Routing games muri meeting sept 9 2010 11 21 system

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: archical Routing Games MURI meeting, Sept 9 2010 11 / 21 System Wardrop Equilibrium Multilevel Wardrop equilibria For a fixed p, we find wardrop equilibrium for each level separately W.E for High priority flow: xl∗H (Tl (xl∗H ) − α(p)) = 0, l ∈ E Tl (xl∗H ) − α(p) ≥ 0, l ∈ E K ￿ l =1 xl∗H = r (1 − p) Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 11 / 21 System Wardrop Equilibrium Multilevel Wardrop equilibria For a fixed p, we find wardrop equilibrium for each level separately W.E for High priority flow: xl∗H (Tl (xl∗H ) − α(p)) = 0, l ∈ E Tl (xl∗H ) − α(p) ≥ 0, l ∈ E K ￿ l =1 xl∗H = r (1 − p) W.E. for the low priority flow: xl∗L (Tl (xl∗H + xl∗L ) − β (p)) = 0, l ∈ E Tl (xl∗H + xl∗L ) − β (p) ≥ 0, l ∈ E K ￿ l =1 xl∗L = γ rp Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 11 / 21 System Wardrop Equilibrium Multilevel Wardrop equilibria For a fixed p, we find wardrop equilibrium for each level separately W.E for High priority flow: xl∗H (Tl (xl∗H ) − α(p)) = 0, l ∈ E Tl (xl∗H ) − α(p) ≥ 0, l ∈ E K ￿ l =1 xl∗H = r (1 − p) W.E. for the low priority flow: xl∗L (Tl (xl∗H + xl∗L ) − β (p)) = 0, l ∈ E Tl (xl∗H + xl∗L ) − β (p) ≥ 0, l ∈ E K ￿ l =1 xl∗L = γ rp ¯ α(p) = α(p) + C H and β (p) = β (p) + C L are the costs per packet at W.E. ¯ Vijay Kamble (IIT Kharagpur, INDIA) Hierarchical Routing Games MURI meeting, Sept 9 2010 11 / 21 System Wardrop Equilibrium S.W.E. Definition (System Wardrop equilibrium) ¯ ¯ The flow profiles x ∗H , x ∗L and p∗ constitute a System Wardrop equilibrium if either of the three conditions are satisfied: ¯ ¯ p∗ ∈ (0, 1), x ∗H and x ∗L satisfy the multilevel W.E. conditions and ¯ α (p ∗ ) = β (p ∗ ) ¯ ¯ ¯ p∗ = 1, x ∗L sa...
View Full Document

Ask a homework question - tutors are online