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

5.3 Periodical Re-Optimization
With regard to the optimization objective of throughput maximization, we need some
additional notation. The execution characteristics of a hypothetical finite message subsequence
M ′ with M ′ ⊆ M are described by two major statistics:
• Total Execution Time W (M ′ ): The total execution time of a finite message subsequence
is determined by W (M ′ ) = ∑ W (p ′ ) as the sum of the execution time of all
partitioned plan instances required to execute all messages m i ∈ M ′ .
• Total Latency Time T L (M ′ ): The total latency time of a finite message subsequence
is determined by T L (M ′ ) = t out (m |M ′ |) − t i (m 1 ) as the time between receiving the
first message until the last message has been executed (both with regard to the
subsequence M ′ ). This includes overlapping execution time and waiting time.
Following these prerequisites, we now formally define the multi-flow optimization problem.
Definition 5.2 (Multi-Flow Optimization Problem (P-MFO)). Maximize the message
throughput with regard to a hypothetical finite message subsequence M ′ . The optimization
objective φ is to execute M ′ with minimal latency time:
φ = max |M ′ |
= min T L (M ′ ). (5.2)
∆t
There, two additional restrictions must hold:
1. Let lc denote a soft latency constraint that must not be exceeded in expectation. Then,
the condition ∀m i ∈ M ′ : T L (m i ) ≤ lc must hold.
2. The external behavior must be serialized according to the incoming message order.
Thus, the condition ∀m i ∈ M ′ : t out (m i ) ≤ t out (m i+1 ) must hold as well.
Finally, the P-MFO describes the search for the optimal waiting time ∆tw with regard to
φ and the given constraints.
Based on the horizontal partitioning of message queues, Figure 5.10 illustrates the basic
temporal aspects that need to be taken into account, for a scenario with partitioning
attribute selectivity of sel = 1.0.
p’ i :
p’ 1
∆tw(P’)
W(P’)
^
T L
T i :
p’ 2
p’ 3
m i
t i (m i )
T L (m i )
∆tw(P’) W(P’)
t out (m i )
T 2
∆tw(P’)
T 3
W(P’)
time t
Figure 5.10: P-MFO Temporal Aspects (with ∆tw > W (P ′ ))
Essentially, an instance p ′ i of a rewritten plan P ′ is initiated periodically at T i , where the
period is determined by the waiting time ∆tw. A message partition b i is then executed by
p ′ i with an execution time of W (P ′ ). Finally, we want to minimize the total latency time
ˆT L (M ′ ) in order to solve the defined optimization problem. Comparing ∆tw and W (P ′ ),
we have to distinguish the following three cases:
• Case 1: ∆tw = W (P ′ ): We wait exactly for the period of time that is required for
executing partition b i before executing b i+1 . This is the simplest model and results
in the full utilization by a single plan. As we will show this specific case can be one
desirable aim with regard to the optimization objective φ.
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