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Client-Server Assignment for Internet Distributed Systems

Client-Server Assignment for Internet Distributed Systems. Overview. Introduction Problem Definition Problem Model Solution Conclusion. Introduction. Internet - Distributed System Example: Email,IMS. Features: 1 . Communication Load Clients assigned to two different servers.

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Client-Server Assignment for Internet Distributed Systems

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  1. Client-Server Assignment for Internet Distributed Systems

  2. Overview • Introduction • Problem Definition • Problem Model • Solution • Conclusion

  3. Introduction • Internet - Distributed System • Example: Email,IMS

  4. Features: • 1. Communication Load • Clients assigned to two different servers. • Clients assigned to same server. • 2. Load Balancing • Use fewer servers. Servers are heavily loaded

  5. Observations:

  6. Problem Definition • Optimal client server assignment for a pre-specified trade-off between load balance and communication load. • Emerging Applications: • Social networks Eg: Facebook • Distributed database system, Eg: MapReduce

  7. Communication Model • Initially assign clients to a system with 2 servers (Sa, Sb) • Then we extend the 2-server solution to multiple servers. • Xi = 1, client i is assigned to Sa • Xi = -1, client i is assigned to Sb • : data rate from client i to client j.

  8. Communication Load • if i and j are assigned to same server. • 2 if clients are assigned to 2 different servers. • Total communication load, • If i and j are assigned to different servers, • = -1

  9. Load Balance • Load balance, D =

  10. D can be expressed as, • Refer link • Adding D to objective function will make the function non-quadratic. • Hence we modify D,

  11. Equivalent formula of D, • D = , • where • Refer link • As, = 1, • = • Refer link

  12. Optimization problem: • Minimize: • Subject to : • Where: • = • is an arbitrary co-efficient (0≤≤1)

  13. Objective function : • minimize • Where we define, • Refer link

  14. Semidefinite Programming • Semidefinite programming is a class of convex optimization. • : set of real Symmetric matrices. • A matrix is called positive semidefiniteif , for all • It satisfies strict quadratic programming

  15. Solution: • minimize: tr( • subject to: • Solution Matrix = • W-> Matrix with diagonal elements 0 and Wi,j • U -> symmetric & Positive semidefinite matrix

  16. Conclusion • 1. Hard problems could be formulated as a optimization problem and solved. • 2. optimization problems, are widely used in tremendous number of application areas, such as transportation, production planning, logisticsetc.

  17. Presented by : Swathi Balakrishna

  18. Extra information: • Transform program into Vector program: • Minimize: • Subject to: = 1,

  19. Vector programming -> Semidefinite programming • W-> Matrix with diagonal elements 0 and Wi,j • U -> symmetric & Positive semidefinite matrix • minimize: tr( • subject to:

  20. Solution Matrix = • Cholesky Factorization: • Obtain V= ( • Satisfying . • Final solution: • Round n vectors (to n integers (

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