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A. S. Semenov
simply accept input and return a result. Let each container run on its own server. Server
does not share global memory and communicates exclusively through messaging.
The model algorithm is constructed as follows.
Let upper indexes R (Receive) and S (Send) be the inputs and outputs for the
container e 0 , respectively, then a container program is defined by Eq. 21.3.
E =
R
{e 0 }
S
(21.3)
A distributed program E consists of a set of n asynchronous container programs
R {e 0 }
S ,
R {e 1 }
S ,
R {e 2 }
S , …,
R {e n }
S
∈ E, which interact through containers transmitted
over the network, and a number of containers n vary over time in accordance with
the requirements.
Components fulfill also a role of communication programs between container
programs. The component program is designated as
R {c}
S and cannot be divided.
Depending on each specific case, the operation to receive (R) and to send (S) can
be redefined, which is indicated by the appropriate upper index for the curly brace.
If there is no index, then an operation is not applied.
Definition 2 Container-component model E = f
n (
R {e 0 }
S ,
R {c}
S , ), where ƒ
n : E
→ E is a recursive mapping of a set E in itself by operations, n = 0, 1,…, k is a step
of mapping,
R {e 0 }
S is an initial container program,
R {c}
S is a component program,
= { ≡ (1/r, N), ↓, n ++, n–} is an ordered set of uniquely invertible operations, ≡(1/r,
N)
R {e}
S is an operation of prototyping container program
R {e}
S with parameters,
r is a scaling ratio (it means that container program is divided into r containers and
component programs), N is a number of self-similar container programs
R {e}
S after
division, 1/r = N; ↓: E’ → e is an insert set E’ in the container e, n++ is an increment
operation, n = n + 1, n– is a decrement operation, n = n − 1.
Components obtained by the prototyping operation are used also to simulate
message passing between neighboring container programs and the container program
from which they are prototyped. Figure 21.3 shows an intercommunication between
the initial program
R {e 0 }
S and subprograms
R {e
1
1 }
S and
R {e
1
3 }
S if r = 1/3 and n =
1. Graphically, container is depicted by a rectangle. Nested containers are depicted
by the nested rectangles. Component is depicted by a gray rectangle.
21.3.2 Container-Component Model Integrated
with the Box-Counting Method
Let each container e ∈ E be a box of square size and the side of the box equal to u(t),
where u(t) is the control signal sent to the elastic system, see Fig. 21.4. Initial boxcontainer and u 0 (t) is corresponded to e 0 ∈ E. Graphically, box-container is depicted
by a rectangle. Nested containers are depicted by nested rectangles. The component
is depicted by yellow rectangle. The capacity curve is analyzed by the box-container
counting dimension. The ideas of the method are different from a box counting:
A. S. Semenov
simply accept input and return a result. Let each container run on its own server. Server
does not share global memory and communicates exclusively through messaging.
The model algorithm is constructed as follows.
Let upper indexes R (Receive) and S (Send) be the inputs and outputs for the
container e 0 , respectively, then a container program is defined by Eq. 21.3.
E =
R
{e 0 }
S
(21.3)
A distributed program E consists of a set of n asynchronous container programs
R {e 0 }
S ,
R {e 1 }
S ,
R {e 2 }
S , …,
R {e n }
S
∈ E, which interact through containers transmitted
over the network, and a number of containers n vary over time in accordance with
the requirements.
Components fulfill also a role of communication programs between container
programs. The component program is designated as
R {c}
S and cannot be divided.
Depending on each specific case, the operation to receive (R) and to send (S) can
be redefined, which is indicated by the appropriate upper index for the curly brace.
If there is no index, then an operation is not applied.
Definition 2 Container-component model E = f
n (
R {e 0 }
S ,
R {c}
S , ), where ƒ
n : E
→ E is a recursive mapping of a set E in itself by operations, n = 0, 1,…, k is a step
of mapping,
R {e 0 }
S is an initial container program,
R {c}
S is a component program,
= { ≡ (1/r, N), ↓, n ++, n–} is an ordered set of uniquely invertible operations, ≡(1/r,
N)
R {e}
S is an operation of prototyping container program
R {e}
S with parameters,
r is a scaling ratio (it means that container program is divided into r containers and
component programs), N is a number of self-similar container programs
R {e}
S after
division, 1/r = N; ↓: E’ → e is an insert set E’ in the container e, n++ is an increment
operation, n = n + 1, n– is a decrement operation, n = n − 1.
Components obtained by the prototyping operation are used also to simulate
message passing between neighboring container programs and the container program
from which they are prototyped. Figure 21.3 shows an intercommunication between
the initial program
R {e 0 }
S and subprograms
R {e
1
1 }
S and
R {e
1
3 }
S if r = 1/3 and n =
1. Graphically, container is depicted by a rectangle. Nested containers are depicted
by the nested rectangles. Component is depicted by a gray rectangle.
21.3.2 Container-Component Model Integrated
with the Box-Counting Method
Let each container e ∈ E be a box of square size and the side of the box equal to u(t),
where u(t) is the control signal sent to the elastic system, see Fig. 21.4. Initial boxcontainer and u 0 (t) is corresponded to e 0 ∈ E. Graphically, box-container is depicted
by a rectangle. Nested containers are depicted by nested rectangles. The component
is depicted by yellow rectangle. The capacity curve is analyzed by the box-container
counting dimension. The ideas of the method are different from a box counting: