# We studying its characteristics vijay kamble iit

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Unformatted text preview: le (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 8 / 21 Overview Our Contributions A framework for modeling such Hierarchical Non-atomic Routing games with two priority levels Extending the concept of Wardrop equilibrium to such games: System Wardrop Equilibrium (S.W.E.) Studying its Characteristics Existence, Uniqueness, Computation Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 8 / 21 System Wardrop Equilibrium Outline 1 Overview System Wardrop Equilibrium Existence, Uniqueness Application and Conclusion 2 3 4 Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 9 / 21 System Wardrop Equilibrium The model Consider A Network Topology given by G = (E , {s, d }). |E | = K Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 10 / 21 System Wardrop Equilibrium The model Consider A Network Topology given by G = (E , {s, d }). |E | = K Total ﬂow demand r (packets per sec). Two levels: High Priority, Low priority Low priority ﬂow γ rp, High priority ﬂow r (1 − p). p ∈ [0, 1], γ is the compression factor. Total ﬂow routed: ¯(p) = r (γ p + (1 − p)) r ¯¯¯ Flows: xlH , xlL , xl = xlH + xlL , Proﬁles: x H , x L , x Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 10 / 21 System Wardrop Equilibrium The model Consider A Network Topology given by G = (E , {s, d }). |E | = K Total ﬂow demand r (packets per sec). Two levels: High Priority, Low priority Low priority ﬂow γ rp, High priority ﬂow r (1 − p). p ∈ [0, 1], γ is the compression factor. Total ﬂow routed: ¯(p) = r (γ p + (1 − p)) r Link delay per packet functions Tl . For High priority ﬂow: Tl (xlH ), For Low priority ﬂow: Tl (xl ) (High priority ﬂow unaffected by Low priority ﬂow) Cost per packet for routing as High priority: C H , Low Priority: C L Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 10 / 21 ¯¯¯ Flows: xlH , xlL , xl = xlH + xlL , Proﬁles: x H , x L , x System Wardrop Equilibrium Multilevel Wardrop equilibria For a ﬁxed p, we ﬁnd wardrop equilibrium for each level separately Vijay Kamble (IIT Kharagpur, INDIA) Hier...
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## This note was uploaded on 09/27/2010 for the course EE 229 taught by Professor R.srikant during the Spring '09 term at University of Illinois, Urbana Champaign.

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