The Value of Information in Selfish Routing Simon Scherrer, Adrian - PowerPoint PPT Presentation

The Value of Information in Selfish Routing Simon Scherrer, Adrian Perrig, Stefan Schmid 27th International Colloquium on Structural Information and Communication Complexity (SIROCCO) June 29 - July 1, 2020 The Value of Information in Selfish Routing | | 1 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Network-based path selection A 2 A 4 p e 1 A 1 A 3 A 5 A 7 e 2 A 6 Suboptimal No robustness paths to failures The Value of Information in Selfish Routing | | 2 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Source-based path selection A 2 A 4 p 1 p 2 e 1 A 1 A 3 A 5 A 7 e 2 p 3 A 6 Suboptimal Best path No robustness Fast rerouting paths for use case to failures on failure The Value of Information in Selfish Routing | | 3 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Network-based path selection: Network operator view The Value of Information in Selfish Routing | | 4 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Source-based path selection: Network operator view The Value of Information in Selfish Routing | | 5 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Goals of our work Revisit selfish-routing concepts to investigate two issues arising in emerging path-aware Internet architectures: ▪ Impact of information: What network state information should be shared with end-hosts? ▪ Impact on network operators: What is the impact of selfish routing on the cost of network operators? The Value of Information in Selfish Routing | | 6 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Price of Anarchy: Three components C Social cost function C(F eq ) PoA = F opt Social optimum C(F opt ) F eq Equilibrium The Value of Information in Selfish Routing | | 7 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Adapted Wardrop model of source-based path selection e 2 e 3 d = (d 1,2 , d 3,4 ) = (1, 1) A 2 F = (F α , F γβ , F β , F αγ ) α β f = (f α , f β , f γ ) γ A 1 A 3 c α (f α ) = 1 e 1 e 4 C π ( F ) = Σ ℓ ∈ π c ℓ 2 c β (f β ) = f β c γ (f γ ) = f γ The Value of Information in Selfish Routing | | 8 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Total cost functions and social optima End-host cost function: C * = Σ end-hosts Σ paths flow on path · path cost = Σ π ∈ Π F π · C π ( F ) = Σ ℓ ∈ L f ℓ · c ℓ (f ℓ ) (classic) F * = argmin F C * ( F ) End-host optimum: Network-operator cost function: C # = Σ links link cost = Σ ℓ c ℓ (f ℓ ) F # = argmin F C # ( F ) Network-operator optimum: The Value of Information in Selfish Routing | | 9 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Characterizing social optima: Suboptimal path flow pattern C π ( F ) C α (F α ) d = (d 1,2 ) = (1) C β (F β ) F = (F α , F β ) Δ C α + C( F ) = C α (F α ) + C β (F β ) δ C α ∃ δ . | Δ C α + | < | Δ C β - | δ ⇒ C can be reduced Δ C β - C β 1 F π The Value of Information in Selfish Routing | | 10 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Characterizing social optima: Optimal path flow pattern C π ( F ) C α (F α ) ∀ δ . | Δ C α + | > | Δ C β - | C β (F β ) ⇒ C cannot be reduced Δ C α + m = ∂C/∂F α ⇒ C is optimal δ C α ∂C/∂F α = ∂C/∂F β ⇒ ∀ δ . | Δ C α + | > | Δ C β - | m = ∂C/∂F β ⇒ C is optimal δ Δ C β - C β 1 F π The Value of Information in Selfish Routing | | 11 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Socially optimal marginal costs ∂C( F )/∂F π is the marginal cost of path π given path-flow pattern F A path-flow pattern F is optimal w.r.t. a cost function C ∈ {C * ,C # } if for every origin-destination pair : F α , …, F ρ > 0 F σ , …, F ω = 0 ∂C( F ) ∂C( F ) ∂C( F ) ∂C( F ) = … = ≤ ≤ … ≤ ∂F σ ∂F ω ∂F α ∂F ρ The Value of Information in Selfish Routing | 12 | Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Social optimum: Comparison (Example) α 2 C α (F α ) = F α F # = (F α , F β , F γ ) = (½, 0, ½) β C β (F β ) = 2 F β A 1 A 2 e 1 e 2 F * = (F α , F β , F γ ) = (⅔, ⅓, 0) + 2 γ C γ (F γ ) = F γ Different optima! Network operators prefer usage of links with little variable cost (here: γ ) The Value of Information in Selfish Routing | | 13 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Price of Anarchy: Where are we? C Total cost function C(F eq ) PoA = F opt Social optimum C(F opt ) F eq Equilibrium The Value of Information in Selfish Routing | | 14 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Equilibrium with latency-only information (LI equilibrium) α C α = 2 d = (d 1,2 ) = (1) A 1 A 2 F = (F α , F β ) e 1 e 2 = (1, 0) β C β = 2 F = (1,0) is an LI equilibrium ⇒ C α = C β The Value of Information in Selfish Routing | | 15 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Characterizing the LI equilibrium A path flow pattern F is an LI equilibrium if for every origin-destination pair : F α , …, F ρ > 0 F σ , …, F ω = 0 C α ( F ) = … = C ρ ( F ) ≤ C σ ( F ) ≤ … ≤ C ω ( F ) The Value of Information in Selfish Routing | | 16 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Equilibrium with perfect information (PI equilibrium) α : c α (f α ) = f α d (1) = (d 1,2 ) = (1) f α = F α + 1 A 1 A 2 F (1) = (F α , F β ) e 1 e 2 f β = F β + 1 β : c β (f β ) = 2 Minimize selfish cost C (1) ( F (1) ) = F α ·(F α + 1) + F β ·2 ⇒ (F α , F β ) = (⅔, ⅓) is a PI equilibrium The Value of Information in Selfish Routing | | 17 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Characterizing the PI equilibrium A path flow pattern F is a PI equilibrium if for every origin-destination pair of any end-host e: F α , …, F ρ > 0 F σ , …, F ω = 0 ∂C (e) ( F ) ∂C (e) ( F ) ∂C (e) ( F ) ∂C (e) ( F ) = … = ≤ ≤ … ≤ ∂F α ∂F ω ∂F σ ∂F ρ The Value of Information in Selfish Routing | | 18 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

Capturing the value of information Information Latency-only Perfect assumption Information (LI) Information (PI) Equilibrium F 0 F + C( F 0 ) C( F + ) Price of Anarchy PoA 0 = a PoA + = a C( F opt ) C( F opt ) Δ = Value of Information ( VoI ) The Value of Information in Selfish Routing | | 19 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

The benefits of information VoI > 0 The Value of Information in Selfish Routing | | 20 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

The benefits of information: Network of parallel links (cf. Roughgarden 2003) Σ k d k,T = 1 e 1 α c α (f α ) = 1 A 1 A 2 ... F = (F 1 α , F 1 β , ... e T β c β (f β ) = f β F K α , F K β ,) e K EH Opt: F * s.t. f β = 1/2 LI Eq: F 0 s.t. f β = 1 NO Opt: F # s.t. f β = 0 PI Eq: F + s.t. f β = K/(K+1) The Value of Information in Selfish Routing | | 21 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

The benefits of information: Network of parallel links LI equilibrium PI equilibrium PoA *+ = PoA *0 = End-host (K 2 + K + 1)/(K 2 + 2K + 1) · 4/3 4/3 perspective ≤ PoA *0 Network- PoA #+ = PoA #0 = operator 1+ K/(K + 1) 2 ≤ 2 = PoA #0 perspective The Value of Information in Selfish Routing | | 22 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

The benefits of information: Network of parallel links LI equilibrium PI equilibrium PI equilibrium PoA *+ = PoA *0 = End-host cheaper than (K 2 + K + 1)/(K 2 + 2K + 1) · 4/3 4/3 perspective ≤ PoA *0 LI equilibrium Network PoA #+ = PoA #0 = VoI > 0 operator 1+ K/(K + 1) 2 ≤ 2 = PoA #0 perspective The Value of Information in Selfish Routing | | 23 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

The drawbacks of information VoI < 0 The Value of Information in Selfish Routing | | 24 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

The drawbacks of information: Ladder network 2 h 1 c h1 (f h1 ) = f h1 A 11 A 12 e 11 e 12 d = (d 11,12 , d 21,22 ) c v1 (f v1 ) = f v1 = (1, 1) v 2 v 1 F → = (1, 0, 1, 0) c v2 (f v2 ) = f v2 A 21 A 22 e 21 e 22 h 2 c h2 (f h2 ) = f h2 2 Direct-only F → is universally optimal: F → = F * = F # The Value of Information in Selfish Routing | | 25 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

The drawbacks of information: Ladder network 2 h 1 c h1 (f h1 ) = f h1 F → = (1, 0, 1, 0) A 11 A 12 e 11 e 12 c v1 (f v1 ) = f v1 v 2 v 1 c v2 (f v2 ) = f v2 A 21 A 22 e 21 e 22 h 2 c h2 (f h2 ) = f h2 2 C 1H ( F → ) = 1 = C 1V ( F → ) ⇒ F → = F 0 (LI equilibrium is optimal) The Value of Information in Selfish Routing | | 26 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020

The drawbacks of information: Ladder network 2 h 1 c h1 (f h1 ) = f h1 F → = (1, 0, 1, 0) A 11 A 12 e 11 e 12 F ~ = (0.9, 0.1, 1, 0) c v1 (f v1 ) = f v1 v 2 v 1 c v2 (f v2 ) = f v2 A 21 A 22 e 21 e 22 h 2 c h2 (f h2 ) = f h2 2 C (1) ( F → ) = 1 > C (1) ( F ~ ) = 0.87 ⇒ F → ≠ F + (PI equilibrium is suboptimal) The Value of Information in Selfish Routing | | 27 Simon Scherrer, Adrian Perrig, Stefan Schmid @ SIROCCO 2020