Information Technology Reference
InDepth Information
Then, the formula to compute the influence of the previous resources on the
current resources in processing time is defined as follow:
n−
1
1
t
r
n
,r
n−
1
,r
n−
2
,r
n−
3
,...r
2
,r
1
=(1+
SR
r
n
,r
i
)
∗
t
(2)
n
−
1
i
=1
Where,
t
r
n
,r
n−
1
,r
n−
2
,r
n−
3
,...r
2
,r
1
means the processing time of
r
n
when its previous
resources are
r
1
,
r
2
,
r
3
...
r
n−
1
and t is the average processing time of
r
n
no matter
who performs the previous tasks.
4TheProbemMod l
The task allocation problem can be modeled as MDPs. The traditional MDPs
can be simply described as follow: the agent can choose an action from the set
of actions; then the environment changed and the agent goes into another state
after executing that action, and it receives the action's immediate payoff [14]. A
MDPs is a tuple
<S,A,P,R>
,where:

S
is a set of possible states of the environment;

A
is a set of possible actions of the system;

P
is a state transfer function, which input
S
×
A
, then output a real number,
namely
ʴ
(
s, a
(
s
))
ₒ
S
,where
s
∈
S
,
a
(
s
)
∈
A
,
a
(
s
) means the set of actions
in state
s
;

R
is a immediate payoff function, which input
S
×
A
, then output a real
number, namely
ʴ
(
s, a
(
s
))
ₒ
S
,where
s
∈
S
,
a
(
s
)
∈
A
,
a
(
s
) means the set
of actions in state
s
.
In the following part, the detail of the MDPs for the task allocation problem
will be described.
4.1 State Space
Let
S
be a set of states,
S
∈
T
×
WL
.Where:

let
T
be a finite set of tasks;

let
WL
be a set of the workload of all resources.
For example, considering a particular state
s
˄
=(
t, wl
˄
), where:

t
T
, is a task in the workflow model;

˄
is the moment of the making decision when an enabled work item should
be allocated;

wl
∈
∈
WL
,
wl
∈{
r.wl

r
∈
R
}
, which is one possible condition of all candidate
resources work list.