Selfish Behavior and Stability of the Internet: A Game-Theoretic Analysis of TCP Presented by Shariq Rizvi CS 294-4: Peer-to-Peer Systems

The Issue Bulk of bytes transferred on the internet is TCP TCP offers “socially responsible” congestion control Network end-points free to play selfish (tweak TCP parameters) “Players” want to maximize throughput for their TCP flows How does the internet perform under Nash equilibrium?

Nash Equilibrium “A Nash equilibrium, named after John Nash, is a set of strategies, one for each player, such that no player has incentive to unilaterally change her action. Players are in equilibrium if a change in strategies by any one of them would lead that player to earn less than if she remained with her current strategy.”

Why model as a game? Aggressive congestion control => higher loss rates Loss recovery incurs some “cost” Aggressive congestion control not always beneficial Specific parameter settings give maximum “gain” to an end-point given settings for other end-points

The TCP Game TCP flows F 1, …, F n Additive Increase Multiplicative Decrease (AIMD) algorithm for congestion control and avoidance Each flow F i can tweak its α i (≥1) and β i (0≤β i ≤1)

Simplifying Assumptions Common loss recovery strategies (timeout, fast retransmission etc.) All flows are endless Single common bottleneck (dumb-bell topology for simulations) Identical round trip times Symmetric Nash equilibrium

Factors Affecting The Game Congestion control parameters Nature of loss recovery algorithm Loss assignment at bottleneck router

End-point behavior Rounds of transmission, RTT long N i t – Number of outstanding packets of F i in round t L i t – Number of lost packets for F i in round t N i t+1 – Depends on Congestion control parameters Penalty function – loss recovery

Penalty Models Slow-start Restransmission without timeouts Timeout and slow-start

Queue Management Simple FIFO drop-tail Over-flow point spanning one round At overflow point, L i = α i RED All flows experience common packet loss rate p p is a function of congestion control parameters

Simulation Methodology Fix values of α and β for flows F 1, …, F n-1 Vary parameter values for F n “around” these values Find the local maximum for the average value of goodput G n Use these as new values of α and β; continue Stop when chosen α and β offer the local maximum This is the Nash equilibrium

Results: Gentle Penalty and Drop-Tail Undesirable Desirable Both allowed to vary: (α=15, β=0.98) (Goodput=0.95 MbPS, Loss Rate=26%)

Other Drop-tail results With severe penalty – undesirably low goodput With hybrid penalty – Efficient Nash equilibrium (old internet)

RED Gateways Severe penalty – Low goodput, undesirable Gentle penalty – Equilibrium is unfair (highly aggressive) Hybrid penalty – Better than above two but worse compared to default parameter setting

Conclusion All schemes employing RED queue management result in inefficient Nash equilibria Solution: Modify queue management Fair queueing is complex (per-flow info) Attempt preferential dropping of packets (greater loss to aggressive flows)

CHOKe A preferential dropping scheme Maintains a FIFO buffer When queue occupancy is more than some threshold, drop packets from same flow High loss rate and possible under- utilization Improve CHOKe!

CHOKe+ Less aggressive packet-dropping Drop packets of a flow, only if their number in buffer exceeds some threshold Isolates aggressive flow from the rest Ensures that increase in loss rate is just sufficient to discourage aggression More desirable Nash equilibria

Related Paper “TCP Congestion Control with a Misbehaving Receiver” Computer Comm. Review, 1999