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

5 Multi-Flow Optimization
partition contains k ′ messages), use Equation 5.6 and compute min ˆT L with
∆tw | min ˆT L (M ′ , R · ∆tw) with
′ ˆT L (M ′ , R · ∆tw) ∆tw = 0
ˆT L(M ′′ , R · ∆tw) ∆tw∆tw > 0,
(5.7)
where ˆT L ′ and ˆT
′′
L
are the first and second partial deviation of the total latency function
ˆT L with repect to ∆tw. If such a local minimum exists, we check the validity condition
of (0 ≤ W (P ′ , k ′ ) ≤ ∆tw) ∧ (0 ≤ ˆT L ≤ lc). If ∆tw < W (P ′ , k ′ ), we search for ∆tw =
W (P ′ , k ′ ). Further, if ˆTL > lc, we search for the specific ∆tw with ˆT L (∆tw) = lc. If
such a local minimum does not exist, we use the lower border of the function interval to
compute ∆tw with
∆tw | min ˆT L (M ′ , R · ∆tw) with ˆTL (M ′ , R, ∆tw) = W (M ′ , ∆tw · R) + ∆tw, (5.8)
where this lower border of W (M ′ , k ′ ) + ∆tw is given at ∆tw = W (P ′ , k ′ ), where W (P ′ , k ′ )
depends itself on ∆tw. In dependence on the load situation, there might not be a valid
∆tw = W (P ′ , k ′ ) with ∆tw ≥ 0. In this overload situation, we compute the maximum
number of messages per batch k ′′ by
k ′′ | W (M ′ , k ′′ ) + ∆tw = T L (M ′ , k ′′ ) = lc. (5.9)
In this case, the waiting time is exactly ∆tw = W (P ′′ , k ′′ ) and thus we have a full utilization.
However, due to the overload situation, we do not execute the partition with
all collected messages k ′ but only with the k ′′ messages, while the k ′ − k ′′ messages are
reassigned to the end of the partition tree (and with regard to serialized external behavior,
the outrun counters are increased accordingly). This ensures lowest possible latency of
single messages. Thus, we achieve highest throughput, but the input queue size increases.
We use an example to illustrate this whole computation approach.
Example 5.8 (Waiting Time Computation). Recall the Example 5.7 and assume a fixed
message rate R = 4 msg /s (overload situation for instance-based execution due to W (P 2 ) =
0.53 s ), a latency constraint lc = 200 s, and a selectivity of sel = 0.01. In order to compute
∆tw, we use the following ˆT L function (w.r.t. Equation 5.6):
⌈ |M
ˆT L (M ′ ′ ⌉
|
, R · ∆tw) =
· ∆tw
R · ∆tw
+ W (o 1 ) + W (o 2 ) + W (o 3 ) + (W (o 4 ) + W (o 5 ) + W (o 6 )) · R · ∆tw.
We then set M ′ = (R · ∆tw)/sel to the worst-case of k ′ = R · ∆tw messages for all 1/sel
distinct partitions and thus get
⌈ ⌉ 1
ˆT L (M ′ , R · ∆tw) = · ∆tw
sel
+ W (o 1 ) + W (o 2 ) + W (o 3 ) + (W (o 4 ) + W (o 5 ) + W (o 6 )) · R · ∆tw.
Based on this obtained function, we see that the deviation according to ∆tw will lead
to a constant function and thus, no local minimum exist. Hence, we determine ∆tw at
∆tw = W (P ′ 2 , k′ ) with
∆tw = W (P ′ 2, R · ∆tw)
∆tw = W (o 1 ) + W (o 2 ) + W (o 3 ) + (W (o 4 ) + W (o 5 ) + W (o 6 )) · R · ∆tw
∆tw = 1 − (W (o 4) + W (o 5 ) + W (o 6 )) · R
W (o 1 ) + W (o 2 ) + W (o 3 )
≈ 1.8056 s.
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