Thesis Presentation Presentation April 2010 DOI: - - PDF document

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Thesis Presentation

Presentation · April 2010

DOI: 10.13140/RG.2.2.16296.78089

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Reliability and Trust Computations in Grid

Gutha Jaya Krishna 08MCMI02 M.Tech.(Artificial Intelligence)

Abstract

• Minimally allocating resources on the grid to maximize the

grid service reliability with trust integration using deterministic state space search.

• This project deals with developing modeling and evaluation

algorithms to evaluate the grid service reliability.

• Based on the grid service reliability evaluation, we present a model

for the grid resource allocation problem which uses trust to effectively solve it.

Introduction

• Grid is a network of n computing nodes say G1, G2, ... Gn

capable to perform Services say, {S1, S2, ..... Sm} by exploiting h resources say, {R1, R2, ......Rh}.

• Grid Computing (or the use of computational grids) System is

the combination of computer resources (R1,R2,..,Rn) from multiple administrative domains applied to perform tasks, usually scientific, technical or business problems.

What is Reliability?

• In general, reliability is the ability of a network or system or

program to perform and maintain its functions in routine circumstances, as well as hostile or unexpected circumstances.

• Here reliability is a probability(In range 0 to 1). One means

high reliability and zero means low reliability.

• Reliability of Grid computing systems depends upon
• 1. Task processing time.
• 2. Communication time.
• 3. Rate of failure of grid elements

What is Trust?

• Trust is the firm belief in the entity to behave as expected and

this firm belief is a dynamic value which may change with behavior and context of time.

• Here trust is in range of 0 to 1.

Important Terms :

• L(i,j) : Link between nodes Gi and Gj.
• D(i,j) : Total size of data exchanged through the link L(i,j).
• S(i,j) : Mean speed of data exchange through the link L(i,j).
• T(i,j) : D(i,j)/S(i,j) , communication time between node i and j.
• Assumption Made:The failure occurring at node and link both

follow the Poisson process.

j). L(i, link

• f

failure

• f

Rate λ i. node

• f

failure

• f

Rate λ

: j i, : i

Related Work on Reliability Computations :[1]

reliable). is services all

• f

MRST

• ne

Pr(atleast OGSR where ) E E E Pr( ) E Pr( ) E E Pr( ) Pr(E ) Pr(E : (OGSR) y Reliabilit Service Grid 6.Overall reliable) is service a

• f

MRST

• ne

Pr(atleast GSR where ) E E E ( ) E Pr( ) E E Pr( ) Pr(E ) Pr(E : (GSR) y Reliabilit Service 5.Grid R R R : MRST

• f

ity 4.Reliabil e : nodes root

• non
• f

ity 3.Reliabil e : links

• f

ity 2.Reliabil e : node root

• f

ity 1.Reliabil

N 1

• N

1 N 2 1 2 1 N 1

• N

1 N 2 1 2 1 nodes root

• non

Links root n j MRST G .T(j)

• MRST

j) L(i, j) (i, .T

• T(n))

(t(m)

• j

c , j j i n

Related work on Trust Computations :[2]

1. and between where TV ) 1 ( TV TV 5. 1. and between where (Rel_OGSR) ) 1 ( T TV 4. X

• 1

T 3. resources free

• f

number Total need satisfying resources free available

• f

number Minimum X 2. resources free available

• f

trust represents T assume We 1.

1 K k

Deterministic State Space Search

• State space search is a process used in the field of artificial

intelligence (AI) in which successive configurations or states of an instance are considered, with the goal of finding a goal state with a desired property.

• State space search as used in AI differs from traditional

computer science search methods because the state space is implicit: the typical state space graph is much too large to generate and store in memory. Instead, nodes are generated as they are explored, and typically discarded there after.

• A solution to a combinatorial search instance may consist of

the goal state itself, or of a path from some initial state to the goal state.

General Search Process

Search Strategies Used

Brute-Force Search

Speeding Up Brute-Force Search

• Avoiding Repeated States
• Forward Search
• Backward Search
• Bi-directional Search
• 2-Way Split Backward Search
• M-Way Split Backward Search

Avoiding Repeated States

One way to speed up a brute-force algorithm is to reduce the search space, that is, the set of candidate solutions. This reducing the search space is achieved by avoiding repeated states by following strategies:

• Do not return to state just came from.
• Do not create path with cycles in them(do not create a node

same as any ancestor).

• Do not generate any state that was ever generated before.

Forward Search

Backward Search

Bi-directional Search

2-Way Split Backward Search

2-Way Split Backward Search is an algorithm proposed to improve the search process by dividing the search space into two parts one at the back and one in the middle. These are explained in steps below:

• 1. If the mid-way search yields better results than at the back

then start from the middle and split the other half from middle to front and repeat the process.

• 2. Else start from back ignore the search space from mid-way

and split the half from backward point to mid-way into another half and repeat the process.

M-Way Split Backward Search

• We can increase the number of splits(M=2,3,4,...,N/2) to

speed up the search process where M < N/2(N is total number

• f plys in the search space) at the cost of increased

computations.

• Generally 2,3 Way split are optimal in terms of computations

and search speed when number of plys are less.

Proposed System

Example illustrating proposed system

Initial Allocation Matrix for considered example

Grid Configuration and an Instance

Links L(1,2) L(1,3) L(2,3) L(2,4) L(3,4) Speed 30 20 40 50 45 Failure Rate(λ) 0.001 0.002 0.003 0.004 0.005 Service Processing Time (Sec) Necessary Resources Exchanged Information S1 30 1110 500,400,300 S2 50 0011 200,600 Node G1 G2 G3 G4 Failure rate(λ) 0.001 0.002 0.003 0.004

Example illustrating proposed system

Step-1 : Generate the Resource Allocation Matrix with all possible free resources from Initial Allocation Matrix

Initial Resource Allocation for considered example

Step-1 : Generate the Resource Allocation Matrix with all possible free resources from Initial Allocation Matrix

Initially we take an assumption that resource allocation with all possible free resources allocated. This approach helps the search procedure to search backward. The algorithm for this assumption is given below.

Algorithm : Resource Allocation Matrix with all possible free resources allocated

Step-2 : Compute Overall Grid Service Reliability(OGSR):

Step-2(a) : Generate all possible MRST’s(Minimum Resource Spanning Tree) of each service.

Service S1 needs R1,R2,R3 resources for the resource allocation shown below:

Step-2(a) : Generate all possible MRST’s(Minimum Resource Spanning Tree) of each service.

Step-2(a) : Algorithm to Generate all possible MRST’s

list} from RST the e else{remov MRST} possible { links)

• f

no. RST 1)

• nodes
• f

no. 3.if((RST RST j)RST ( such that s RST'

• f

links the 2.Remove list; a into s RST' se insert the and need the satisfying s) Trees(RST'

• Sub

the 1.Generate : steps in three algorithm the

• f

n Explanatio

i; j

Step 2(b) : Compute reliability of MRST’s

Computing Reliability for MRST-4 . To compute reliability of whole MRST-4 compute the reliability of its individual elements like:

• Communication Links.
• Root Node.
• Non-Root Nodes.

Step 2(b) :Algorithms to compute reliability of MRST’s

Reliability of Communication links of MRST-4: Reliability of Donor nodes of MRST-4: Reliability of Root node of MRST-4: Reliability of MRST-4:

Step 2(c) : Compute the Conditional Probability for the MRST’s of services

Conditional Probability is reformulated as below:

Algorithm for above mentioned reformulated conditional probability is given above

Working times of MRST-1 and MRST-2 are given below Conditional elements that can fail MRST-1 and MRST-2 and keep MRST-3 to be

• perational.

Probability that MRST-1 succeeds is given by: Probability that MRST-2 succeeds is given by:

Step 2(d) : Compute reliability of the services

Algorithm for Calculation of Reliability for the services is given below

Step 2(e) : Repeat step 2(b)(ii), 2(c), 2(d) to compute the Overall Grid Service Reliability(OGSR) of all services

Algorithm for Calculation of Overall Grid Service Reliability(OGSR) is given below:

The working times of MRST’s of services S1 and S2 are given below Working times for OGSR(i.e S1 and S2 combined) is calculated by summing up the working times of MRST’s of services S1 and S2. After calculating the working times for OGSR(i.e S1 and S2 combined) steps 2(b), 2(c), 2(d) are repeated to compute OGSR.

Step 3 : Use 2-Way Split Backward Search with trust integration to find the minimal resource allocation with maximal reliability

Step 3(a) : Generate possible resource allocation matrices using 2-Way Split Backward Search algorithm

Following number of combination’s of free resource allocations for a split of each iteration In first iteration for total 8 free resources(-1) 8 possible combination’s of resource allocations are generated(i.e. 8C7 = 8 where 7 is number of free resources allocated(1) while keeping remaining one resource not allocated(0)) for Mth ply and 70 possible combination’s of resource allocations are generated(i.e. 8C4 = 70 where 4 is number of free resources allocated(1) while keeping remaining 4 resources not allocated(0)) for Lth = M/2 ply. Similarly for remaining iterations.

Algorithm for generating possible resource allocation matrices using 2-Way Split Backward Search algorithm

Step 3(b) : Repeat step-2 to compute the Overall Grid Service Reliability for possible resource allocation matrices

Compute OGSR using step-2 For the Resource Allocation Matrices generated using 2-Way Split Backward Search.

Step 3(c) : Use trust computations to find out the minimal allocation with maximal reliability

Algorithm for using trust computations to find out the minimal allocation with maximal reliability

So, the minimal resource allocation for the example considered is shown below:

Future work

• We can use multiple copies of resources at particular grid

node, upgrade to real time system, etc.

• We can use M-way split where M < n/2 for generating minimal

resource allocation with maximal reliability using trust.

• We can simulate on GRIDSIM or we can do it real time on

PRAGMA Grid.

References

[1] Poh K.L. Dai Y.S., Xie M. “Reliability analysis of grid computing systems”. In IEEE Pacific Rim International Symposium

• n

Dependable Computing(PRDC2002), pages 97–104, June 2002. [2] Kam-Wing Ng Woodas W.K. Lai.“ A time frame based trust model for grids". In Grid and Cooperative Computing(GCC),pages190-195,December 2005. [3] Foster I., “The anatomy

• f

the grid: Enabling Scalable Virtual Organizations”. Proceedings International Symposium

• n

Cluster Computing and the Grid, 15-18 May 2001 pages 6-7. [4] Yuan-Shun Dai , Xiao-Long Wang.“Optimal resource allocation on grid systems for maximizing service reliability using genetic algorithm”. Reliability Engineering and system safety 91 (2006) 1071-1082.