SEKE 2012 Proceedings - Knowledge Systems Institute

(Notice that r i - (TS 1 ) ≤ 0) In order to execu te T 3 , the
requirement on resource r i is:
r i + (TS 3 ) + r i + (TS 2 ) + r i - (TS 2 ) + r i + (TS 1 ) + r i - (TS 1 );
…
Therefore, the requirement on resource r i of executing the
procedural branch, denoted by Rq(r i ) is
Rq(r i ) = max{ r i + (TS 1 ),
r i + (TS 2 ) + r i + (TS 1 ) + r i - (TS 1 ),
…
r i + (TS n ) + ∑ k=1 n-1 (r i + (TS k ) + r i - (TS k ))} (7)
The net resource consumption is
Rc(r i ) = ∑ k=1 s (r i + (TS k ) + r i - (TS k )) (8)
The overall resource requirement of executing the
procedural branch is
R r = (Rq(r 1 ), Rq(r 2 ), … Rq(r s )) (9)
For an ES-block composed of w procedural branches,
we use f ormula (9) to calcu late the resource requirement
for each branc h, excluding the starting and ending tasks.
Denote by Rq k (r i ) the requirement on resource r i of branch
k. Because in any given execution instance the workflow
can only choose one branch to execute, therefore, the
resource requirement of the ES-block on r i should be
Rq(r i ) = max{Rq k (r i ) | k=1,2, .., w} (10)
Notice that it is possible t hat the maximum value in
formula (7) may be identified on different branches for
different resources. For exa mple, executing branch on e
may demand more on resource A than B, while executing
branch two may demand more on resource B than A. But
the overall resource requirement is a co mbination of worst
case (the maximum demand) for each type of resources.
The maximum net resource consumption on r i is
Rc(r i ) = max{Rc k (r i ) | k=1,2, .., w} (11)
For a PS-block composed of w procedural branches, we
again use formula (9) to calculate the resource requirement
for each branc h, excluding the starting and ending tasks.
Denote by Rq k (r i ) the requirement on resource r i of branch
k. Because these branches will execute concurrently, the
worst case (maximum demand for a resource) would be a
state in which all branches reach maximum demand for a
given resource. Therefore, the resource requirement of the
PS-block on r i should be
Rq(r i ) = ∑ k=1 w Rq k (r i ) (12)
The net resource consumption on r i is
Rc(r i ) = ∑ k=1 w Rc k (r i ) (13)
The overall workflow MRC analysis is carried out by
the analysis of PS-blocks and ES-blocks and then replacing
each of them with a task that is equivalent to the block in
terms of maximum resource requirement and resou rce
consumption. It starts f rom inter-most blocks. B efore we
formally describe th e algorithm, let us illustrate the idea
using the example the right-most workflow in Fig. 4(c)
first. In this workflow, there are two internal most blocks:
ES-block, composed of TS 221 , TS 222 and TS 223 and
TS 220 .
PS-bock, composed of TS 231 , TS 232 and TS 233 and
TS 230 .
For the ES block, we replace the two branches with a new
task T 22 , while for the PS-block, we replace the three
branches with a n ew task T 23 , as ill ustrated in Fig. 5(a).
Now there is on ly one block in Fig. 5, which starts with
TS 21 and ends with TS 200 and has two branches, each
having three tasks. We replace each branch with a sing le
new task, and then replace the two branches (now each
branch has only one task) with a new task. After that, only
one branch is left in the ROWN.
TS 1
TS 21
TS 221 TS 231
TS 22
TS 23
TS 220
TS 200
TS 100
Fig. 5. An equivalent ROWN to Fig. 4(c).
For any type of blocks, when all its branches are
replaced with a si ngle task TS b , the equivalent resource
parameters of TS b for resource r i are:
r + i (TS b ) = Rq(r i ) (14)
r - i (TS b ) = Rq(r i ) - Rc(r i ) (15)
If the block is an ES -block, Rq(r i ) and Rc(r i ) are given by
(10) and (11), respectively. If it is a PS-block, they are
given by (12) and (13).
MRC analysis algorithm
TS 230
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