Lagrange quality of service routing
First Claim
1. A method for determining a delay constrained least cost path in a multi-path communication system, the method comprising the steps of:
- finding a first path with a minimum cost and first path delay;
finding a second path with minimum delay and second path cost;
determining the delay constrained least cost path based, in part, on the first path and second path by using a Lagrange relaxation variable, comprising;
calculating a Lagrange relaxation variable; and
,determining the delay constrained least cost path based on the Lagrange relaxation variable;
wherein the step of calculating a Lagrange relaxation variable comprises;
calculating a first sum equal to the cost of the first path less the cost of the second path;
calculating a second sum equal to the delay of the first path less the delay of the second; and
,dividing the first sum by the second sum.
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Abstract
A method for practical QoS routing, which provides a solution to the delay constrained least cost routing problem, is presented. The method uses the concept of aggregated costs and finds the optimal multiplier based on Lagrange relaxation. The method is polynomial in running time, and produces a theoretical lower bound (i.e. optimal solution), along with the result. The differences between the lower bound and result are small, indicating the quality of the result. Additionally, by further relaxing the desire for an optimal solution, an option is provided to control the trade-off between running time of the algorithm and quality of the result.
56 Citations
17 Claims
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1. A method for determining a delay constrained least cost path in a multi-path communication system, the method comprising the steps of:
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finding a first path with a minimum cost and first path delay; finding a second path with minimum delay and second path cost; determining the delay constrained least cost path based, in part, on the first path and second path by using a Lagrange relaxation variable, comprising; calculating a Lagrange relaxation variable; and
,determining the delay constrained least cost path based on the Lagrange relaxation variable; wherein the step of calculating a Lagrange relaxation variable comprises; calculating a first sum equal to the cost of the first path less the cost of the second path; calculating a second sum equal to the delay of the first path less the delay of the second; and
,dividing the first sum by the second sum. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
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12. A method for determining a delay constrained least cost path, in a multi-path communication system, the method comprising the steps of:
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finding a first path with minimum cost and a first path delay;
finding a second path with minimum delay and a second path cost;generating a series of Lagrange relaxation variables, each Lagrange relaxation variable having an associated third path, each third path having a delay and cost; and determining the delay constrained least cost path, based on the first path, second path, Lagrange relaxation variable, and third path. - View Dependent Claims (13)
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14. A method for determining a least cost path satisfying multiple constraints in a multi-path communication system, the method comprising the steps of:
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finding multiple paths, one for each of multiple constraints, each of the multiple paths having a different minimum constraint, a first multiple path being a minimal cost path; calculating a first set of multiple Lagrange relaxation variables, one for each of the multiple constraints; determining a minimizing path that minimizes a first multi-term modified cost function; calculating a second multi-term modified cost function using the first multiple path; and determining the least cost path satisfying multiple constraints. - View Dependent Claims (15, 16, 17)
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Specification