Non-blocking multicast switching system and a method for designing thereof

A non-blocking multicast switching system, comprising:

• three stages of an input stage, a middle stage, and an output stage, said respective stages comprising a plurality of switches capable of multicasting,
• wherein each switch of the input stage comprises n1 input ports,
• each switch of the output stage comprises n2 output ports,
• each switch of the input stage comprises at least one line connected to each of all switches of the middle stage,
• each switch of the middle stage comprises at least one line connected to each of all switches of the output stage,
• a signal of said each line is multiplexed k times at maximum, where k≧2, said each line has k channels at maximum, and
• in cases where number of switches of the output stage is r2 and number of switches of the middle stage is m, (A1) is established:
• m
• >
• min
• 1
• ≤
• x
• ≤
• min
• ⁢
• {
• n
• 2
• -
• 1
• ,
• r
• 2
• }
• ⁢
• {
• ⌊
• (
• n
• 1
• -
• 1
• k
• )
• ⁢
• x
• ⌋
• +
• (
• n
• 2
• -
• 1
• )
• ⁢
• r
• 2
• 1
• x
• }
• .
• (
• A
• ⁢
• ⁢
• 1
• )

A design method for a non-blocking multicast switching system, the system comprising:

• three stages of an input stage, a middle stage, and an output stage, said respective stages comprising a plurality of switches capable of multicasting,
• wherein each switch of the input stage comprises at least n1 input ports,
• each switch of the output stage comprises at least n2 output ports,
• each switch of the input stage comprises at least one line connected to each of all switches of the middle stage,
• each switch of the middle stage comprises at least one line connected to each of all switches of the output stage,
• a signal of said each line is multiplexed k times at maximum, where k≧2, and
• in cases where number of switches of the output stage is r2 and number of switches of the middle stage is m, (A1) is established:
• m
• >
• min
• 1
• ≤
• x
• ≤
• min
• ⁢
• {
• n
• 2
• -
• 1
• ,
• r
• 2
• }
• ⁢
• {
• ⌊
• (
• n
• 1
• -
• 1
• k
• )
• ⁢
• x
• ⌋
• +
• (
• n
• 2
• -
• 1
• )
• ⁢
• r
• 2
• 1
• x
• }
• .
• (
• A
• ⁢
• ⁢
• 1
• )

A design method for a non-blocking multicast switching system, the system comprising:

• three stages of an input stage, a middle stage, and an output stage, said respective stages comprising a plurality of switches capable of multicasting,
• wherein each switch of the input stage comprises n1 input ports,
• each switch of the output stage comprises n2 output ports,
• each switch of the input stage comprises at least one line connected to each of all switches of the middle stage,
• each switch of the middle stage comprises at least one line connected to each of all switches of the output stage,
• a signal of said each line is multiplexed k times at maximum, where k≧2, and
• in cases where number of switches of the output stage is r2 and number of switches of the middle stage is m, (A1) is established:
• m
• >
• min
• 1
• ≤
• x
• ≤
• min
• ⁢
• {
• n
• 2
• -
• 1
• ,
• r
• 2
• }
• ⁢
• {
• ⌊
• (
• n
• 1
• -
• 1
• k
• )
• ⁢
• x
• ⌋
• +
• (
• n
• 2
• -
• 1
• )
• ⁢
• r
• 2
• 1
• x
• }
• .
• (
• A
• ⁢
• ⁢
• 1
• )

A non-blocking multicast switching system, comprising:

• three stages of an input stage, a middle stage, and an output stage, said respective stages comprising a plurality of switches capable of multicasting,
• wherein each switch of the input stage comprises at least n1 input ports,
• each switch of the output stage comprises at least n2 output ports,
• each switch of the input stage comprises at least one line connected to each of all switches of the middle stage,
• each switch of the middle stage comprises at least one line connected to each of all switches of the output stage,
• a signal of said each line is multiplexed k times at maximum, where k≧2, and
• in cases where x is a value satisfying the following formula (A1),
• m
• >
• min
• 1
• ≤
• x
• ≤
• min
• ⁢
• {
• n
• 2
• -
• 1
• ,
• r
• 2
• }
• ⁢
• {
• ⌊
• (
• n
• 1
• -
• 1
• k
• )
• ⁢
• x
• ⌋
• +
• (
• n
• 2
• -
• 1
• )
• ⁢
• r
• 2
• 1
• x
• }
• (
• A1
• )
• number of switches of the output stage is r2, maximum number of lines between the middle stage and the output stage is N′, in which all channels in the respective lines are busy, N′is (n2−1)r2, and number of switches of the middle stage m′refine is obtained based on the Refining Algorithm in the following Table 1
• TABLE 1
• Algorithm:
• Refinement
• Inputs:
• n2, r2, x, m′, N′
• Outputs:
• mrefine′;
• c1, c2, . . . , cx
• begin
• 01:
• mm′ = m′;
• // initialization
• 02:
• cc1 = cc2 = . . . = ccx = 0;
• // initialization
• 03:
• while (ccx == 0) {
• 04:
• cc
• 1
• =
• ⌊
• N
• ′
• mm
• ′
• ⌋
• ;
• 05:
• for (i = 2;
• i ≦ x;
• i++){
• 06:
• cc
• i
• =
• ⌊
• (
• n
• 2
• -
• 1
• )
• *
• cc
• i
• -
• 1
• )
• mm
• ′
• ⌋
• ;
• 07:
• }
• 08:
• if (ccx == 0) {
• 09:
• mrefine′ = mm′;
• // save the value
• 10:
• c1 = cc1;
• c1 = cc1;
• . . . ;
• cx = ccx // save the values
• 11:
• }
• 12:
• mm′ = mm′ − 1;
• 13:
• } //end while
• end.

A non-blocking multicast switching system, comprising:

• three stages of an input stage, a middle stage, and an output stage, said respective stages comprising a plurality of switches capable of multicasting,
• wherein each switch of the input stage comprises n1 input ports,
• each switch of the output stage comprises n2 output ports,
• each switch of the input stage comprises at least one line connected to each of all switches of the middle stage,
• each switch of the middle stage comprises at least one line connected to each of all switches of the output stage,
• a signal of said each line is multiplexed k times at maximum, where k≧2, said each line has k channels at maximum, and
• in cases where x is a value satisfying the following formula (A1),
• m
• >
• min
• 1
• ≤
• x
• ≤
• min
• ⁢
• {
• n
• 2
• -
• 1
• ,
• r
• 2
• }
• ⁢
• {
• ⌊
• (
• n
• 1
• -
• 1
• k
• )
• ⁢
• x
• ⌋
• +
• (
• n
• 2
• -
• 1
• )
• ⁢
• r
• 2
• 1
• x
• }
• (
• A1
• )
• number of switches of the output stage is r2, maximum number of lines between the middle stage and the output stage is N′, in which all channels in the respective lines are busy, N′ is (n2−1)r2, and number of switches of the middle stage m′refine is obtained based on the Refining Algorithm in the following Table 1.
• TABLE 1
• Algorithm:
• Refinement
• Inputs:
• n2, r2, x, m′, N′
• Outputs:
• mrefine′;
• c1, c2, . . . , cx
• begin
• 01:
• mm′ = m′;
• // initialization
• 02:
• cc1 = cc2 = . . . = ccx = 0;
• // initialization
• 03:
• while (ccx == 0) {
• 04:
• cc
• 1
• =
• ⌊
• N
• ′
• mm
• ′
• ⌋
• ;
• 05:
• for (i = 2;
• i ≦ x;
• i++){
• 06:
• cc
• i
• =
• ⌊
• (
• n
• 2
• -
• 1
• )
• *
• cc
• i
• -
• 1
• )
• mm
• ′
• ⌋
• ;
• 07:
• }
• 08:
• if (ccx == 0) {
• 09:
• mrefine′ = mm′;
• // save the value
• 10:
• c1 = cc1;
• c1 = cc1;
• . . . ;
• cx = ccx // save the values
• 11:
• }
• 12:
• mm′ = mm′ − 1;
• 13:
• } //end while
• end.

A non-blocking multicast switching system, comprising:

• three stages of an input stage, a middle stage, and an output stage, said respective stages comprising a plurality of switches capable of multicasting,
• wherein each switch of the input stage comprises at least n1 input ports,
• each switch of the output stage comprises at least n2 output ports,
• each switch of the input stage comprises at least one line connected to each of all switches of the middle stage,
• each switch of the middle stage comprises at least one line connected to each of all switches of the output stage,
• a signal of said each line is multiplexed k times at maximum, where k≧2, and
• in cases where x is a value satisfying the following formula (A1),
• m
• >
• min
• 1
• ≤
• x
• ≤
• min
• ⁢
• {
• n
• 2
• -
• 1
• ,
• r
• 2
• }
• ⁢
• {
• ⌊
• (
• n
• 1
• -
• 1
• k
• )
• ⁢
• x
• ⌋
• +
• (
• n
• 2
• -
• 1
• )
• ⁢
• r
• 2
• 1
• x
• }
• (
• A1
• )
• number of switches of the output stage is r2, maximum number of lines between the middle stage and the output stage is N′, in which all channels in the respective lines are busy, N′ is (n2−1)r2, and number of switches of the middle stage m′refine is obtained based on the Refining Algorithm in the following
• TABLE 1
• Algorithm:
• Refinement
• Inputs:
• n2, r2, x, m′, N′
• Outputs:
• mrefine′;
• c1, c2, . . . , cx
• begin
• 01:
• mm′ = m′;
• // initialization
• 02:
• cc1 = cc2 = . . . = ccx = 0;
• // initialization
• 03:
• while (ccx == 0) {
• 04:
• cc
• 1
• =
• ⌊
• N
• ′
• mm
• ′
• ⌋
• ;
• 05:
• for (i = 2;
• i ≦ x;
• i++){
• 06:
• cc
• i
• =
• ⌊
• (
• n
• 2
• -
• 1
• )
• *
• cc
• i
• -
• 1
• )
• mm
• ′
• ⌋
• ;
• 07:
• }
• 08:
• if (ccx == 0) {
• 09:
• mrefine′ = mm′;
• // save the value
• 10:
• c1 = cc1;
• c1 = cc1;
• . . . ;
• cx = ccx // save the values
• 11:
• }
• 12:
• mm′ = mm′ − 1;
• 13:
• } //end while
• end.

A design method for a non-blocking multicast switching system, the system comprising:

• three stages of an input stage, a middle stage, and an output stage, said respective stages comprising a plurality of switches capable of multicasting,
• wherein each switch of the input stage comprises n1 input ports,
• each switch of the output stage comprises n2 output ports,
• each switch of the input stage comprises at least one line connected to each of all switches of the middle stage,
• each switch of the middle stage comprises at least one line connected to each of all switches of the output stage,
• a signal of said each line is multiplexed k times at maximum, where k≧2, and
• in cases where x is a value satisfying the following formula (A1),
• m
• >
• min
• 1
• ≤
• x
• ≤
• min
• ⁢
• {
• n
• 2
• -
• 1
• ,
• r
• 2
• }
• ⁢
• {
• ⌊
• (
• n
• 1
• -
• 1
• k
• )
• ⁢
• x
• ⌋
• +
• (
• n
• 2
• -
• 1
• )
• ⁢
• r
• 2
• 1
• x
• }
• (
• A1
• )
• number of switches of the output stage is r2, maximum number of lines between the middle stage and the output stage is N′, in which all channels in the respective lines are busy, N′is (n2−1)r2, and number of switches of the middle stage m′refine is obtained based on the Refining Algorithm in the following
• TABLE 1
• Algorithm:
• Refinement
• Inputs:
• n2, r2, x, m′, N′
• Outputs:
• mrefine′;
• c1, c2, . . . , cx
• begin
• 01:
• mm′ = m′;
• // initialization
• 02:
• cc1 = cc2 = . . . = ccx = 0;
• // initialization
• 03:
• while (ccx == 0) {
• 04:
• cc
• 1
• =
• ⌊
• N
• ′
• mm
• ′
• ⌋
• ;
• 05:
• for (i = 2;
• i ≦ x;
• i++){
• 06:
• cc
• i
• =
• ⌊
• (
• n
• 2
• -
• 1
• )
• *
• cc
• i
• -
• 1
• )
• mm
• ′
• ⌋
• ;
• 07:
• }
• 08:
• if (ccx == 0) {
• 09:
• mrefine′ = mm′;
• // save the value
• 10:
• c1 = cc1;
• c1 = cc1;
• . . . ;
• cx = ccx // save the values
• 11:
• }
• 12:
• mm′ = mm′ − 1;
• 13:
• } //end while
• end.