Cost-Based Optimization of Integration Flows - Datenbanken ...

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