Cache Capacity Allocation for BitTorrent-like Systems to Minimize - PowerPoint PPT Presentation

Problem Definition Bandwidth Allocation Evaluation Conclusions Cache Capacity Allocation for BitTorrent-like Systems to Minimize Inter-ISP Traffic Valentino Pacifici, Frank Lehrieder, Gy¨ orgy D´ an School of Electrical Engineering Institute of Computer Science KTH Royal Institute of Technology University of W¨ urzburg Stockholm, Sweden W¨ urzburg, Germany Orlando, March 29, 2012 V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 1 / 17

Problem Definition Bandwidth Allocation Evaluation Conclusions P2P Traffic P2P Traffic • Up to 70 % of network traffic • Source of Inter-ISP traffic ⇒ cost for low level ISPs Decreasing Inter-ISP traffic 1 Locality awareness 2 P2P caching Cache ISP 1 "rest of internet" V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 2 / 17

Cache ISP 1 "rest of internet" Problem Definition Bandwidth Allocation Evaluation Conclusions P2P Caching P2P Caching Cache resource management 1 Storage capacity ⇒ cache eviction (LRU,LFU,GDS,ARC,...) 2 Bandwidth ⇒ not actively managed (e.g. Web caches) Should bandwidth be actively managed so as to minimize the amount of Inter-ISP traffic? V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 3 / 17

Cache ISP 1 "rest of internet" Problem Definition Bandwidth Allocation Evaluation Conclusions P2P Caching P2P Caching Cache resource management 1 Storage capacity ⇒ cache eviction (LRU,LFU,GDS,ARC,...) 2 Bandwidth ⇒ not actively managed (e.g. Web caches) Should bandwidth be actively managed so as to minimize the amount of Inter-ISP traffic? V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 3 / 17

Problem Definition Bandwidth Allocation Evaluation Conclusions P2P Caching P2P Caching Cache resource management 1 Storage capacity ⇒ cache eviction (LRU,LFU,GDS,ARC,...) 2 Bandwidth ⇒ not actively managed (e.g. Web caches) Should bandwidth be actively managed so as to minimize the amount of Inter-ISP traffic? Cache ISP 1 "rest of internet" V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 3 / 17

Problem Definition Bandwidth Allocation Evaluation Conclusions System Model System Model without Cache • Set of ISPs I = { 1 , . . . , I } , Set of swarms S = { 1 , . . . , S } • Markovian model of system dynamics • System state Z i,s ( t ) = ( X i,s ( t ) , Y i,s ( t )) • Parameters ( λ i,s , θ, γ, µ, η ) γY i,s λ i,s q i,s X i,s µ ( ηX s + Y s ) X i,s Y i,s q i,s = X s � �� � available upload rate θX i,s Swarm s , ISP i • Incoming inter-ISP traffic rate I i,s ( Z s ( t ) , . ) V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 4 / 17

Problem Definition Bandwidth Allocation Evaluation Conclusions System Model System Model without Cache • Set of ISPs I = { 1 , . . . , I } , Set of swarms S = { 1 , . . . , S } • Markovian model of system dynamics • System state Z i,s ( t ) = ( X i,s ( t ) , Y i,s ( t )) • Parameters ( λ i,s , θ, γ, µ, η ) γY i,s λ i,s q i,s X i,s µ ( ηX s + Y s ) X i,s Y i,s q i,s = X s � �� � available upload rate θX i,s Swarm s , ISP i • Incoming inter-ISP traffic rate I i,s ( Z s ( t ) , . ) V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 4 / 17

Problem Definition Bandwidth Allocation Evaluation Conclusions System Model System Model with Cache • Set of ISPs I = { 1 , . . . , I } , Set of swarms S = { 1 , . . . , S } • Markovian model of system dynamics • System state Z i,s ( t ) = ( X i,s ( t ) , Y i,s ( t )) • Parameters ( λ i,s , θ, γ, µ, η,κ i,s ) • K i < ∞ bandwidth capacity of cache in ISP i γY i,s λ i,s q i,s X i,s µ ( ηX s + Y s )+ κ i,s X i,s Y i,s q i,s = X s � �� � available upload rate θX i,s Swarm s , ISP i • Incoming inter-ISP traffic rate I i,s ( Z s ( t ) , κ i,s ( t )) V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 5 / 17

Problem Definition Bandwidth Allocation Evaluation Conclusions Optimal Allocation Cache Bandwidth Allocation Problem • Cache bandwidth allocation of ISP i at time t κ i ( t ) = ( κ i, 1 ( t ) , . . . , κ i,S ( t )) �� � � � � • Defined by policy π : κ i ( t ) = F π Z ( u ) κ i ( u ) u<t , u<t V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 6 / 17

Problem Definition Bandwidth Allocation Evaluation Conclusions Optimal Allocation Cache Bandwidth Allocation Problem • Cache bandwidth allocation of ISP i at time t κ i ( t ) = ( κ i, 1 ( t ) , . . . , κ i,S ( t )) �� � � � � • Defined by policy π : κ i ( t ) = F π Z ( u ) κ i ( u ) u<t , u<t • Expected incoming inter-ISP traffic under allocation policy π �� T � � C π i ( Z (0) , T ) = E π I i,s ( Z s ( t ) , κ i,s ( t )) dt Z (0) 0 s ∈S V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 6 / 17

Problem Definition Bandwidth Allocation Evaluation Conclusions Optimal Allocation Cache Bandwidth Allocation Problem • Cache bandwidth allocation of ISP i at time t κ i ( t ) = ( κ i, 1 ( t ) , . . . , κ i,S ( t )) �� � � � � • Defined by policy π : κ i ( t ) = F π Z ( u ) κ i ( u ) u<t , u<t • Expected incoming inter-ISP traffic under allocation policy π �� T � � C π i ( Z (0) , T ) = E π I i,s ( Z s ( t ) , κ i,s ( t )) dt Z (0) 0 s ∈S Find the optimal policy π ∗ ∈ Π s.t. 1 π ∈ Π C π T C π inf i ( Z (0)) = inf π lim sup i ( Z (0) , T ) . T →∞ V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 6 / 17

Problem Definition Bandwidth Allocation Evaluation Conclusions Optimal Allocation Cache Bandwidth Allocation Problem • Cache bandwidth allocation of ISP i at time t κ i ( t ) = ( κ i, 1 ( t ) , . . . , κ i,S ( t )) �� � � � � • Defined by policy π : κ i ( t ) = F π Z ( u ) κ i ( u ) u<t , u<t • Expected incoming inter-ISP traffic under allocation policy π �� T � � C π i ( Z (0) , T ) = E π I i,s ( Z s ( t ) , κ i,s ( t )) dt Z (0) 0 s ∈S Find the optimal policy π ∗ ∈ Π s.t. 1 π ∈ Π C π T C π inf i ( Z (0)) = inf π lim sup i ( Z (0) , T ) . T →∞ V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 6 / 17

Problem Definition Bandwidth Allocation Evaluation Conclusions Optimal Allocation Existence of Optimal Stationary Policy γY i,s λ i,s • Markov Decision Process q i,s ( κ i,s ) < Z , K , Q ( κ ) , I ( z, κ ) > X i,s Y i,s θX i,s Theorem There exists an optimal stationary policy π ∗ ∈ Π that minimizes C π i ( Z (0)) The optimal policy π ∗ • Stationary: κ i ( t ) is only a function of the system state Z ( t ) • Calculation requires steady state probabilities • Prohibitive even for few ISPs and swarms • Use of simple approximations to gain insight... V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 7 / 17

Problem Definition Bandwidth Allocation Evaluation Conclusions Optimal Allocation Existence of Optimal Stationary Policy γY i,s λ i,s • Markov Decision Process q i,s ( κ i,s ) < Z , K , Q ( κ ) , I ( z, κ ) > X i,s Y i,s θX i,s Theorem There exists an optimal stationary policy π ∗ ∈ Π that minimizes C π i ( Z (0)) The optimal policy π ∗ • Stationary: κ i ( t ) is only a function of the system state Z ( t ) • Calculation requires steady state probabilities • Prohibitive even for few ISPs and swarms • Use of simple approximations to gain insight... V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 7 / 17

Problem Definition Bandwidth Allocation Evaluation Conclusions Allocation Policies One-Step Look Ahead (OLA) • Minimize the incoming inter-ISP traffic rate given the system state � κ i ( t ) = arg min I i,s ( Z s ( t ) , κ i,s ) κ i ∈K i s ∈S • Short term approximation → disregards system dynamics V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 8 / 17

Problem Definition Bandwidth Allocation Evaluation Conclusions Allocation Policies One-Step Look Ahead (OLA) • Minimize the incoming inter-ISP traffic rate given the system state � κ i ( t ) = arg min I i,s ( Z s ( t ) , κ i,s ) κ i ∈K i s ∈S • Short term approximation → disregards system dynamics 0.2 Optimal κ i ( t ) leads to equal Swarm 1 0.18 Swarm 2 marginal traffic saving for every Inter−ISP traffic savings [Mbit/s] 0.16 Swarm 3 swarm 0.14 0.12 0.1 0.08 ∂I i,s ( z s , κ i,s ) κ i,s > 0 ⇒ = ζ 0.06 ∂κ i,s 0.04 ∂ − I i,s ( z s , κ i,s ) 0.02 κ i,s = 0 ⇒ ≥ ζ ∂κ i,s 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Cache bandwidth K 1 of ISP 1 [Mbit/s] V. Pacifici, F. Lehrieder, G. D´ an () INFOCOM 2012 March 29, 2012 8 / 17