Cost-Based Optimization of Integration Flows - Datenbanken ...
Cost-Based Optimization of Integration Flows - Datenbanken ...
Cost-Based Optimization of Integration Flows - Datenbanken ...
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4.4 <strong>Cost</strong>-<strong>Based</strong> Vectorization for Multiple Plans<br />
Algorithm 4.4 Heuristic Multiple Plan Vectorization (A-HMPV)<br />
Require: plans P , maximum constraint K<br />
1: P ′ ← ∅, free ← K<br />
2: for i ← 1 to⌊h do // determine ⌋ local maximum constraints for each plan<br />
R<br />
3: K i ← 1 + i·W (P i )<br />
∑ · (K − h) h // 1 ≤ K<br />
j=1 R j·W (P j ) i ≤ K<br />
4: free ← free − K i<br />
5: for i ← 1 to h do // cost-based plan vectorization for each plan<br />
6: P i ′ i)<br />
7: if k i ′ ≤ K i then<br />
8: P ′ ← P ′ ∪ P i<br />
′<br />
9: P ← P − P i<br />
10: free ← free + (K i − k ′ )<br />
11: for i ← 1 to ⌈|P | do // distribute ⌉ remaining threads across remaining plans<br />
R<br />
12: K i ← 1 + i·W (P i )<br />
∑ · (free − |P |) h<br />
j=1 R j·W (P j )<br />
13: for i ← 1 to |P | do // plan vectorization restricting k ′ for each remaining plan<br />
14: if K i ≤ free then<br />
15: P i ′ i, K i )<br />
// restricted cost-based plan vectorization<br />
16: free ← free − K i<br />
17: else<br />
18: P i ′ i, free)<br />
// restricted cost-based plan vectorization<br />
19: free ← 0<br />
20: return P ′<br />
check that the number <strong>of</strong> free elements and hence, the global constraint, is not exceeded.<br />
We use the following example to illustrate this algorithm.<br />
Example 4.11 (Multiple Plan Vectorization). Recall Example 4.10 with the maximum<br />
constraint <strong>of</strong> K = 7 and assume the following monitored execution statistics:<br />
P a : W (P a ) = 8 ms, R a = 5 msg/s<br />
P b : W (P b ) = 17 ms, R b = 2.5 msg /s<br />
P c : W (P c ) = 16 ms, R c = 7 msg/s.<br />
In a first step, we compute the local maximum constraint for the individual plans:<br />
⌊ ⌋<br />
⌊ ⌋<br />
⌊ ⌋<br />
40<br />
42.5<br />
112<br />
P a : K a = 1+<br />
194.5 · 4 = 1, P b : K b = 1+<br />
194.5 · 4 = 1, P c : K c = 1+<br />
194.5 · 4 = 3.<br />
In a second step, we compute the cost-based vectorized plan <strong>of</strong> each deployed plan and<br />
check that the resulting number <strong>of</strong> execution buckets k i does not exceed K i . Figure 4.17(a)<br />
shows the result <strong>of</strong> this step. In detail, only P c is accepted. Hence, we reduce the number<br />
<strong>of</strong> free buckets from free = 7 to free = 4. Furthermore, in a third step, we distribute the<br />
remaining buckets with<br />
⌈ ⌉<br />
⌈ ⌉<br />
40<br />
42.5<br />
P a : K a = 1 +<br />
82.5 · 2 = 2, P b : K b = 1 +<br />
82.5 · 2 = 3.<br />
115