-MP or not

20. Agenda • Introduction • Problem formulation • Development of MSNRA-GA • Experimental results • Conclusions and further research

21. Development of MSNRA-GA • Determination of the GA’s parameters

22. Development of MSNRA-GA • Representation of a chromosome

23. Development of MSNRA-GA • Evolution process I. Selection operator Directs the MSNRA-GA to search toward a better region in the solution space. Determined from the fitness value of the chromosome (MSN reliability). Higher fitness value has a higher probability of being selected.

24. Development of MSNRA-GA The roulette wheel selection is implemented twice so that two chromosomes are selected to be the parents.

25. Development of MSNRA-GA II. Crossover operator Offspring are produced by the parents. The good genes is preserved in the next generation. Step 1: Randomly choose crossover point(CP)

26. Development of MSNRA-GA Step 2: Exchange

27. Development of MSNRA-GA Step 3: Modify

28. Development of MSNRA-GA III. Mutation operator The study develops a hybrid mutation method that combines simple mutation with uniform mutation. First, MuP is stochastically generated. Secondly, the gene at this point is mutated

29. Development of MSNRA-GA Condition 1: The mutated gene is the same as that of another in the child.

30. Development of MSNRA-GA Condition 2: The mutated gene is not the same as the others in the child. IV. Terminal condition When the number of iterations is 1000.

31. Agenda • Introduction • Problem formulation • Development of MSNRA-GA • Experimental results • Conclusions and further research

32. Experimental results • Experiments are grouped into three parts: (1) MSNRA-GA is compared with the implicit enumeration method to show its efficiency (2) Implemented on six random networks and four commonly used networks. (3) A real computer network, Taiwan Academic Network (TANET).

33. Experimental results (1) Comparison with the implicit enumeration method in terms of the optimal reliability and CPU time. • MSNRA-GA’s parameters: • Using a simple network

34. Experimental results

35. Experimental results

36. Experimental results (2) Experiment in ten networks 6 random networks:

37. Experimental results (2) Experiment in ten networks 4 commonly used networks:

38. Experimental results (2) Experiment in ten networks Parameters:

39. Experimental results

40. Experimental results

41. Experimental results Discussions: I. Number of edges , Avg. CPU time (non-linearly) , Avg. maximal MSN reliability II. Number of MPs , Avg. CPU time Avg. maximal MSN reliability

42. Experimental results (3) The experiments in TANET Parameters: Discuss 18 pairs of Popsize and gtime.

43. Experimental results MSN reliability is not reduced nor increase significantly as the Popsize changes.

44. Agenda • Introduction • Problem formulation • Development of MSNRA-GA • Experimental results • Conclusions and further research

45. Conclusions and further research • The paper presents a novel optimization problem for computer networks to search for the optimal resource assignment with maximal MSN reliability. • Also develop an optimization method named MSNRA-GA, based on the SGA, to solve this MSNRA problem. • Experimental results reveal that the MSNRA-GA has better computational efficiency than the implicit enumeration method and practice for large networks.

46. Conclusions and further research • This paper focuses on the terminal-pair connectivity. • The MSN reliability for multiple origins to multiple destinations is also an important issue worthy studying in the future. • This problem can be developed into a multi-objective resource assignment problem, including maximizing the MSN reliability and minimizing resource assignment cost, or can consider the time constraint and multi-commodity transmission.

47. Thanks for your attention !!!