Tunable QoS-Aware NetworkSurvivability

Jose Yallouz Joint work with Ariel Orda

Department of Electrical Engineering, Technion

Intr

oduc

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Introduction • Survivability – the capability of the network to maintain

service continuity in the presence of failures.

• Single Link Failure Model assumes that at most one link failure should be handled in the network.

• Protection is a type of pre-planning process established before a failure occurs.

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Intr

oduc

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Tunable survivability• Full survivability - (100%) protection against network single failures. • Establishment of pairs of disjoint paths. • This scheme is often too restrictive.

• Tunable survivability allows any desired degree of survivability in the range 0% to 100%.

• Increase the space of feasible solutions.

• In our work, we focus on the combination of survivability and other QoS additive criteria.• delay, jitter, cost.

common link

=0.01

=0.99

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Model Formulation

• Network represented by a directed graph, G = (V, E)• : additive QoS target on link e (such as delay, cost, etc)• : failure probability of link e• Given a pair of source and target nodes s and t, a survivable

connection is a pair of paths (not necessarily disjoint).

• The survivability level of is defined:• The probability that all common links are operational• ()• 1 ()

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1-0.01=(0.99)-survivability level

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Model Formulation• The weight of can be defined in 2 forms:

• CT - counting the common links twice

• average delay (over the employed paths)

• CO - counting the common links once

• A cost charged for the utilization of the links

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CO-Weight: 1+10+100+1+1=113

𝑤𝑒2 ∙𝑤𝑒

CT-Weight: 100+10+1+1+2=114

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Problem Illustration

• Transmission delay can be reduced drastically by slightly alleviating the survivability requirement of the connection.

(1-0.01)2=(0.99)2-survivability levelCT-Weight: 10+10+1+1+1=24

1-0.01=(0.99)-survivability levelCT-Weight: 100+10+1+1+1=114

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Optimization Problems

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The

Stru

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CT

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The Structure of CT Solutions

S t

criticallink

vi vj

𝜋 1

𝜋 2

• Definition 1: Given a survivable connection a critical link is a link that is common to both paths and . • The set of critical links of a survivable connection

• .

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The Structure of CT Solutions• Definition 1: WS(s,t) is the set of all the weight-shortest paths

between s and t . • Definition 2: An in-all-weight-shortest-paths link is a link e

that is common to all paths in WS(s,t). • The set of in-all-weight-shortest-paths links

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S t

In-all-weight-shortest path links

The

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The Structure of CT Solutions• Theorem: Any survivable connection that is an optimal solution

of the respective CT-Constrained QoS Max-Survivability Problem is such that all its critical links are in-all-weight-shortest-paths links.

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S t

criticallink

vi vj

𝜋 1

𝜋 2

S tvi vj

In-all-weight-shortest path links

Algo

rithm

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Algorithmic Scheme• Problem CT-CQMS is NP-Hard.• A reduction from the Partition Problem (PP)

• Pseudo polynomial and Fully Polynomial Time Approximation Scheme (FPTAS) solutions are proposed

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Algo

rithm

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Algorithm for the CT Problem– Establishing QoS Aware p-survivable connection

• Graph transformation:• “critical link” transformation :

• For each link e in :

• “disjoint link” transformation : For each couple of nodes and in :

• Find the shortest survivable path under a weight constrain B, according to any Approximation Algorithm Restricted Shortest Path.

𝑾 (𝝅𝟏 )

𝑾 (𝝅𝟐 )

(We, Pe)

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st

survivable connection

Algo

rithm

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Algorithm for the CT Problem– Establishing QoS Aware p-survivable connection

• Find a weight-shortest path between s and the t

• Graph transformation:• “critical link” transformation :

• For each link e in :

• “disjoint link” transformation : For each couple of nodes and in :

• Find the shortest survivable path under a weight constrain B, according to any Approximation Algorithm Restricted Shortest Path.

𝑾 (𝝅𝟏 )

𝑾 (𝝅𝟐 )

(We, Pe)

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Algo

rithm

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Algorithm for the CT Problem

S T

P=0.01

W=4

P=0.03

W=1

P=0.02

W=1

P=0.01

W=1

P=0.01

W=3

• Find the most survivable connection where its CT-weight is restricted to 8.

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max ∏𝜋1∩𝜋2

(1−𝑝𝑒)𝑠 . 𝑡 ∑𝑒∈𝜋1

𝑤𝑒+ ∑𝑒∈ 𝜋2

𝑤𝑒≤8

Algo

rithm

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Algorithm for the CT Problem

S T

P=0.01

W=4

P=0.03

W=1

P=0.02

W=1

P=0.01

W=1

P=0.01

W=3

1. Find a minimum weight shortest path between s and t.

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Algo

rithm

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Algorithm for the CT Problem

S T

P=0.01

W=4

P=0.03

W=1

P=0.02

W=1

P=0.01

W=1

P=0.01

W=3

2. “critical link” transformation• For each link e in :

S=-ln0.97

W=2

S=-ln0.98

W=2

S=-ln0.99

W=2

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(We, Pe)

Algo

rithm

Algorithm for the CT Problem

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S T

P=0.01

W=4

P=0.03

W=1

P=0.02

W=1

P=0.01

W=1

P=0.01

W=3

P=0

W=6

P=0

W=5P=0

W=9

3. “disjoint link” transformation• For each pair of nodes and in :

𝑾 (𝝅𝟏 )

𝑾 (𝝅𝟐 )

Algo

rithm

Algorithm for the CT Problem

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S T

• Find the most survivable connection where its weight is restricted to 8

P=0

W=6

P=0

W=5P=0

W=9

4. Solve the Restricted Shortest Path Problem min (

S=-ln0.97

W=2

S=-ln0.98

W=2

S=-ln0.99

W=2

Algo

rithm

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Algorithm for the CT Problem

S T

P=0.01

W=4

P=0.03

W=1

P=0.02

W=1

P=0.01

W=1

P=0.01

W=3

• Find the most survivable connection where its CT-weight is restricted to 8.

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max ∏𝜋1∩𝜋2

(1−𝑝𝑒)𝑠 . 𝑡 ∑𝑒∈𝜋1

𝑤𝑒+ ∑𝑒∈ 𝜋2

𝑤𝑒≤8

Sim

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Power Law simulations for different values of (percentage of “fast” links).

Simulation • Assuming different ratios of “slow” and “fast” delay links.

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Delay improved

by 50%

Conc

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Conclusion

• Optimization problems combining the survivability level and an additive QoS criteria.

• Characterized fundamental properties of CT-problems.• Established algorithmic schemes.• Comprehensive simulations show the advantage of tunable

survivability.• Our scheme can be implemented in state of the art architectures

such as MPLS.

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THANKS!!22