Approximate QoS Optimization using Hill Climbing Algorithm - Prof. Tarek Abdelzaher, Study notes of Computer Science

Download Approximate QoS Optimization using Hill Climbing Algorithm - Prof. Tarek Abdelzaher and more Study notes Computer Science in PDF only on Docsity! 1 QoS Optimization Multiple QoS Levels QoS Adaptation
Notion of QoS levels
Video server can serve movies at three resolutions:
Level1: 40% CPU, 100% Utility
Level2: 30% CPU, 70% Utility
Level3: 10% CPU, 10% Utility
Same server can broadcast news at three resolutions:
Level1: 30% CPU, 100% Utility
Level2: 20% CPU, 90% Utility
Level3: 10% CPU, 60% Utility
Customers pay
$1/hr of movie streaming
65 cents/hr of news streaming
Degraded QoS levels are discounted proportionally to their utility
How to maximize server revenue? QoS Optimization U=0 U=10 U=20 U=30 U=40 U=50 U=60 U=70 U=80 U=90 U=100 Client1 Client2 Client3 Client4 Client5 QoS Optimization U=0 U=10 U=20 U=30 U=40 U=50 U=60 U=70 U=80 U=90 U=100 Client1 Client2 Client3 Client4 Client5 i U S (i, U) Optimal reward from serving i clients using U% of server utilization δ=10 Optimal Algorithm U=0 U=10 U=20 U=30 U=40 U=50 U=60 U=70 U=80 U=90 U=100 Client1 Client2 Client3 Client4 Client5 i U S (i, U) Optimal reward from serving i clients using U% of server utilization for i=1 to #Clients for U=0 to 100 step δ compute S(i,U) δ=10 Optimal Algorithm U=0 U=10 U=20 U=30 U=40 U=50 U=60 U=70 U=80 U=90 U=100 Client1 Client2 Client3 Client4 Client5 i U S (i, U) Optimal reward from serving i clients using U% of server utilization for i=1 to #Clients for U=0 to 100 step δ compute S(i,U) δ=10 Ri[k]: Reward for serving client i at QoS level k Ui[k]: utilization of QoS level k of client i S(i,U) = maxk {Ri[k] + S(i-1,U-Ui[k])} 2 QoS Optimization Example
Example
Client 1, 2:
Level1: 40% CPU, $1
Level2: 30% CPU, $0.7
Level3: 10% CPU, $0.1
Client 3, 4:
Level1: 30% CPU, $0.65
Level2: 20% CPU, $0.6
Level3: 10% CPU, $0.4 QoS Optimization Example
Example
Client 1, 2:
Level1: 40% CPU, $1
Level2: 30% CPU, $0.7
Level3: 10% CPU, $0.1
Client 3, 4:
Level1: 30% CPU, $0.65
Level2: 20% CPU, $0.6
Level3: 10% CPU, $0.4 U i [k] Ri [k] i k Example U=0 U=10 U=20 U=30 U=40 U=50 U=60 U=70 U=80 U=90 U=100 Client1 Client2 Client3 Client4 i U δ=10 Ri[k]: Reward for serving client i at QoS level k Ui[k]: utilization of QoS level k of client i S(i,U) = maxk {Ri[k] + S(i-1,U-Ui[k])} Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 U i [k] Ri [k] Example U=0 U=10 U=20 U=30 U=40 U=50 U=60 U=70 U=80 U=90 U=100 Client1 Client2 Client3 Client4 i U δ=10 Ri[k]: Reward for serving client i at QoS level k Ui[k]: utilization of QoS level k of client i S(i,U) = maxk {Ri[k] + S(i-1,U-Ui[k])} Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 U i [k] Ri [k]0 0.1(3) 0.1(3) 0.7(2) 1(1) 1(1) 1(1) 1(1) 1(1) 1(1) 1(1) Example U=0 U=10 U=20 U=30 U=40 U=50 U=60 U=70 U=80 U=90 U=100 Client1 Client2 Client3 Client4 i U δ=10 Ri[k]: Reward for serving client i at QoS level k Ui[k]: utilization of QoS level k of client i S(i,U) = maxk {Ri[k] + S(i-1,U-Ui[k])} Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 U i [k] Ri [k]0 0.1(3) 0.1(3) 0.7(2) 1(1) 1(1) 1(1) 1(1) 1(1) 1(1) 1(1) 0 0.1(3) 0.2(3) 0.7(2) 1(1) 1.1(1) 1.4(1) 1.7(1) 2(1) 2(1) 2(1) Example U=0 U=10 U=20 U=30 U=40 U=50 U=60 U=70 U=80 U=90 U=100 Client1 Client2 Client3 Client4 i U δ=10 Ri[k]: Reward for serving client i at QoS level k Ui[k]: utilization of QoS level k of client i S(i,U) = maxk {Ri[k] + S(i-1,U-Ui[k])} Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 U i [k] Ri [k]0 0.1(3) 0.1(3) 0.7(2) 1(1) 1(1) 1(1) 1(1) 1(1) 1(1) 1(1) 0 0.1(3) 0.2(3) 0.7(2) 1(1) 1.1(1) 1.4(1) 1.7(1) 2(1) 2(1) 2(1) 0 0.4(3) 0.6(2) 0.7(2) 1.1(3) 1.4(3) 1.6(2) 1.8(3) 2.1(3) 2.4(3) 2.6(2) 5 Approximate QoS Optimization Hill Climbing Algorithm Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 0,0,0,0 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope promotion if overload then take minimum slope demotion End Loop 0% Promote 3 to L3: Slope=0.4/0.1=4 0,0,L3,0 Promote 4 to L3: Slope=0.4/0.1=4 0,0,L3,L3 10% 20% Promote 1 to L1: Slope=1/0.4=2.5 L1,0,L3,L360% Approximate QoS Optimization Hill Climbing Algorithm Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 0,0,0,0 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope promotion if overload then take minimum slope demotion End Loop 0% Promote 3 to L3: Slope=0.4/0.1=4 0,0,L3,0 Promote 4 to L3: Slope=0.4/0.1=4 0,0,L3,L3 10% 20% L1,0,L3,L3 L1,L1,L3,L3 60% Promote 1 to L1: Slope=1/0.4=2.5 Promote 2 to L1: Slope=1/0.4=2.5 Approximate QoS Optimization Hill Climbing Algorithm Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 0,0,0,0 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope promotion if overload then take minimum slope demotion End Loop 0% Promote 3 to L3: Slope=0.4/0.1=4 0,0,L3,0 Promote 4 to L3: Slope=0.4/0.1=4 0,0,L3,L3 10% 20% L1,0,L3,L3 L1,L1,L3,L3 60% Promote 1 to L1: Slope=1/0.4=2.5 Promote 2 to L1: Slope=1/0.4=2.5 Reward 2.8 Approximate QoS Optimization Restricted Hill Climbing Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 0,0,0,0 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope single level promotion if overload then take minimum slope single level demotion End Loop 0% Approximate QoS Optimization Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 0,0,0,0 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope single level promotion if overload then take minimum slope single level demotion End Loop 0% Promote 3 to L3: Slope=0.4/0.1=4 0,0,L3,0 Promote 4 to L3: Slope=0.4/0.1=4 0,0,L3,L3 10% 20% Promote 1 or 2 to L3: Slope=0.1/0.1=1 Restricted Hill Climbing Promote 3 or 4 to L2: Slope=0.2/0.1=2 Approximate QoS Optimization Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 0,0,0,0 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope single level promotion if overload then take minimum slope single level demotion End Loop 0% Promote 3 to L3: Slope=0.4/0.1=4 0,0,L3,0 Promote 4 to L3: Slope=0.4/0.1=4 0,0,L3,L3 10% 20% Promote 1 or 2 to L3: Slope=0.1/0.1=1 Restricted Hill Climbing Promote 3 or 4 to L2: Slope=0.2/0.1=2 6 Approximate QoS Optimization Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 0,0,0,0 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope single level promotion if overload then take minimum slope single level demotion End Loop 0% Promote 3 to L3: Slope=0.4/0.1=4 0,0,L3,0 Promote 4 to L3: Slope=0.4/0.1=4 0,0,L3,L3 10% 20% Restricted Hill Climbing Promote 3 to L2: Slope=0.2/0.1=2 0,0,L2,L3 30% Approximate QoS Optimization Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 0,0,0,0 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope single level promotion if overload then take minimum slope single level demotion End Loop 0% Promote 3 to L3: Slope=0.4/0.1=4 0,0,L3,0 Promote 4 to L3: Slope=0.4/0.1=4 0,0,L3,L3 10% 20% Promote 3 to L2: Slope=0.2/0.1=2 0,0,L2,L3 0,0,L2,L2 30% 40%Promote 4 to L2: Slope=0.2/0.1=2 Promote 3 or 4 to L1: Slope=0.05/0.1=0.5 Promote 1 or 2 to L3: Slope=0.1/0.1=1 Approximate QoS Optimization Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 0,0,0,0 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope single level promotion if overload then take minimum slope single level demotion End Loop 0% Promote 3 to L3: Slope=0.4/0.1=4 0,0,L3,0 Promote 4 to L3: Slope=0.4/0.1=4 0,0,L3,L3 10% 20% Promote 3 to L2: Slope=0.2/0.1=2 0,0,L2,L3 0,0,L2,L2 30% 40%Promote 4 to L2: Slope=0.2/0.1=2 Promote 3 or 4 to L1: Slope=0.05/0.1=0.5 Promote 1 or 2 to L3: Slope=0.1/0.1=1 Approximate QoS Optimization Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope single level promotion if overload then take minimum slope single level demotion End Loop 50% L3,0,L2,L2 Approximate QoS Optimization Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope single level promotion if overload then take minimum slope single level demotion End Loop 50% L3,0,L2,L2 L3,L3,L2,L2 Promote 2 to L2: Slope=0.1/0.1=1 60% Approximate QoS Optimization Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope single level promotion if overload then take minimum slope single level demotion End Loop 50% L3,0,L2,L2 L3,L3,L2,L2 Promote 2 to L3: Slope=0.1/0.1=1 60% L2,L3,L2,L2 Promote 1 to L2: Slope=0.6/0.2=3 80% 7 Approximate QoS Optimization Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope single level promotion if overload then take minimum slope single level demotion End Loop 50% L3,0,L2,L2 L3,L3,L2,L2 Promote 2 to L3: Slope=0.1/0.1=1 60% L2,L3,L2,L2 Promote 1 to L2: Slope=0.6/0.2=3 80% L1,L3,L2,L2 Promote 1 to L1: Slope=0.6/0.2=3 90% Approximate QoS Optimization Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope single level promotion if overload then take minimum slope single level demotion End Loop 50% L3,0,L2,L2 L3,L3,L2,L2 Promote 2 to L3: Slope=0.1/0.1=1 60% L2,L3,L2,L2 Promote 1 to L2: Slope=0.6/0.2=3 80% L1,L3,L2,L2 Promote 1 to L1: Slope=0.6/0.2=3 90% L1,L3,L1,L2 Promote 3 to L1: Slope=0.05/0.1=0.5 100% Approximate QoS Optimization Client 1, 2: Level1: 40% CPU, $1 Level2: 30% CPU, $0.7 Level3: 10% CPU, $0.1 Client 3, 4: Level1: 30% CPU, $0.65 Level2: 20% CPU, $0.6 Level3: 10% CPU, $0.4 R i [new] - R i [old] U i [new] - U i [old] Slope = Loop if underutilized then take maximum slope single level promotion if overload then take minimum slope single level demotion End Loop 50% L3,0,L2,L2 L3,L3,L2,L2 Promote 2 to L3: Slope=0.1/0.1=1 60% L2,L3,L2,L2 Promote 1 to L2: Slope=0.6/0.2=3 80% L1,L3,L2,L2 Promote 1 to L1: Slope=0.6/0.2=3 90% L1,L3,L1,L2 Promote 3 to L1: Slope=0.05/0.1=0.5 100% Reward 2.3