INTRODUCTION

Reliability

Network reliability is a measure of the ability of a network to carry out a desired network operation.

Network reliability is usually based on whether the nodes, or the links between nodes, operate successfully.

NETWORK RELIABILTY

INTRODUCTION

TYPE OF NETWORK

NETWORK RELIABILITY EVALUATION

MINPATH

MINCUTS

SUM OF DISJOINT PRODUCT

KDH88 ALGORITHM

CAREL ALGORITHM

RELIABILITY OF MULTICAST NETWORK

EVENT TREE

FAULT TREE

LITERATURE REVIEW

PROBLEM IDENTIFICATION

RESEARCH OBJECTIVE

REFERENCES

CONTENT

**CAPACITY RELATED RELIABILITY EVALUATION FOR MULTI-CAST NETWORK**

TYPES OF NETWORK

On the basis of reliability network is classified as

.

MIN PATH

Pathset

A set of components (edges) whose operation implies (guarantees) system operation.

Minpath

A minimal Pathset

Ex．K={v1,v4}

**Saurabh Dubey (12/PIT/090)**

**SCHOOL OF INFORMATION AND COMMUNICATION TECHNOLGY GAUTAM BUDDHA UNIVERSITY**

**Dr. Rajesh Mishra**

**Supervised By:**

**Presentation on M Tech Dissertation Part 1 Progress Work**

**Presented By:**

Undirected Networks

Directed Networks

Mixed Networks

K = set of nodes

V = all nodes

MINCUTS

Cutset

A set of components (edges) whose failure implies (guarantees) system failure

Mincut

A minimal Cutset

Ex．K={v1,v4}

SDP are used to find out the reliability of Mesh type network.

SDP based approach is used to find out the reliability expression in more efficient and compact manner.

SDP are used to calculate the reliability of K-terminal network.

SDP

Approach implemented by using Boolean algebra

Ex. Two terminal reliability between v1, v4

Minpath: ab, cd, ade, bce

Can be expressed with the following Boolean expression:

AB V CD V ADE V BCE

R(G) = Pr [AB V CD V ADE V BCE =1]

Probability for each ∨path which operates

correctly can be simply calculated as follows:

Pr[AB]=papb, Pr[CD]=pcpd, ...

However, R(G) can not be directly

calculated when there exists Pr of the

paths which are not disjoint event

(exclusive).

RELIABILITY

CLASSIFICATION OF SDP

SVI Approach

In SVI approach wherein variables are inverted sequentially one at a time

In SVI minimization of the expression has been achieved through the pathset or cutset.

MVI Approach

In MVI approach a group of variables are inverted at once.

In MVI not only the ordering of pathset or cutset but the simultaneous inversions of a group of variables are inverted at once.

KDH88

KDH88 is an MVI extension of SVI algorithm proposed by Abraham. Using the min path sets, it recursively generates the terms for each path set.

Path sets : {(1,6), (2,7), (4,8), (1,3,7), (2,3,6), (2,5,8), (4,5,7), (1,3,5,8), (4,5,3,6)}

Cut sets : {(1,2,4), (6,7,8), (1,2,5,8), (1,3,7,8), (2,3,4,6), (4,5,6,7), (1,3,4,5,7), (2,3,5,6,8)}

Let path number seven i.e. {4,5,7} be made disjoint with all its predecessors. KDH88 would be

{(1-P1)*(1-P2)*(1-P8)*P4*P 5*P8 + P1*(1-P2)*(1-P8)*(1-P3)*(1-P6) *P4*P5*P7 }

CAREL ALGORITHM AND MULTICAST NETWORK RELIABILITY

CAREL ALGORITHM

CAREL algorithm is proposed by (Soh& Rai-91), it uses the boolean algebraic manipulation.

It proposing 4 operators

COMpare

REDuce

CoMBine

GENerate

ALGORITHM

IS

For all the path sets Ti, i= 1, 2, 3, … m

Obtain conditional cube (CC) set by eliminating the common element present.

Obtain minimal conditional cube set (MCC) i.e. if conditional cube set then MCC divides into two group i.e. IG & DG

IG = 2nd and 3rd term

DG = 1st and 4th term

Compute TR (Terminal Reliability)

Path sets {(1,6), (2,7), (4,8), (1,3,7), (2,3,6), (2,5,8), (4,5,7), (1,3,5,8), (4,5,3,6)}

For path set number 7 CAREL would be

(1-P1)*(1-P2)*(1-P8)*P4* P5* P7 + P1 (1-P3)*(1-P6)*(1-P2)*(1-P8)*P4* P5* P7

EVENT TREE ANALYSIS

We can say that multicast network is a type of tree type network

So the reliability of multicast network would be calculated by

Event Tree

Fault Tree

MUTICAST NETWORK RELIABILITY

Event tree is an inductive analytical diagram in which an event is analyzed using Boolean logic to examine a chronological series of subsequent events or consequences. Example

FAULT TREE ANALYSIS

What ?

A structured team analysis of the possible underlying causes of a known equipment failure.

When ?

root cause analysis of a failure is needed

Why?

- (outcomes)

A better understanding of the root causes of a failure.

A better set of action plans to eliminate those root causes.

Fault tree analysis is an effect and cause diagram that uses standard symbols developed in the defense industry and is used heavily in safety engineering. FTA is a structured approach for analyzing the root causes of a failure mode not yet fully understood.

EXAMPLE OF FAULT TREE

LITERATURE SURVEY

PROBLEM IDENTIFICATION

According to above literature survey the following problems are identifies.

In multicast network replicate copy of data is saved at the sender, so the overhead (buffer) is increased at the source or intermediate nodes (router). It needs flow based reliability algorithms for avoiding the congestion in these nodes.

When a group is form in a multicast network simultaneously if a member joins or leaves the group every time access control and authentication will require. Finally, it is required an efficient reliable-flow-mobility based protocols.

In the multicast network the group is dynamic so rekeying is required, Further few factors i.e. energy consumption, security, congestion, and packet drop problems arises due to unreliable behavior of these networks . Here it is required to proper connectivity between all source, destination, and intermediate nodes for reducing these factors effects.

The approaches those are mention in the literature are not efficient for multicast network in the terms of delay, congestion, availability, reliability, security etc. So Qos based approaches may further enhanced.

RESEARCH OBJECTIVE

REFERENCES

[1] Chandrasheker T. and N.K. Goyal, An approach to evaluate multiple node pair reliability for simultaneous capacity requirements, International Journal of Performability Engineering, vol. 9, no. 4, pp. 340-350, 2013.

[2] Hassan M.R., Reliability evaluation of multi-source multi-sink stochastic-flow network under quickest path and system capacity constraints, SDIWC, vol. 12, no. 3, pp. 166-172, 2013.

[3] Mishra R. and S.K. Chaturvedi, A cutset based unified framework to evaluate network reliability measures, IEEE Transaction on Reliability, vol. 58, no. 4, pp. 658-666, 2009

[4] Aggarwal K.K., A fast flgorithm for the performance index of a telecommunication network, IEEE Trans. Reliability, vol.37, no. 1, pp. 65-69, 1988.

[5] Cook J.L. and J.E. Ramirez, Reliability of capacitated mobile ad hoc networks, Journal of risk and reliability, vol.221, no. 2 pp. 307-17, 2007.

Base paper- Chandrasheker T. and N.K. Goyal, An Approach to Evaluate Multiple Node Pair Reliability for Simultaneous Capacity Requirements, international journal of performability Engineering,Vol.9,month,2013.

In this paper author proposed a cut set based approach to evaluate reliability of multi node pair capacity related reliable (MNPCRR) network.

It helps network designers in assessing and optimizing network performance with effectiveness.

The reliability measure considering both connectivity and capacity as success criteria for a node pair is called capacity related reliability

Aggarwal K.K., A Fast Algorithm for the Performance Index of a Telecommunication Network. IEEE Trans. Reliability., apr. 1988; R-37(1):65-69.

In this paper author suggest a faster method for deriving the symbolic expression of performance index in a compact form, because the capacity of several sub networks must be computed, an efficient procedure for capacity determination is also suggested.

Hassan M.R., Reliability Evaluation of Multi-Source Multi-Sink Stochastic-flow Network under Quickest Path And, System Capacity constrains.

In this paper author present an algorithm to determine the probability called system reliability for source-sink pair.

RESEARCH GAPS

This approach is help full for finding the reliability of K terminal simultaneously. It will not applicable to find the reliability of multiple node or all node.

This approach is not use full for multicast network in the terms of Delay Congestion & Availability.

RESEARCH GAP

In this paper author does not discuss the issues of delay and congestion in network.

Based on above observations the following major objective are set:

To study the multicast network reliability.

To proposed an modified algorithm for evaluation of multicast network reliability.

Compare and validate the result by using event tree analysis

[

7] Huang N., Dong H., Chen H.Y., Xing L. and R. Kang, A network reliability evaluation method based on application and topological structure, Maintenance and Reliability, vol.54, no. 3, pp. 77-83, 2011

8] Cook J.L., Picatinny A. and J.E. Ramirez- Marquez, “Capacitated reliability for ad-hoc network”, under U.S. Government research work, 2007.

[9] Soh Siesteng and Suresh Rai, An efficient cutset approach for evaluating communication-network reliability with heterogeneous link-capacities, IEEE Transactions on Reliability, vol. 54, no. 1,pp. 133-144, 2005.

[10] Rai Suresh, Veerarghavan and K.S. Trivedi, A survey of efficient reliability computation using disjoint products approach Networks, John Wiley & Sons, Inc.,vol. 25, pp. 147-163, 1995.

[11] Soh S., Rai S. and R.R. Brooks, “Performance issues in wireless communication network”, issues Handbook of Performability Engineering, pp. 1047-1067, 2008.

[12] Villavarde B.C., Rea S. and D. Pesch, “In Route – A QoS aware route selection algorithm for industrial wireless sensor networks”, Journal of Ad Hoc Networks, pp. 1-25, 2011.

**THANK YOU**

k-terminal reliability

Probability that there exist operating paths between every pair of nodes in K

Two terminal reliability

Probability that there exist operating path between 2 nodes (|K| = 2)

All terminal reliability

Probability that there exist operating paths between all nodes (K=V)