Properties of Some Tridiagonal Matrices and Their Application to Boundary Value Problems

Fischer, Charlotte Froese; Usmani, Riaz A.

doi:10.1137/0706014

Cited by 97 publications

(32 citation statements)

References 6 publications

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“…Noting that H i and K i , i = 1, ..., N , are definite positive matrices, as can be proved by exploiting again results in [10], the positivity of H …”

Section: Problem 1 Find a Global Minimum For The Cost Functionmentioning

confidence: 90%

“…The matrix H N is definite positive, as can be easily proved by exploiting some results in [10], so that J is strictly convex in R N . The solution of Problem 1 is given in the following theorem.…”

Section: Problem 1 Find a Global Minimum For The Cost Functionmentioning

confidence: 99%

“…where H i , i = 1, ..., N , is an i × i matrix defined according to (10) and K i is the following i × i matrix:…”

Section: Problem 1 Find a Global Minimum For The Cost Functionmentioning

confidence: 99%

“…Poisson process with parameter λ = ; -the last one is related to the amount of bandwidth of each request, and follows a uniform distribution on the integers of the interval [1,10].…”

Section: An Application To Simulated Datamentioning

confidence: 99%

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Optimal Capacity Provisioning for Label Switched Paths in MPLS Networks

Bruni

Scoglio

Vergari

2002

NETWORKING 2002: Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile A

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Abstract. Optimal control is a possible approach to Internet traffic engineering, which aims to achieve QoS guarantees and efficiency in network resources use. The goal can be better achieved by using the MultiProtocol Label Switching technique (MPLS), which provides increased scalability, manageability and enhanced QoS functions in IP-based networks. In this context, this paper proposes a method to find the optimal capacity provisioning for a Label Switched Path (LSP) of a MPLS network. The optimal capacity allocation for a given time interval is computed with respect to a quadratic cost function including a switching cost and a management cost for the whole network. The unique optimal solution is analytically computed assuming the knowledge of the offered traffic for the whole control interval. Furthermore, a sub-optimal on line solution is proposed which only requires the knowledge of a narrow sliding window of the offered traffic. Optimal and sub-optimal solutions are compared with respect to a simulated case study, enlightening the simplicity and, at the same time, the effectiveness of the second one.

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“…Noting that H i and K i , i = 1, ..., N , are definite positive matrices, as can be proved by exploiting again results in [10], the positivity of H …”

Section: Problem 1 Find a Global Minimum For The Cost Functionmentioning

confidence: 90%

Section: Problem 1 Find a Global Minimum For The Cost Functionmentioning

confidence: 99%

“…where H i , i = 1, ..., N , is an i × i matrix defined according to (10) and K i is the following i × i matrix:…”

Section: Problem 1 Find a Global Minimum For The Cost Functionmentioning

confidence: 99%

“…Poisson process with parameter λ = ; -the last one is related to the amount of bandwidth of each request, and follows a uniform distribution on the integers of the interval [1,10].…”

Section: An Application To Simulated Datamentioning

confidence: 99%

See 2 more Smart Citations

Optimal Capacity Provisioning for Label Switched Paths in MPLS Networks

Bruni

Scoglio

Vergari

2002

NETWORKING 2002: Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile A

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“…3.7(i)). From the theory of monotone matrices (Henrici, [i] This follows from Fischer and Usmani [8]. Now from (7.1), (7.4), and (7.9) (7.9), it ollows that IEll < h4(b a)2M6/2304 + 0(h6) 0(h4).…”

Section: Solution Of Nonlinear Equations (I 3)mentioning

confidence: 99%