On Flow-Aware CSMA in Multi-Channel Wireless Networks Mathieu - PowerPoint PPT Presentation

On Flow-Aware CSMA in Multi-Channel Wireless Networks Mathieu Feuillet Joint work with Thomas Bonald CISS 2011

Outline Model Background Standard CSMA Flow-aware CSMA Conclusion

Outline Model Background Standard CSMA Flow-aware CSMA Conclusion

Conflict graphs The network is represented by a set of conflict graphs, one per channel. 3 Channel 1 1 2 Channel 2 1 2 3

Conflict graphs The network is represented by a set of conflict graphs, one per channel. 3 Channel 1 1 2 Channel 2 1 2 3 Conflict graphs on different channels can be different.

Conflict graphs Channel 1 1 2 3 Channel 2 1 2 3 Schedules: ◮ ∅, { ( 1 , 1 ) } , { ( 2 , 1 ) } , { ( 3 , 1 ) } , { ( 1 , 1 ) , ( 3 , 1 ) } .

Conflict graphs Channel 1 1 2 3 Channel 2 1 2 3 Schedules: ◮ ∅, { ( 1 , 1 ) } , { ( 2 , 1 ) } , { ( 3 , 1 ) } , { ( 1 , 1 ) , ( 3 , 1 ) } .

Conflict graphs Channel 1 1 1 2 3 Channel 2 1 2 3 Schedules: ◮ ∅, { ( 1 , 1 ) } , { ( 2 , 1 ) } , { ( 3 , 1 ) } , { ( 1 , 1 ) , ( 3 , 1 ) } .

Conflict graphs Channel 1 1 2 2 3 Channel 2 1 2 3 Schedules: ◮ ∅, { ( 1 , 1 ) } , { ( 2 , 1 ) } , { ( 3 , 1 ) } , { ( 1 , 1 ) , ( 3 , 1 ) } .

Conflict graphs Channel 1 1 2 3 3 Channel 2 1 2 3 Schedules: ◮ ∅, { ( 1 , 1 ) } , { ( 2 , 1 ) } , { ( 3 , 1 ) } , { ( 1 , 1 ) , ( 3 , 1 ) } .

Conflict graphs Channel 1 1 1 2 3 3 Channel 2 1 2 3 Schedules: ◮ ∅, { ( 1 , 1 ) } , { ( 2 , 1 ) } , { ( 3 , 1 ) } , { ( 1 , 1 ) , ( 3 , 1 ) } .

Conflict graphs Channel 1 1 2 3 Channel 2 1 2 3 Schedules: ◮ ∅, { ( 1 , 1 ) } , { ( 2 , 1 ) } , { ( 3 , 1 ) } , { ( 1 , 1 ) , ( 3 , 1 ) } . ◮ { ( 1 , 2 ) } , { ( 2 , 2 ) } , { ( 3 , 2 ) } , { ( 1 , 2 ) , ( 3 , 2 ) } .

Conflict graphs Channel 1 1 2 3 Channel 2 1 2 3 Schedules: ◮ ∅, { ( 1 , 1 ) } , { ( 2 , 1 ) } , { ( 3 , 1 ) } , { ( 1 , 1 ) , ( 3 , 1 ) } . ◮ { ( 1 , 2 ) } , { ( 2 , 2 ) } , { ( 3 , 2 ) } , { ( 1 , 2 ) , ( 3 , 2 ) } . ◮ { ( 1 , 1 ) , ( 2 , 2 ) } , { ( 1 , 2 ) , ( 2 , 1 ) , ( 3 , 1 ) } ,. . .

Conflict graphs Channel 1 1 1 2 3 Channel 2 1 2 2 3 Schedules: ◮ ∅, { ( 1 , 1 ) } , { ( 2 , 1 ) } , { ( 3 , 1 ) } , { ( 1 , 1 ) , ( 3 , 1 ) } . ◮ { ( 1 , 2 ) } , { ( 2 , 2 ) } , { ( 3 , 2 ) } , { ( 1 , 2 ) , ( 3 , 2 ) } . ◮ { ( 1 , 1 ) , ( 2 , 2 ) } , { ( 1 , 2 ) , ( 2 , 1 ) , ( 3 , 1 ) } ,. . .

Conflict graphs Channel 1 1 2 2 3 Channel 2 1 1 2 3 3 Schedules: ◮ ∅, { ( 1 , 1 ) } , { ( 2 , 1 ) } , { ( 3 , 1 ) } , { ( 1 , 1 ) , ( 3 , 1 ) } . ◮ { ( 1 , 2 ) } , { ( 2 , 2 ) } , { ( 3 , 2 ) } , { ( 1 , 2 ) , ( 3 , 2 ) } . ◮ { ( 1 , 1 ) , ( 2 , 2 ) } , { ( 1 , 2 ) , ( 2 , 1 ) , ( 3 , 1 ) } ,. . .

Time-scale separation We assume time-scale separation between flow-level and packet-level dynamics. ◮ At the packet level, the number of flows is fixed. ◮ At the flow level, the packet-level dynamics are at equilibrium: the throughput of each node is the fraction of time it is active.

Time-scale separation We assume time-scale separation between flow-level and packet-level dynamics. ◮ At the packet level, the number of flows is fixed. ◮ At the flow level, the packet-level dynamics are at equilibrium: the throughput of each node is the fraction of time it is active. Example: 1 2 3 ϕ 1 = p { 1 } + p { 1 , 3 } , ϕ 2 = p { 2 } , ϕ 3 = p { 3 } + p { 1 , 3 } .

Capacity Region Defined as the set of all feasible link throughputs � ϕ k = i : k ∈ S i p i Throughput of node k Probability of schedule i Schedule i

Capacity Region Defined as the set of all feasible link throughputs � ϕ k = i : k ∈ S i p i Throughput of node k Probability of schedule i Schedule i Example: 1 2 3 Schedules: ∅, { 1 } , { 2 } , { 3 } , { 1 , 3 } . Capacity region: { ϕ 1 + ϕ 2 ≤ 1 , ϕ 2 + ϕ 3 ≤ 1 } .

Stability region Defined as the set of traffic intensities such that the network is stable. ρ k = λ k × σ k Example: ρ 1 ρ 2 ρ 3 1 2 3 The stability region depends on the algorithm.

Stability region Defined as the set of traffic intensities such that the network is stable. ρ k = λ k × σ k Flows arrival rate

Stability region Defined as the set of traffic intensities such that the network is stable. ρ k = λ k × σ k Mean flow size Flows arrival rate

Stability region Defined as the set of traffic intensities such that the network is stable. ρ k = λ k × σ k Traffic intensity Mean flow size Flows arrival rate

Optimal stability region The stability region of any algorithm is included in the capacity region. The interior of the capacity region is called the optimal stability region.

Optimal stability region The stability region of any algorithm is included in the capacity region. The interior of the capacity region is called the optimal stability region. Example: 1 2 3 Optimal stability region: { ρ 1 + ρ 2 < 1 , ρ 2 + ρ 3 < 1 } .

Outline Model Background Standard CSMA Flow-aware CSMA Conclusion

Maximal Weight scheduling T assiulas & Ephremides 92 � max w i ( x ) = x k k ∈ S i

Maximal Weight scheduling T assiulas & Ephremides 92 � max w i ( x ) = x k k ∈ S i Example: 1 2 3 x 1 + x 3 > x 2 ⇒ schedule { 1 , 3 } x 1 + x 3 < x 2 ⇒ schedule { 2 }

Suboptimal algorithms Maximal queue scheduling Mc Keown 95 Dimakis & Walrand 06 Efficiency 8 9 ≈ 0 . 89 max x k

Suboptimal algorithms Maximal queue scheduling Mc Keown 95 Dimakis & Walrand 06 Efficiency 8 9 ≈ 0 . 89 max x k Maximal size scheduling Charporkar, Kar & Sarkar 95 Bonald & Massoulié 01 Efficiency ≈ 0 . 76 max | S i |

Optimal Algorithms Adaptative rate-based CSMA Jiang & Walrand 08 ◮ Measure the packet input and output rates and adapt the back-off accordingly. ◮ Learning algorithm.

Optimal Algorithms Adaptative rate-based CSMA Jiang & Walrand 08 ◮ Measure the packet input and output rates and adapt the back-off accordingly. ◮ Learning algorithm. Adaptative queue based CSMA Rajagopolan, Shah & Shin 09 ◮ Adapt the back-off according to the loglog of the queue length. ◮ Some technical assumptions.

Outline Model Background Standard CSMA Flow-aware CSMA Conclusion

Standard CSMA Probe a channel at random, after some random backoff time. 1 1 1 1 1 α/ 2 α/ 2 Back-off Transmission Back-off ∼ exp ( α ) ∼ exp ( 1 ) ∼ exp ( α ) α ϕ 1 ( x ) = 1 + α

Standard CSMA Probe a channel at random, after some random backoff time. 1 1 1 1 1 α/ 2 α/ 2 Back-off Transmission Back-off ∼ exp ( α ) ∼ exp ( 1 ) ∼ exp ( α ) α ϕ 1 ( x ) = 1 + α � α → ∞ � α Stability region: ρ 1 < − − − → { ρ 1 < 1 } 1 + α

Standard CSMA � w i ( x ) = ( k , j ) ∈ S i α k , j ✶ { x k > 0 } Ratio of transmission time to Weight of schedule i virtual backoff time at link k on channel j Example: Assume α k , j = α for k = 1 , 2 , 3 and j = 1 , 2. 1 2 3 α 1 α 1 α 1 1 2 3 α α α 1 1 1 1 2 3

Standard CSMA � w i ( x ) = ( k , j ) ∈ S i α k , j ✶ { x k > 0 } Ratio of transmission time to Weight of schedule i virtual backoff time at link k on channel j Example: Assume α k , j = α for k = 1 , 2 , 3 and j = 1 , 2. 1 2 3 α 1 α 1 α 1 1 2 3 α α α 1 1 1 1 2 3 w i ( x ) = 1 ∅ :

Standard CSMA � w i ( x ) = ( k , j ) ∈ S i α k , j ✶ { x k > 0 } Ratio of transmission time to Weight of schedule i virtual backoff time at link k on channel j Example: Assume α k , j = α for k = 1 , 2 , 3 and j = 1 , 2. 1 1 2 3 α 1 α 1 α 1 1 2 3 α α α 1 1 1 1 2 3 { ( 1 , 1 ) } : w i ( x ) = α

Standard CSMA � w i ( x ) = ( k , j ) ∈ S i α k , j ✶ { x k > 0 } Ratio of transmission time to Weight of schedule i virtual backoff time at link k on channel j Example: Assume α k , j = α for k = 1 , 2 , 3 and j = 1 , 2. 1 1 2 3 α 1 α 1 α 1 1 2 3 α α α 1 1 1 1 2 2 3 w i ( x ) = α 2 { ( 1 , 1 ) , ( 2 , 2 ) } :

Standard CSMA � w i ( x ) = ( k , j ) ∈ S i α k , j ✶ { x k > 0 } Ratio of transmission time to Weight of schedule i virtual backoff time at link k on channel j Example: Assume α k , j = α for k = 1 , 2 , 3 and j = 1 , 2. 1 1 2 3 3 α 1 α 1 α 1 1 2 3 α α α 1 1 1 1 2 2 3 w i ( x ) = α 3 { ( 1 , 1 ) , ( 2 , 2 ) , ( 3 , 1 ) } :

Standard CSMA � w i ( x ) = ( k , j ) ∈ S i α k , j ✶ { x k > 0 } Ratio of transmission time to Weight of schedule i virtual backoff time at link k on channel j Example: Assume α k , j = α for k = 1 , 2 , 3 and j = 1 , 2. 1 2 3 α 1 α 1 α 1 1 2 3 α α α 1 1 1 1 2 3 w i ( x ) = α n for n active links

Standard CSMA � ϕ k ( x ) = i : k ∈ S i p i ( x ) Probability of Throughput of link k schedule i Example: Assume α k , j = α for k = 1 , 2 , 3 and j = 1 , 2. 1 2 3 α 1 α 1 α 1 1 2 3 α α α 1 1 1 1 2 3 2 α + 6 α 2 + 2 α 3 2 α + 4 α 2 + 2 α 3 ϕ 1 ( x ) = ϕ 3 ( x ) = 1 + 6 α + 8 α 2 + 2 α 3 , ϕ 2 ( x ) = 1 + 6 α + 8 α 2 + 2 α 3

Suboptimality of standard CSMA 1 channel α ≫ 1 1 Optimal Actual 1 2 3 0 . 8 0 . 6 Homogeneous case ρ 2 0 . 4 ρ 1 = ρ 2 = ρ 3 0 . 2 Efficiency ≈ 0 . 84. 0 0 0 . 2 0 . 4 0 . 6 0 . 8 1 ρ 1 = ρ 3