# Systems, Man & Cybernetics - October 2015 - 12

```Q[i, j](t) is the qualification value of agent i on role j at
time t; T[i, j](t) = 1 means that agent i is assigned with
role j at time t; and the following:
v (t) = v (Q (t), W (t), T (t),)
m=1 n=1

= | | Q [i, j] (t) # W [ j] (t) # T [i, j] .
i=1 j=1

because we do not concentrate on the process of AE.
◆ Definition 19: Dynamic group role assignment (DGRA)
[15], [16] is a process to conduct multiple AEs and GRAs
based on the GS of group g. With this definition, we
refer to GRA as static GRA (SGRA).
◆ Definition 20: The static group performance, C s, of group
x
g in period [0, x ] is defined as # v (t) dt; i.e., as follows:
0

m-1 n-1

# | | Q [i, j] (t) # W [j] (t) # T [i, j] (t) dt.
x

0

i=0 i=0

◆ Definition 21: The dynamic group performance C of

group g in period [0, x ] with p role assignments is
x
defined as # v (t) dt, where
0

p-1 m-1 n-1

v (t) = | | | Q [i, j] (t) # W [j] (t) # T k*[i, j] (t),
k=0 i=0 j=0

and T k*[i, j] (t) is the kth optimal assignment matrix.
◆ Definition 22: Adaptive collaboration (AC) is a methodology that is composed of a series of models, processes, and algorithms to conduct collaboration with
DGRA in group g to obtain high group performance
C in time period [0, x ].
We have proved that AC is beneficial when agents
follow a fatigue model in their performance changes [18].
Here, we compose a more general model for agent performance change.
◆ Definition 23: The agent performance model is defined
as follows:
Q [i, j] (t) = a ij sin (~ ij t + i ij) + b ij
(0 # i 1 m, 0 # j 1 n),

(4)

0.95
0.9
0.85
Qualification

0.8
0.75

Case 1
Case 2
Case 3
Case 4
Case 5

0.7
0.65
0.6
0.55
0.5
0.45

0

50 100 150 200 250 300 350 400 450 500
Time

Figure 3. Examples for changing qualifications with

sine functions.

12

IEEE SyStEmS, man, & CybErnEtICS magazInE October 2015

where a ij is the maximal change for agent i's qualification on role j, i.e., Q[i, j]; b ij is a constant to express
an agent i's median ability value on role j; ~ ij expresses the period for agent i's qualification on role j to
change; and i ij is the initial phase for the sine function that determines the initial qualification of agent i
on role j and the trend of Q[i, j]'s change.
In fact, b ij - a ij and b ij + a ij are the minimum and
maximum qualification values; the initial qualification
value of agent i on role j, i.e., Q[i, j](0), is a ij sin i ij + b ij .
Note that to make (4) more practical and follow the
assumption of Q in Definition 9, we assume the following:
a ij + 0.5 # b ij # 1 - a ij (0 # a ij # 0.25),
1 - a ij # b ij # a ij + 0.5 (0.25 1 a ij # 0.5),

(5)
(6)

where (5) and (6) make Q[i, j] ! [0, 1].
This definition, in fact, considers different performance
changes of agents in a group, such as monotonically
increasing or decreasing, periodic changing or constant,
up-down and down-up changing. Figure 3 shows different
performance curves of agents on roles.
The Architecture and the Self-*
Properties of an ACS
In an ACS, a role engine manages roles and agents, evaluates agent-to-role suitability, and conducts AC. The role
engine sits on top of an operating system (Figure 4) [15],
[16]. This architecture is naturally derived from the
E-CARGO model [15], [16], [21]; i.e., a group is composed of
agents that are assigned with roles regulated by an environment with classes of objects. From the hierarchical
viewpoint, the E-CARGO components are in one level.
The role engine is a platform to support the work of a
group, i.e., collaboration. From this viewpoint, a traditional process involves an agent performing its current role.
Therefore, a process is considered to be an agent and its
current role. When a process is scheduled, an agent and
its current role (rc) and potential roles (A p) are loaded
into the memory space of this process, and then the code
segment of the agent is executed on the central processing
unit (CPU). In this view of a role-based system, roles in a
and scheduling. Agents are loaded based on the requirements of a group in an environment that is composed of
roles. After agents are loaded, they work according to
their current roles, and the current roles may be switched
under the commands of the role engine based on the
group state. In an ACS, roles are designed, stored, and
managed by a role engine on a computer including hardware and an operating system (OS). Roles are the media
for intercomputer communications by their message
exchanges and interfaces used by the agents. Roles manage message passing and receiving. A role is used to regulate the behaviors and check the performance of an agent,

```

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