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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
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 . 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 ))
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 ))
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
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