Client-Server Assignment for Internet Distributed Systems

Overview

• Introduction• Problem Definition• Problem Model• Solution• Conclusion

IntroductionInternet - Distributed System Example: Email,IMS

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

Observations:

Problem Definition

Optimal client server assignment for a pre-specified trade-off between load balance and communication load.

Emerging Applications:1. Social networks Eg: Facebook

2. Distributed database system, Eg: MapReduce

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 SaXi = -1, client i is assigned to Sb : data rate from client i to client j.

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

Load Balance

Load balance, D =

D can be expressed as, Refer link

Adding D to objective function will make the function non-quadratic.

Hence we modify D,

Equivalent formula of D, D = , where Refer link

As, = 1,= Refer link

Optimization problem:

Minimize:

Subject to :

Where:

=

is an arbitrary co-efficient (0≤ ≤1)

Objective function : minimize

Where we define,

Refer link

Semidefinite Programming Semidefinite programming is a class of convex

optimization. : set of real Symmetric matrices. A matrix is called positive semidefinite if ,

for all It satisfies strict quadratic programming

Solution: minimize: tr( subject to: Solution Matrix =

W-> Matrix with diagonal elements 0 and Wi,jU -> symmetric & Positive semidefinite matrix

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, logistics etc.

Presented by : Swathi Balakrishna

Extra information:Transform program into Vector program:

Minimize:

Subject to: = 1,

Vector programming -> Semidefinite programming

W-> Matrix with diagonal elements 0 and Wi,jU -> symmetric & Positive semidefinite matrix minimize: tr( subject to:

Solution Matrix = Cholesky Factorization: Obtain V= ( Satisfying .

Final solution:Round n vectors (to n integers (