Systems, devices, and methods utilizing port dimensioning strategies
View Patent ↗Methods, systems, and devices utilizing port dimensioning strategies for supporting, for example, bandwidth-on-demand (“BoD”) services in networks. At a given node, the traffic load consists of several components, such as an access component, which is generated by demands terminated at that node, and a transit component, which is generated by demands that transit electronically through the node. Given the BoD load at a node, as well as a target BoD average blocking probability, a desired static allocation of the ports is provided between ports of a first type (such as client-side ports) and ports of a second type (such as network-side ports). In addition, a dynamic sharing strategy of the ports is also disclosed.
1. A communications device, comprising:
N ports, wherein N is an integer number greater than 1;
s ports of a first type, wherein s is a positive integer number;
N−s ports of a second type; wherein s is a value which results in a minimum result for the expression pP A +(1−p)P T ; wherein
p is a first type load ratio, comprising the ratio of a first type load to a total load;
P A is a blocking probability associated with the first type load and is a function of s; and
P T is a blocking probability associated with a second type load and is a function of s.
2. The device of claim 1 , wherein:
ports of the first type are client side ports; and
ports of the second type are network side ports.
3. The device of claim 2 , wherein:
P A =E[ρp,s];
P T =E [(1−p)ρ,└(N−2s)/2┘], wherein
E[α,n]=(α n /n!)/(Σ i=0 n (α i )/i!), such that the terms α, n, and i are defined according to the Erlang-B formula;
ρ=traffic load on the device in Erlangs.
4. The device of claim 1 , wherein s is a positive integer number less than N/2.
5. The device of claim 4 , wherein the ports of the second type include:
s access load ports; and
N−2s transit ports.
6. The device of claim 5 , wherein the N−s ports of the second type are dynamically allocated between access-load ports and transit ports.
7. The device of claim 6 , wherein all of the N−s ports of the second type are dynamically allocated as transit ports.
8. The device of claim 7 , wherein no more than s ports of the second type are dynamically allocated as access-load ports.
9. The device of claim 6 , wherein:
P
A
=
{
∑
n
2
=
s
2
⌈
N
/
2
⌉
-
s
-
2
P
(
s
,
n
2
)
+
∑
n
1
=
0
⌊
s
/
2
⌋
P
(
2
n
1
,
N
-
s
)
if
N
-
s
is
even
∑
n
2
=
s
2
⌈
N
/
2
⌉
-
s
-
2
P
(
s
,
n
2
)
+
∑
n
1
=
1
⌈
s
/
2
⌉
P
(
2
n
1
-
1
,
N
-
s
-
1
)
if
N
-
s
is
odd
P
T
=
∑
n
1
=
0
⌊
s
/
2
⌋
P
(
2
n
1
,
2
⌊
(
N
-
s
)
/
2
⌋
)
+
∑
n
1
=
1
⌈
s
/
2
⌉
P
(
2
n
1
-
1
,
2
⌈
(
N
-
s
)
/
2
⌉
-
1
)
P
(
n
1
,
n
2
)
=
p
(
n
1
,
n
2
)
∑
(
i
,
j
)
∈
S
p
(
i
,
j
)
for
(
n
1
,
n
2
)
∈
S
p
(
n
1
,
n
2
)
=
[
p
ρ
]
n
1
[
(
1
-
p
)
ρ
]
n
2
-
n
1
2
n
1
!
n
2
-
n
1
2
!
and S is the set of (n 1 ,n 2 ) satisfying n 1 =0, 1, 2, . . . s; and
n
2
=
{
n
1
,
n
1
+
2
,
…
,
N
-
s
if
n
1
,
N
-
s
are
of
same
parity
n
1
,
n
1
+
2
,
…
,
N
-
s
-
1
if
N
-
s
+
n
1
is
odd
wherein ρ=traffic load on the device in Erlangs.
10. A communications system, comprising:
a plurality of transmitters;
a plurality of receivers;
transmission media connecting the plurality of transmitters with the plurality of receivers;
at least one amplifier between at least one of the transmitters and at least one of the receivers; and
at least one communications device between at least one of the transmitters and at least one of the receivers, wherein the communications device includes:
N ports, wherein N is an integer number greater than 1;
s ports of a first type, wherein s is a positive integer number;
N−s ports of a second type; wherein s is a value which results in a minimum result for the expression pP A +(1−p)P T ; wherein
p is a first type load ratio, comprising the ratio of a first type load to a total load;
P A is a blocking probability associated with the first type load and is a function of s; and
P T is a blocking probability associated with a second type load and is a function of s.
11. The system of claim 10 , wherein:
P A =E[ρp,s];
P T =E[(1−p)ρ,└(N−2s)/2┘], wherein
E[α,n]=(α n /n!)/(Σ i=0 n (α i )/i!) such that the terms α, n, and i are defined according to the Erlang-B formula;
ρ=traffic load on the device in Erlangs.
12. The system of claim 10 , wherein:
P
A
=
{
∑
n
2
=
s
2
⌈
N
/
2
⌉
-
s
-
2
P
(
s
,
n
2
)
+
∑
n
1
=
0
⌊
s
/
2
⌋
P
(
2
n
1
,
N
-
s
)
if
N
-
s
is
even
∑
n
2
=
s
2
⌈
N
/
2
⌉
-
s
-
2
P
(
s
,
n
2
)
+
∑
n
1
=
1
⌈
s
/
2
⌉
P
(
2
n
1
-
1
,
N
-
s
-
1
)
if
N
-
s
is
odd
P
T
=
∑
n
1
=
0
⌊
s
/
2
⌋
P
(
2
n
1
,
2
⌊
(
N
-
s
)
/
2
⌋
)
+
∑
n
1
=
1
⌈
s
/
2
⌉
P
(
2
n
1
-
1
,
2
⌈
(
N
-
s
)
/
2
⌉
-
1
)
P
(
n
1
,
n
2
)
=
p
(
n
1
,
n
2
)
∑
(
i
,
j
)
∈
S
p
(
i
,
j
)
for
(
n
1
,
n
2
)
∈
S
p
(
n
1
,
n
2
)
=
[
p
ρ
]
n
1
[
(
1
-
p
)
ρ
]
n
2
-
n
1
2
n
1
!
n
2
-
n
1
2
!
and S is the set of (n 1 ,n 2 ) satisfying n 1 =0, 1, 2, s; and
n
2
=
{
n
1
,
n
1
+
2
,
…
,
N
-
s
if
n
1
,
N
-
s
are
of
same
parity
n
1
,
n
1
+
2
,
…
,
N
-
s
-
1
if
N
-
s
+
n
1
is
odd
wherein ρ=traffic load on the device in Erlangs.
13. A method of allocating ports in a communications device having N ports, wherein N is an integer number greater than 1, comprising:
determining a load ratio “p” for the communications device;
determining a blocking probability, P A , associated with a first type load for the communications device, wherein the blocking probability associated with the first type load is a function of s, wherein s is a positive integer number; and
determining a blocking probability, P T , associated with a second type load for the communications device, wherein the blocking probability associated with the second type load is a function of s;
determining a value “s” which results in a minimum value for the expression:
pP A +(1−p)P T ;
allocating s ports of a first type; and
allocating N−s ports of a second type.
14. The method of claim 13 , wherein:
determining the blocking probability P A associated with the first type load includes solving the equation: P A =E[ρp,s];
determining the blocking probability P T associated with the second type load includes solving the equation: P T =E[(1−p)ρ,└(N−2s)/2┘], wherein
E[α,n]=(α n /n!)/(Σ i=0 n (α i )/i!), such that the terms a, n, and i are defined according to the Erlang-B formula;
ρ=traffic load on the device in Erlangs.
15. The method of claim 13 , wherein allocating s ports of a first type includes allocating a positive integer number that is less than half of the total ports N as ports of a first type.
16. The method of claim 15 , wherein allocating ports of a second type includes:
allocating s access load ports; and
allocating N−s transit ports.
17. The method of claim 16 , further comprising dynamically allocating ports of the second type between access load ports and transit ports.
18. The method of claim 17 , further comprising dynamically allocating all of the ports of the second type as transit ports.
19. The method of claim 18 , further comprising dynamically allocating no more than s ports of the second type as access load ports.
20. The method of claim 18 , wherein
determining the blocking probability P A associated with the first type load includes solving the equation:
P
A
=
{
∑
n
2
=
s
2
⌈
N
/
2
⌉
-
s
-
2
P
(
s
,
n
2
)
+
∑
n
1
=
0
⌊
s
/
2
⌋
P
(
2
n
1
,
N
-
s
)
if
N
-
s
is
even
∑
n
2
=
s
2
⌈
N
/
2
⌉
-
s
-
2
P
(
s
,
n
2
)
+
∑
n
1
=
1
⌈
s
/
2
⌉
P
(
2
n
1
-
1
,
N
-
s
-
1
)
if
N
-
s
is
odd
determining the blocking probability P T associated with the second type load includes solving the equation:
P
T
=
∑
n
1
=
0
⌊
s
/
2
⌋
P
(
2
n
1
,
2
⌊
(
N
-
s
)
/
2
⌋
)
+
∑
n
1
=
1
⌈
s
/
2
⌉
P
(
2
n
1
-
1
,
2
⌈
(
N
-
s
)
/
2
⌉
-
1
)
wherein
:
P
(
n
1
,
n
2
)
=
p
(
n
1
,
n
2
)
∑
(
i
,
j
)
∈
S
p
(
i
,
j
)
for
(
n
1
,
n
2
)
∈
S
p
(
n
1
,
n
2
)
=
[
p
ρ
]
n
1
[
(
1
-
p
)
ρ
]
n
2
-
n
1
2
n
1
!
n
2
-
n
1
2
!
and S is the set of (n 1 ,n 2 ) satisfying n 1 =0, 1, 2, s; and
n
2
=
{
n
1
,
n
1
+
2
,
…
,
N
-
s
if
n
1
,
N
-
s
are
of
same
parity
n
1
,
n
1
+
2
,
…
,
N
-
s
-
1
if
N
-
s
+
n
1
is
odd
wherein ρ=traffic load on the device in Erlangs.