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Infocompres - A Theoretical Framework for Hierarchical...

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A Theoretical Framework for Hierarchical Routing Games Vijay Kamble (IIT Kharagpur) Eitan Altman (INRIA Sophia-Antipolis) Rachid El Azouzi (LIA, University of Avignon) Vinod Sharma (IISc Bangalore) UC Berkeley, Sept 9 2010 Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 1 / 21
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Outline 1 Overview 2 System Wardrop Equilibrium 3 Existence, Uniqueness 4 Application and Conclusion Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 2 / 21
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Overview Outline 1 Overview 2 System Wardrop Equilibrium 3 Existence, Uniqueness 4 Application and Conclusion Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 3 / 21
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Overview Non-Atomic Routing Games Consider Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 4 / 21
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Overview Non-Atomic Routing Games Consider A Network of directed arcs without cycles Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 4 / 21
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Overview Non-Atomic Routing Games Consider A Network of directed arcs without cycles A population of packets belonging to a finite number of classes Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 4 / 21
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Overview Non-Atomic Routing Games Consider A Network of directed arcs without cycles A population of packets belonging to a finite number of classes A source node and a destination node for each class with the packets arriving at the source nodes in the form of a flow. Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 4 / 21
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Overview Non-Atomic Routing Games Consider A Network of directed arcs without cycles A population of packets belonging to a finite number of classes A source node and a destination node for each class with the packets arriving at the source nodes in the form of a flow. A delay function per packet on each arc of the Network due to congestion which depends on the flow through that arc. Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 4 / 21
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Overview Non-Atomic Routing Games Consider A Network of directed arcs without cycles A population of packets belonging to a finite number of classes A source node and a destination node for each class with the packets arriving at the source nodes in the form of a flow. A delay function per packet on each arc of the Network due to congestion which depends on the flow through that arc. Problem How do we route the flow on the network so that the least delay path is chosen for each packet? Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 4 / 21
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Overview Non-Atomic Routing Games Consider A Network of directed arcs without cycles A population of packets belonging to a finite number of classes A source node and a destination node for each class with the packets arriving at the source nodes in the form of a flow.
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