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

5.3 Periodical Re-Optimization
Relative Execution Time
W(P’,k’) / k’
instance-based
latency constraint lc
total execution time W(M’,k’)
+ ∆tw
Total Latency Time
TL(M’)
instance-based
partitioned (v2)
partitioned
min TL
partitioned (v1)
lower bound
Waiting
Time ∆tw
(a) ∆tw → W (P ′ )/k ′ Influence
(b) ∆tw → T L(M ′ ) Influence
Waiting
Time ∆tw
Figure 5.12: Search Space for Waiting Time Computation
• Figure 5.12(b): On the one side, an increasing waiting time ∆tw linearly increases
the latency time ˆT L because the waiting time is directly included in ˆT L . On the
other side, an increasing ∆tw causes a decreasing relative execution time and thus,
indirectly decreases ˆT L because the execution time is included in ˆT L . The result of
these two influences, in the general case of arbitrary extended cost functions, is a
non-linear total latency time function that has a local minimum (v1) or not (v2). In
any case, due to the validity condition, the total latency function is defined for the
closed interval T L (M ′ , k ′ ) ∈ [W (M ′ , k ′ ) + ∆tw, lc] and hence, both global minimum
and maximum exist. Given these characteristics, we compute the optimal waiting
time with regard to latency time minimization and hence, throughput maximization.
For waiting time computation, we need some additional notation. We monitor the incoming
message rate R ∈ R and the value selectivity sel ∈ (0, 1] according to the partitioning
attributes. For the sake of a simple analytical model, we only consider uniform value
distributions of the partitioning attributes. However, it can be extended via histograms for
value-based selectivities as well. The first partition will contain k ′ = R·sel·∆tw messages.
For the i-th partition with i ≥ 1/sel, k ′ is computed by k ′ = R · ∆tw, independently of
the selectivity sel. A low selectivity implies many partitions b i but only few messages per
partition per time unit (|b i | = R · sel). However, the high number of partitions b i forces
us to wait longer (∆tw/sel) until the start of execution of such a partition such that the
batch size only depends on message rate R and the waiting time ∆tw.
Based on the relationship between the waiting time ∆tw and the number of messages
per batch k ′ , we can compute the waiting time, where ˆT L is minimal by
∆tw | min ˆT L (∆tw) ∧ Ŵ (M ′ , ∆tw) ≤ ˆT L (M ′ , ∆tw) ≤ lc (5.5)
Using Equation 5.4 and assuming a fixed message rate R with 1/sel distinct items according
to the partitioning attribute, we can substitute k ′ with R · ∆tw and get
⌈ |M
ˆT L (M ′ , k ′ ′ ⌉
|
) =
k ′ · ∆tw + W (P ′ , k ′ )
⌈ |M
ˆT L (M ′ ′ ⌉
|
, R · ∆tw) =
· ∆tw + W (P ′ , R · ∆tw).
R · ∆tw
(5.6)
Finally, we set the cardinality of the hypothetical message subsequence to the worst case
by M ′ = k ′ /sel = (R · ∆tw)/sel (execution of all 1/sel distinct partitions, where each
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