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

5 Multi-Flow Optimization
k ′ . Figure 5.11 illustrates the resulting relative execution time per message (analytical
consideration) with varying batch size k ′ ∈ {1, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100}. We
observe a decreasing relative execution time per message W (P 2 ′, k′ )/k ′ with increasing k ′ ,
and that this relative execution time asymptotically tends to a lower bound.
Using the double-metric cost model in combination with its extension for message partitions,
we now can compute the total execution time W (M ′ , k ′ ) and the total latency
time T L (M ′ , k ′ ) of finite message subsequences M ′ (with undefined length) by assuming
⌈|M ′ |/k ′ ⌉ = 1/sel instances of a partitioned plan (rounded up to numbers of instances).
• Total Execution Time W (M ′ ): The estimated total execution time Ŵ (M ′ ) of a
message subsequence is computed as the product of the estimated costs per instance
times the number of executed plan instances with
⌈ |M
Ŵ (M ′ , k ′ ) = Ŵ (P ′ , k ′ ′ ⌉
|
) · , (5.3)
where Ŵ (P ′ , k ′ ) is computed as sum over the sequence of extended operator costs
with Ŵ (P ′ , k ′ ) = ∑ m
i=1 Ŵ (o′ , k ′ ).
• Total Latency Time T L (M ′ ): In contrast, the estimated total latency time ˆT L (M ′ )
of a message subsequence is composed of the waiting time ∆tw and the execution
time Ŵ (P ′ , k ′ ). Thus, we compute it depending on the comparison between ∆tw
and Ŵ (P ′ , k ′ ) with
⎧ ⌉
⌈
|M ′ |
⎨
ˆT L (M ′ , k ′ k
· ∆tw +
) =
Ŵ (P ′ , k ′ ) ∆tw ≥ W (P ′ , k ′ )
′
⌉
⎩∆tw + · Ŵ (P ′ , k ′ ) otherwise.
⌈
|M ′ |
k ′
k ′
(5.4)
Due to our defined validity condition, ∆tw < W (P ′ , k ′ ) is invalid. Hence, in the
following we use only the first case of Equation 5.4.
It follows directly that Ŵ (M ′ , k ′ ) ≤ ˆT L (M ′ , k ′ ), where Ŵ (M ′ , k ′ ) + ∆tw = ˆT L (M ′ , k ′ )
is the specific case at ∆tw = W (P ′ , k ′ ). This means, the estimated total latency time
cannot be lower than the estimated total execution time because the latency time additionally
includes the waiting time. Finally, the optimization objective φ of the P-MFO
is to minimize this total latency time function ˆT L under all existing constraints. In the
following, we will explain how to compute the optimal waiting time ∆tw that achieves
this minimization for the general case of arbitrary cost models.
5.3.3 Waiting Time Computation
The intuition of computing the optimal waiting time ∆tw is that the waiting time—and
hence, the batch size k ′ —strongly influences the execution time of single plan instances.
The latency time then depends on that execution time. Figure 5.12 conceptually illustrates
the resulting two inverse influences that our computation algorithm exploits:
• Figure 5.12(a): For partitioned plans, an increasing waiting time ∆tw causes decreasing
relative execution time per message W (P ′ , k ′ )/k ′ and total execution time
W (M ′ , k ′ ), which are both non-linear functions that asymptotically tend towards a
lower bound. In contrast, ∆tw has no influence on instance-based execution.
146