SEKE 2012 Proceedings - Knowledge Systems Institute

II.
RESOURCE-ORIENTED WORKFLOW MODEL
A workflow is composed of tasks that execute in a
specific order. A task is an activity or an event. We assume
a task is ato mic. When it g ets started, it is g uaranteed to
finish. An important implication of this assumption is all
required resources to finish the task will be held by the task
until it is done.
Workflows are case-based. Every piece of work is
executed for a specific case. For example, an incident is a
case for an incident response workflow. A patient visit is a
case for the emergency department workflow.
Workflow execution requires resources. Workflows are
executed by humans or machines, which are du rable
resources. When Petri nets are used to model a workflow,
these kinds of resources can be specif ied using tokens.
Besides workflow executors, executing a task in a
workflow may consume/occupy other resources and when
a task execution is finished some of these resources may be
released or some new resources may be produced. Petri net
tokens are not suitable to model this class of resources.
A. Task Modeling
A task can be modeled with a transition in a Petri net.
However, in order to catch resources in use when a task is
in execution and released when the task is done, we use
two sequential transitions to model a task, on e modeling
the beginning of the task execution and the other the end of
the task execution.
B
Fig. 1 Petri model of a task.
InExec
Idle
As shown in Fig. 1 (a), transition B represents the
beginning of a task execution; E represents the end of the
task execution. Place InEx represents the task is in
execution, while Idle represents the task is idle. From
reachability analysis perspective, Fig. 1(a) can be reduced
to a sing le transition, which represents the entire task
execution as a sing le logic unit. If there is n o resource
involved in a task execution, then we don’t need to model
it using two transitions.
B. Resource Modeling
We assume there are n types of resources in a system,
and the quantity of each type of resource can be
represented by a non-negative real number. Hence,
resources are described by S = (r 1 , r 2 , …, r n ), where each r i
is a non-negative real number.
A task may hold or co nsume particular resources
during execution and rele ase or p roduce particular
resources once execution is completed. We use R + to
E
describe the resources consumed and/or h eld when
executing a task and use R - to describe resources produced
+
and/or released after task execution is finished, where r i ≥
-
0 and r i ≤ 0 and i = 1, 2, … n.
Resource modeling is based on the two-transition
model. More specifically, for a task TS k , R + (TS k ) is
associated with transition B k and R - (TS k ) is associated with
transition E k .
C. Resource-Oriented Workflow Nets (ROWN)
In [1], a Petri net that models a workflow process is called
a workflow net. A workflow net is a Petri net that satisfies
two requirements. First, it h as one source place and on e
sink place. A token in the source place co rresponds to a
case needs to be handled. A token in the output place
corresponds to a case th at has already been handled.
Secondly, there are no dangling transitions or places.
Formally, a Petri net is PN = (P, T, I, O, M 0 ) if and only
if
1) PN has two special places: i and o. Place i is a source
place: *i = ; Place o is a source place: *i = ,
2) If we add a transit ion t to P N that connects place o
with i, then the resulting Petri net is strong ly
connected.
A resource-constraint workflow net (ROWN) is
workflow net in which a task whose execution requires
resources is rep resented in two sequential transitions: a
transition representing the start of the task and with
resources consumption defined on it, and a transition
representing the end of th e task with resources
production/release defined on it. Mathematically, it i s
defined as a 7-tupe: ROWN = (P, T, R, I, O, M 0 , S 0 ), in
which (T, R) is a pair: f or each T k T, there is an R k R
that specifies resource change associate with the firing of
transition T k . S 0 represents the initially available resources.
D. Transition Firing
A transition t k is enabled under state (M i , S i ) if and only
if
M i ≥ I(t k ), (1)
S i ≥ R(t k ) (2)
Condition (1) stan ds for control-ready, while condition 2
stands for resource-ready. Notice that R(t k ) is R + (t k ) if t k
represents the start of a ta sk; it is R - (t k ) if t k represents the
end of a task; it is a 0 vector if the task represented by t k
does not involve any resource changes. The transition’s
enabledness is affected by resource availability only if it
represents the start of a task.
After an enabled transition t k fires, the new state is
determined by
M j = M i + O(t k ) - I(t k ), (3)
S j = S i - R(t k ). (4)
Eq. (3) is exactly the same as it is for regular Petri nets. Eq.
(4) reflects resource change after firing a transition: if the
transition represents the start of a task, R(t k ) is a p ositive
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