Patent US3079250A successfully refreshed from Google Patents.
Patent US5809399A successfully refreshed from Google Patents.
Patent US5854903A successfully refreshed from Google Patents.
US5854903A
Expired / Lapsed
US
⏱️ 0.0 years remaining
Optimization method for routing and logical network design in multi-service networks
Assignee: Nokia of America Corp
•
Filing: 1995-11-07
•
Granted: 1998-12-29
•
Expires: 2015-11-07
Abstract
Abstract A method is described for network optimization based on a multirate, circuit-switched analysis. Network loss probabilities are determined as a solution of a set of fixed point equations and the sensitivity of network performance, as a function of offered load and loss probabilities, is determined as a solution to a set of linear equations. Because the numerical complexity of solving both the fixed point equations and the sensitivity equations is of an order which renders an exact solution computationally intractable, an asymptotic approximation is applied which yields a solution to the network loss probabilities and network sensitivities. A global optimization procedure is then applied using an iterative, steepest ascent optimization procedure to yield a set of virtual path routings and capacity allocations.
Inventors
- 👤 John A. Morrison
- 👤 Kajamalai Goplaswamy Ramakrishnan
- 👤 Debasis Mitra
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-30 16:43
CPC Classifications
H; H04; H04Q; H04Q11/00; H04Q11/04; H04Q11/0428; H04Q11/0478; H04L; H04L49/00; H04L49/20; H04L49/205; H04L49/25; H04Q3/00; H04Q3/0016; H04L12/00; H04L12/54; H04L12/56; H04L12/5601; H04L2012/5619; H04L2012/562; H04L2012/5623; H04L2012/5625; H04L2012/5626; H04L2012/5629; H04L2012/5631; H04L2012/5632; H04L2012/5678; H04L2012/5684; H04L49/50; H04Q2213/00; H04Q2213/1305; H04Q2213/13141; H04Q2213/13164; H04Q2213/13166; H04Q2213/13332; H04Q2213/13335; H04Q2213/1338; H04Q2213/13399; H04Q2213/13503
Claims Analysis
Total Claims: 62
Claim 1
Independent Claim
117 words
A method for logical network design in a multi-service communications network, said network including a set of switching nodes and a set of connecting links disposed to interconnect at least some of said nodes, comprising the steps of: determining blocking probabilities of a plurality of services for a subset of said set of links; determining sensitivities of network performance as a function of offered loads for a plurality of services and transmission rates: and adjusting said network performance based on said sensitivities and said blocking probabilities; wherein said steps of determining blocking probabilities and determining network performance sensitivities include a computational substep of applying successive asvmptotic approximations, said substep operating to reduce computational complexity for said steps.
Claim 2
Independent Claim
117 words
A method for logical network design in a multi-service communications network, said network including a set of switching nodes and a set of connecting links disposed to interconnect at least some of said nodes, comprising the steps of: determining blocking probabilities of a plurality of services for a subset of said set of links; determining sensitivities of network performance as a function of offered loads for a plurality of services and transmission rates: and adjusting said network performance based on said sensitivities and said blocking probabilities; wherein said steps of determining blocking probabilities and determining network performance sensitivities include a computational substep of applying successive asvmptotic approximations, said substep operating to reduce computational complexity for said steps.
Claim 3
Dependent Claim
18 words
The logical network design method of claim 1 wherein said asymptotic analysis substep includes a Uniform Asymptotic Approximation.
Claim 4
Dependent Claim
39 words
The logical network design method of claim 1 wherein said step of determining blocking probabilities includes the establishment of a set of fixed point equations, and a solution of said equations is carried out using said asymptotic analysis substep.
Claim 5
Dependent Claim
38 words
The logical network design method of claim 1 wherein said network performance sensitivity determining step includes the establishment of a set of linear equations, and a solution of said equations is carried out using said asymptotic analysis substep.
Claim 6
Dependent Claim
19 words
The logical network design method of claim 1 wherein said network performance is defined in terms of network revenue.
Claim 7
Dependent Claim
40 words
The logical network design method of claim 1 wherein said step of adjusting network performance is implemented through an iterative application of said steps of determining blocking probabilities and determining network performance sensitivity until a predetermined performance criterion is reached.
Claim 8
Dependent Claim
82 words
The logical network design method of claim 1 further including a dynamic bifurcation of said network into a first network portion and a second network portion, wherein said application of said steps of determining blocking probabilities and determining network performance sensitivity to said first portion of said network includes an asymptotic analysis substep, said asymptotic analysis substep not being included in said application of said steps of determining blocking probabilities and determining network performance sensitivity to said second portion of said network.
Claim 9
Dependent Claim
75 words
The logical network design method of claim 7 wherein said bifurcation of said network is carried out by assigning a first set of said links comprising said network to said first network portion and a second set of said links comprising said network to said second network portion and wherein said assignment of said network links to said first or said second link sets is related to capacity and loading factors for said network links.
Claim 10
Dependent Claim
83 words
The logical network design method of claim 8 wherein said step of adjusting network performance is implemented through an iterative application of said steps of determining blocking probabilities and determining network performance sensitivity, wherein each said iteration provides a capacity factor for each of said links in said network, and said assignment of said links to said first or said second link sets is related to said provided capacity factor, said assignment being adjusted as said link loads change from iteration to iteration.
Claim 11
Dependent Claim
31 words
The logical network design method of claim 1 further including an adaptation step for application of said method to changes in traffic loads of a plurality of services and source-destination pairs.
Claim 12
Dependent Claim
29 words
The logical network design method of claim 10 wherein said adaptation step effects a re-dimensioning of logical partitions in said logical network in response to said changing traffic conditions.
Claim 13
Dependent Claim
48 words
The logical network design method of claim 1 further including a call admission control substep operating to selectively block arriving traffic from entry to said network in accordance with a defined network performance criteria, wherein said selective blocking is determined with respect to service type and source-destination pair.
Claim 14
Independent Claim
150 words
A method of establishing a plurality of virtual paths in a communications network, said communications network being characterized by a set of switching nodes and a set of connecting links wherein each said virtual path is defined in terms of a subset of said set of nodes and a subset of said set of links, comprising the steps of: determining blocking probabilities of a plurality of services for links included in said plurality of virtual paths; determining sensitivities of network performance as a function of offered loads for a plurality of services and transmission rates: and selecting routes and allocating capacity for said virtual paths in relation to said offered loads based on said sensitivities and said blocking probabilities; wherein said steps of determining blocking probabilities and determining network performance sensitivities include a computational substep of applying successive asymptotic approximations, said substep operating to reduce computational complexity for said steps.
Claim 15
Independent Claim
150 words
A method of establishing a plurality of virtual paths in a communications network, said communications network being characterized by a set of switching nodes and a set of connecting links wherein each said virtual path is defined in terms of a subset of said set of nodes and a subset of said set of links, comprising the steps of: determining blocking probabilities of a plurality of services for links included in said plurality of virtual paths; determining sensitivities of network performance as a function of offered loads for a plurality of services and transmission rates: and selecting routes and allocating capacity for said virtual paths in relation to said offered loads based on said sensitivities and said blocking probabilities; wherein said steps of determining blocking probabilities and determining network performance sensitivities include a computational substep of applying successive asymptotic approximations, said substep operating to reduce computational complexity for said steps.
Claim 16
Dependent Claim
19 words
The method for establishing virtual paths of claim 13 wherein said asymptotic analysis substep includes a Uniform Asymptotic Approximation.
Claim 17
Dependent Claim
40 words
The method for establishing virtual paths of claim 13 wherein said step of determining blocking probabilities includes the establishment of a set of fixed point equations, and a solution of said equations is carried out using said asymptotic analysis substep.
Claim 18
Dependent Claim
39 words
The method for establishing virtual paths of claim 13 wherein said network performance sensitivity determining step includes the establishment of a set of linear equations, and a solution of said equations is carried out using said asymptotic analysis substep.
Claim 19
Dependent Claim
20 words
The method for establishing virtual paths of claim 13 wherein said network performance is defined in terms of network revenue.
Claim 20
Dependent Claim
44 words
The method for establishing virtual paths of claim 13 wherein said step of selecting routes for said virtual paths is implemented through an iterative application of said steps of determining blocking probabilities and determining network performance sensitivity until a predetermined performance criterion is reached.
Claim 21
Dependent Claim
83 words
The method for establishing virtual paths of claim 13 further including a dynamic bifurcation of said network into a first network portion and a second network portion, wherein said application of said steps of determining blocking probabilities and determining network performance sensitivity to said first portion of said network includes an asymptotic analysis substep, said asymptotic analysis substep not being included in said application of said steps of determining blocking probabilities and determining network performance sensitivity to said second portion of said network.
Claim 22
Dependent Claim
76 words
The method for establishing virtual paths of claim 19 wherein said bifurcation of said network is carried out by assigning a first set of said links comprising said network to said first network portion and a second set of said links comprising said network to said second network portion and wherein said assignment of said network links to said first or said second link sets is related to capacity and loading factors for said network links.
Claim 23
Dependent Claim
87 words
The method for establishing virtual paths of claim 20 wherein said step of selecting routes for said virtual paths is implemented through an iterative application of said steps of determining blocking probabilities and determining network performance sensitivity, wherein each said iteration provides a capacity factor for each of said links in said network, and said assignment of said links to said first or said second link sets is related to said provided capacity factor, said assignment being adjusted as said link loads change from iteration to iteration.
Claim 24
Dependent Claim
32 words
The method for establishing virtual paths of claim 13 further including an adaptation step for application of said method to changes in traffic loads of a plurality of services and source-destination pairs.
Claim 25
Dependent Claim
30 words
The method for establishing virtual paths of claim 22 wherein said adaptation step effects a re-dimensioning of said virtual paths in relation to changes in offered load to said network.
Claim 26
Dependent Claim
49 words
The method for establishing virtual paths of claim 13 further including a call admission control substep operating to selectively block arriving traffic from entry to said network in accordance with a defined network performance criteria, wherein said selective blocking is determined with respect to service type and source-destination pair.
Claim 27
Independent Claim
150 words
A method for determining virtual path routings and allocation of bandwidth thereto in a communications network, said communications network being characterized by a set of switching nodes and a set of connecting links, comprising the steps of: determining blocking probabilities and network performance sensitivities of a plurality of services for a subset of said set of connecting links based on offered loads for said plurality of services and a plurality of transmission rates and initial determination of said virtual path routings and bandwidth allocations; evaluating said network sensitivities with respect to a predetermined network performance criterion; iteratively applying said determining step using revised virtual path routings and bandwidth allocations until a network performance gradient is less than a selected threshold; wherein said step of determining blocking probabilities and network performance sensitivities includes a computational substep of applying successive asymptotic approximations, said substep operating to reduce computational complexity for said step.
Claim 28
Independent Claim
150 words
A method for determining virtual path routings and allocation of bandwidth thereto in a communications network, said communications network being characterized by a set of switching nodes and a set of connecting links, comprising the steps of: determining blocking probabilities and network performance sensitivities of a plurality of services for a subset of said set of connecting links based on offered loads for said plurality of services and a plurality of transmission rates and initial determination of said virtual path routings and bandwidth allocations; evaluating said network sensitivities with respect to a predetermined network performance criterion; iteratively applying said determining step using revised virtual path routings and bandwidth allocations until a network performance gradient is less than a selected threshold; wherein said step of determining blocking probabilities and network performance sensitivities includes a computational substep of applying successive asymptotic approximations, said substep operating to reduce computational complexity for said step.
Claim 29
Dependent Claim
23 words
The method for determining virtual path routings and bandwidth allocations of claim 25 wherein said asymptotic analysis substep includes a Uniform Asymptotic Approximation.
Claim 30
Dependent Claim
43 words
The method for determining virtual path routings and bandwidth allocations of claim 25 wherein said determination of blocking probabilities includes the establishment of a set of fixed point equations, and a solution of said equations is carried out using said asymptotic analysis substep.
Claim 31
Dependent Claim
43 words
The method for determining virtual path routings and bandwidth allocations of claim 25 wherein said determination of network performance sensitivities includes the establishment of a set of linear equations, and a solution of said equations is carried out using said asymptotic analysis substep.
Claim 32
Dependent Claim
24 words
The method for determining virtual path routings and bandwidth allocations of claim 25 wherein said evaluation criterion is defined in terms of network revenue.
Claim 33
Dependent Claim
84 words
The method for determining virtual path routings and bandwidth allocations of claim 25 further including a dynamic bifurcation of said network into a first network portion and a second network portion, wherein an application of said step of determining blocking probabilities and network performance sensitivity to said first portion of said network includes an asymptotic analysis substep, said asymptotic analysis substep not being included in application of said step of determining blocking probabilities and network performance sensitivity to said second portion of said network.
Claim 34
Dependent Claim
80 words
The method for determining virtual path routings and bandwidth allocations of claim 30 wherein said bifurcation of said network is carried out by assigning a first set of said links comprising said network to said first network portion and a second set of said links comprising said network to said second network portion and wherein said assignment of said network links to said first or said second link sets is related to capacity and loading factors for said network links.
Claim 35
Dependent Claim
68 words
The method for determining virtual path routings and bandwidth allocations of claim 31 wherein each said iterative application of said determining step provides a capacity factor for each of said links in said network, and said assignment of said links to said first or said second link sets is related to said provided capacity factor, said assignment being adjusted as said link loads change from iteration to iteration.
Claim 36
Dependent Claim
36 words
The method for determining virtual path routings and bandwidth allocations of claim 25 further including an adaptation step for application of said method to changes in traffic loads of a plurality of services and source-destination pairs.
Claim 37
Dependent Claim
34 words
The method for determining virtual path routings and bandwidth allocations of claim 32 wherein said adaptation step effects a re-dimensioning of said virtual paths in relation to changes in offered load to said network.
Claim 38
Dependent Claim
53 words
The method for determining virtual path routings and bandwidth allocations of claim 25 further including a call admission control substep operating to selectively block arriving traffic from entry to said network in accordance with a defined network performance criteria, wherein said selective blocking is determined with respect to service type and source-destination pair.
Claim 39
Dependent Claim
129 words
An object-oriented software system for carrying out a network analysis methodology, and having as an output at least one network performance parameter, said software system comprising: a parser process for determining and compiling network topology data into an object file; a network solver process for determining network blocking probabilities in respect to a plurality of services and network performance sensitivities as a function of offered loads, said network solver process including a computational process for applying successive asymptotic approximations in said network blocking probability and said network performance sensitivity determinations, said substep operating to reduce computational complexity for said determinations; and an optimizer process for evaluating a resultant of said network solver process and causing said network process to be iteratively repeated until said resultant satisfies a defined criterion.
Claim 40
Dependent Claim
129 words
An object-oriented software system for carrying out a network analysis methodology, and having as an output at least one network performance parameter, said software system comprising: a parser process for determining and compiling network topology data into an object file; a network solver process for determining network blocking probabilities in respect to a plurality of services and network performance sensitivities as a function of offered loads, said network solver process including a computational process for applying successive asymptotic approximations in said network blocking probability and said network performance sensitivity determinations, said substep operating to reduce computational complexity for said determinations; and an optimizer process for evaluating a resultant of said network solver process and causing said network process to be iteratively repeated until said resultant satisfies a defined criterion.
Claim 41
Dependent Claim
21 words
The software system of claim 36 wherein said parser process further includes a determination of parameters used in said network analysis.
Claim 42
Dependent Claim
28 words
The software system of claim 37 wherein said parser process still further includes a determination of data encoding an optimization problem to be solved by said software system.
Claim 43
Dependent Claim
27 words
The software system of claim 38 wherein said parser process passes to said optimizer process said object file and any other data determined by said parser process.
Claim 44
Dependent Claim
30 words
The software system of claim 36 wherein a set a actions carried out in the operation of said software system are as depicted in the flow diagram of FIG. 4.
Claim 45
Dependent Claim
15 words
A software system for implementing the methodology of claim 1 in a digital computer system.
Claim 46
Dependent Claim
17 words
A storage means fabricated to contain a set of instructions corresponding to the method of claim 1.
Claim 47
Independent Claim
156 words
A method for logical network design in a multi-service communications network, said network including a set of switching nodes and a set of connecting links disposed to interconnect at least some of said nodes, comprising the steps of: determining blocking probabilities of a plurality of services for a subset of said set of links; determining sensitivities of network performance as a function of offered loads for a plurality of services and transmission rates: adjusting said network performance based on said sensitivities and said blocking probabilities; and dynamically bifurcating said network into a first network portion and a second network portion; wherein said application of said steps of determining blocking probabilities and determining network performance sensitivity to said first portion of said network includes an asymptotic analysis substep, said asymptotic analysis substep not being included in said application of said steps of determining blocking probabilities and determining network performance sensitivity to said second portion of said network.
Claim 48
Independent Claim
156 words
A method for logical network design in a multi-service communications network, said network including a set of switching nodes and a set of connecting links disposed to interconnect at least some of said nodes, comprising the steps of: determining blocking probabilities of a plurality of services for a subset of said set of links; determining sensitivities of network performance as a function of offered loads for a plurality of services and transmission rates: adjusting said network performance based on said sensitivities and said blocking probabilities; and dynamically bifurcating said network into a first network portion and a second network portion; wherein said application of said steps of determining blocking probabilities and determining network performance sensitivity to said first portion of said network includes an asymptotic analysis substep, said asymptotic analysis substep not being included in said application of said steps of determining blocking probabilities and determining network performance sensitivity to said second portion of said network.
Claim 49
Dependent Claim
75 words
The logical network design method of claim 43 wherein said bifurcation of said network is carried out by assigning a first set of said links comprising said network to said first network portion and a second set of said links comprising said network to said second network portion and wherein said assignment of said network links to said first or said second link sets is related to capacity and loading factors for said network links.
Claim 50
Dependent Claim
83 words
The logical network design method of claim 44 wherein said step of adjusting network performance is implemented through an iterative application of said steps of determining blocking probabilities and determining network performance sensitivity, wherein each said iteration provides a capacity factor for each of said links in said network, and said assignment of said links to said first or said second link sets is related to said provided capacity factor, said assignment being adjusted as said link loads change from iteration to iteration.
Claim 51
Independent Claim
193 words
A method of establishing a plurality of virtual paths in a communications network, said communications network being characterized by a set of switching nodes and a set of connecting links wherein each said virtual path is defined in terms of a subset of said set of nodes and a subset of said set of links, comprising the steps of: determining blocking probabilities of a plurality of services for links included in said plurality of virtual paths; determining sensitivities of network performance as a function of offered loads for a plurality of services and transmission rates: selecting routes and allocating capacity for said virtual paths in relation to said offered loads based on said sensitivities and said blocking probabilities; and further including a dynamic bifurcation of said network into a first network portion and a second network portion, wherein said application of said steps of determining blocking probabilities and determining network performance sensitivity to said first portion of said network includes an asymptotic analysis substep, said asymptotic analysis substep not being included in said application of said steps of determining blocking probabilities and determining network performance sensitivity to said second portion of said network.
Claim 52
Independent Claim
193 words
A method of establishing a plurality of virtual paths in a communications network, said communications network being characterized by a set of switching nodes and a set of connecting links wherein each said virtual path is defined in terms of a subset of said set of nodes and a subset of said set of links, comprising the steps of: determining blocking probabilities of a plurality of services for links included in said plurality of virtual paths; determining sensitivities of network performance as a function of offered loads for a plurality of services and transmission rates: selecting routes and allocating capacity for said virtual paths in relation to said offered loads based on said sensitivities and said blocking probabilities; and further including a dynamic bifurcation of said network into a first network portion and a second network portion, wherein said application of said steps of determining blocking probabilities and determining network performance sensitivity to said first portion of said network includes an asymptotic analysis substep, said asymptotic analysis substep not being included in said application of said steps of determining blocking probabilities and determining network performance sensitivity to said second portion of said network.
Claim 53
Dependent Claim
76 words
The method for establishing virtual paths of claim 46 wherein said bifurcation of said network is carried out by assigning a first set of said links comprising said network to said first network portion and a second set of said links comprising said network to said second network portion and wherein said assignment of said network links to said first or said second link sets is related to capacity and loading factors for said network links.
Claim 54
Dependent Claim
87 words
The method for establishing virtual paths of claim 47 wherein said step of selecting routes for said virtual paths is implemented through an iterative application of said steps of determining blocking probabilities and determining network performance sensitivity, wherein each said iteration provides a capacity factor for each of said links in said network, and said assignment of said links to said first or said second link sets is related to said provided capacity factor, said assignment being adjusted as said link loads change from iteration to iteration.
Claim 55
Dependent Claim
32 words
The method for establishing virtual paths of claim 46 further including an adaptation step for application of said method to changes in traffic loads of a plurality of services and source-destination pairs.
Claim 56
Dependent Claim
30 words
The method for establishing virtual paths of claim 49 wherein said adaptation step effects a re-dimensioning of said virtual paths in relation to changes in offered load to said network.
Claim 57
Independent Claim
192 words
A method for determining virtual path routings and allocation of bandwidth thereto in a communications network, said communications network being characterized by a set of switching nodes and a set of connecting links, comprising the steps of: determining blocking probabilities and network performance sensitivities of a plurality of services for a subset of said set of connecting links based on offered loads for said plurality of services and a plurality of transmission rates and initial determination of said virtual path routings and bandwidth allocations; evaluating said network sensitivities with respect to a predetermined network performance criterion; iteratively applying said determining step using revised virtual path routings and bandwidth allocations until a network performance gradient is less than a selected threshold; and further including a dynamic bifurcation of said network into a first network portion and a second network portion, wherein an application of said step of determining blocking probabilities and network performance sensitivity to said first portion of said network includes an asymptotic analysis substep, said asymptotic analysis substep not being included in application of said step of determining blocking probabilities and network performance sensitivity to said second portion of said network.
Claim 58
Independent Claim
192 words
A method for determining virtual path routings and allocation of bandwidth thereto in a communications network, said communications network being characterized by a set of switching nodes and a set of connecting links, comprising the steps of: determining blocking probabilities and network performance sensitivities of a plurality of services for a subset of said set of connecting links based on offered loads for said plurality of services and a plurality of transmission rates and initial determination of said virtual path routings and bandwidth allocations; evaluating said network sensitivities with respect to a predetermined network performance criterion; iteratively applying said determining step using revised virtual path routings and bandwidth allocations until a network performance gradient is less than a selected threshold; and further including a dynamic bifurcation of said network into a first network portion and a second network portion, wherein an application of said step of determining blocking probabilities and network performance sensitivity to said first portion of said network includes an asymptotic analysis substep, said asymptotic analysis substep not being included in application of said step of determining blocking probabilities and network performance sensitivity to said second portion of said network.
Claim 59
Dependent Claim
80 words
The method for determining virtual path routings and bandwidth allocations of claim 49 wherein said bifurcation of said network is carried out by assigning a first set of said links comprising said network to said first network portion and a second set of said links comprising said network to said second network portion and wherein said assignment of said network links to said first or said second link sets is related to capacity and loading factors for said network links.
Claim 60
Dependent Claim
68 words
The method for determining virtual path routings and bandwidth allocations of claim 50 wherein each said iterative application of said determining step provides a capacity factor for each of said links in said network, and said assignment of said links to said first or said second link sets is related to said provided capacity factor, said assignment being adjusted as said link loads change from iteration to iteration.
Claim 61
Dependent Claim
118 words
An object-oriented software system for carrying out a network analysis methodology, and having as an output at least one network performance parameter, said software system comprising: a parser process for determining and compiling network topology data into an object file; a network solver process for determining network blocking probabilities in respect to a plurality of services and network performance sensitivities as a function of offered loads; and an optimizer process for evaluating a resultant of said network solver process and causing said network process to be iteratively repeated until said resultant satisfies a defined criterion; wherein a set of actions carried out in operation of said software system are as depicted in the flow diagram of FIG. 4.
Claim 62
Dependent Claim
118 words
An object-oriented software system for carrying out a network analysis methodology, and having as an output at least one network performance parameter, said software system comprising: a parser process for determining and compiling network topology data into an object file; a network solver process for determining network blocking probabilities in respect to a plurality of services and network performance sensitivities as a function of offered loads; and an optimizer process for evaluating a resultant of said network solver process and causing said network process to be iteratively repeated until said resultant satisfies a defined criterion; wherein a set of actions carried out in operation of said software system are as depicted in the flow diagram of FIG. 4.
References Cited (Backward Citations)
USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 2001-12-28 | 2002-06-29 | 2002-12-29 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 2005-12-28 | 2006-06-29 | 2006-12-29 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 2009-12-28 | 2010-06-29 | 2010-12-29 | $7700.00 | Window Closed / Lapsed |