Efficient Sharing of Resources in Distributed Systems

Transcription

1 Efficient Sharing of Resources in Distributed Systems Debessay (Debish) Fesehaye Kassa Dept. of Computer Science University of Illinois at Urbana-Champaign May 18, 2013 Debish Fesehaye Efficient Sharing 1/ 5

2 Max/Min Fairness Using Efficient Sharing (ES): Method 1 The rate Rd,u(t) = C d,u qd,u(t τ) τ ˆN d,u (t τ) Max/Min: Fractional flows ˆN d,u (t τ) = S d,u(t) R d,u (t τ) = N d,u (t τ) j QoS, SLA check S d,u (t) = N d,u (t τ) j j d,u Rj d,u (t) Per flow weighted share at the link R j d,u (t) R d,u (t τ) Notations: C d,u = Link capacity for down (d) and up (u) links q d,u (t) = Queue size τ = Control interval N d,u (t) = Number of flows j d,u = Rj d,u (t+τ) R j d,u (t) = Priority weight of flow j R j d,u (t) = Rate of flow j j d,u R d,u(t) Debish Fesehaye Efficient Sharing 2/ 5

3 Efficient Sharing Example MaxMin fairness example C u = 100pkts/sec q u(t) = 0pkts τ = 1sec N u = 3 Ru(t) 1 = 10,Ru 2 = 50,RU 3 = 50 pkts/sec u 1 = u 2 = u 3 = 1 R u(t τ) = 50 pkts/sec Debish Fesehaye Efficient Sharing 3/ 5

4 Efficient Sharing Example MaxMin fairness example C u = 100pkts/sec q u(t) = 0pkts τ = 1sec N u = 3 Ru(t) 1 = 10,Ru 2 = 50,RU 3 = 50 pkts/sec u 1 = u 2 = u 3 = 1 R u(t τ) = 50 pkts/sec 10 pkts/sec 50 pkts/sec 100 pkts/sec 50 pkts/sec Debish Fesehaye Efficient Sharing 3/ 5

5 Efficient Sharing Example MaxMin fairness example C u = 100pkts/sec 100 pkts/sec q u(t) = 0pkts τ = 1sec N u = 3 Ru(t) 1 = 10,Ru 2 = 50,RU 3 = 50 pkts/sec u 1 = u 2 = u 3 = 1 10 pkts/sec 50 pkts/sec R u(t τ) = 50 pkts/sec 50 pkts/sec Then ES rate is R(t) = = pkts/sec. Debish Fesehaye Efficient Sharing 3/ 5

6 Efficient Sharing Example MaxMin fairness example C u = 100pkts/sec q u(t) = 0pkts τ = 1sec N u = 3 Ru(t) 1 = 10,Ru 2 = 50,RU 3 = 50 pkts/sec u 1 = u 2 = u 3 = 1 R u(t τ) = 50 pkts/sec Then ES rate is R(t) = 100 Processor sharing (PS): pkts/sec = pkts/sec. R(t) = = pkts/sec. 50 pkts/sec 100 pkts/sec 50 pkts/sec Debish Fesehaye Efficient Sharing 3/ 5

7 Max/Min Fairness Using ES: Method 2 MaxMin fairness: Efficient Sharing Given a resource with capacity X units/sec to be shared by N sources, In this method we set R(t τ) = X N, which is the processor sharing rate. Each source s bottleneck fair (ES) share rate is denoted with R j (t). We also have R j (t) R(t τ) as a source j cannot send higher than its bottleneck fair share. Then the ES rate, R(t) can be given as R(t) = X X = 2 Nj ( Rj (t) R(t τ) ) N. N j R j (t) Debish Fesehaye Efficient Sharing 4/ 5

8 Max/Min Fairness Using ES: Method 2 Then the rate for the example above, in the first iteration (round) becomes MaxMin fairness: Efficient Sharing Given a resource with capacity X units/sec to be shared by N sources, In this method we set R(t τ) = X N, which is the processor sharing rate. Each source s bottleneck fair (ES) share rate is denoted with R j (t). We also have R j (t) R(t τ) as a source j cannot send higher than its bottleneck fair share. Then the ES rate, R(t) can be given as R(t) = X X = 2 Nj ( Rj (t) R(t τ) ) N. N j R j (t) 100 R(t) = 10 = pkts/sec In the second iteration (round) 100 R(t) = 10 = pkts/sec Values of ES rate in next iterations (rounds or RTTs) , , , , Generalized Efficient Sharing (GES) With priority weight, j of flow j, the GES rate R(t) can be given as X R(t) = 2 N. Then N j j R j (t) X Nj ( j R j = (t) R(t τ) ) source j s weighted share becomes j R(t). Debish Fesehaye Efficient Sharing 4/ 5

9 Max/Min Fairness Using ES: Method 3 MaxMin fairness: Efficient Sharing Given a resource with capacity X units/sec to be shared by N sources, Each source s bottleneck fair (ES) share rate is denoted with R j (t). We also have R j (t) C as a source j N(t τ) cannot send higher than its bottleneck fair share. In this method, first N(t) 0; ˆN(t) 0; ˆX(t) 0; for each flow j do N(t) N(t)+1; if (R j (t) < X N(t τ) then ˆX(t) ˆX(t)+R j ; ˆN(t) ˆN(t)+1; end if end for The ES rate R(t) is then given by R(t) = X ˆX(t) ; Ñ(t) = N(t) ˆN(t). Ñ(t) Debish Fesehaye Efficient Sharing 5/ 5

10 Max/Min Fairness Using ES: Method 3 MaxMin fairness: Efficient Sharing Given a resource with capacity X units/sec to be shared by N sources, Each source s bottleneck fair (ES) share rate is denoted with R j (t). We also have R j (t) C as a source j N(t τ) cannot send higher than its bottleneck fair share. In this method, first N(t) 0; ˆN(t) 0; ˆX(t) 0; for each flow j do N(t) N(t)+1; if (R j (t) < X N(t τ) then ˆX(t) ˆX(t)+R j ; ˆN(t) ˆN(t)+1; end if end for The ES rate R(t) is then given by R(t) = X ˆX(t) ; Ñ(t) = N(t) ˆN(t). Ñ(t) ˆN(t) and ˆX(t) are number of flows and sum of rates of the flows bottlenecked at other resources. Debish Fesehaye Efficient Sharing 5/ 5

11 Max/Min Fairness Using ES: Method 3 MaxMin fairness: Efficient Sharing Given a resource with capacity X units/sec to be shared by N sources, Each source s bottleneck fair (ES) share rate is denoted with R j (t). We also have R j (t) C as a source j N(t τ) cannot send higher than its bottleneck fair share. In this method, first N(t) 0; ˆN(t) 0; ˆX(t) 0; for each flow j do N(t) N(t)+1; if (R j (t) < X N(t τ) then ˆX(t) ˆX(t)+R j ; ˆN(t) ˆN(t)+1; end if end for The ES rate R(t) is then given by R(t) = X ˆX(t) ; Ñ(t) = N(t) ˆN(t). Ñ(t) ˆN(t) and ˆX(t) are number of flows and sum of rates of the flows bottlenecked at other resources. Then rate for the example above R(t) = = 45.0 pkts/sec. Debish Fesehaye Efficient Sharing 5/ 5

12 Max/Min Fairness Using ES: Method 3 MaxMin fairness: Efficient Sharing Given a resource with capacity X units/sec to be shared by N sources, Each source s bottleneck fair (ES) share rate is denoted with R j (t). We also have R j (t) C as a source j N(t τ) cannot send higher than its bottleneck fair share. In this method, first N(t) 0; ˆN(t) 0; ˆX(t) 0; for each flow j do N(t) N(t)+1; if (R j (t) < X N(t τ) then ˆX(t) ˆX(t)+R j ; ˆN(t) ˆN(t)+1; end if end for The ES rate R(t) is then given by R(t) = X ˆX(t) ; Ñ(t) = N(t) ˆN(t). Ñ(t) ˆN(t) and ˆX(t) are number of flows and sum of rates of the flows bottlenecked at other resources. Then rate for the example above R(t) = = 45.0 pkts/sec. Generalized Efficient Sharing (GES) With priority weight, j of flow j, the GES rate R(t) can be given as R(t) = X ˆX(t) Ñ(t) j, where the sum is over the j Ñ(t) flows bottlnecked at the current resource with capacity X units/sec. Then source j s weighted share at the current resource becomes j R(t). Debish Fesehaye Efficient Sharing 5/ 5