# Linear Programming and Algorithms for Communication Networks: A Practical Guide to Network Design, Control, and Management

# Linear Programming and Algorithms for Communication Networks: A Practical Guide to Network Design, Control, and Management

## Eiji Oki

Language: English

Pages: 208

ISBN: 2:00184310

Format: PDF / Kindle (mobi) / ePub

Explaining how to apply to mathematical programming to network design and control, **Linear Programming and Algorithms for Communication Networks: A Practical Guide to Network Design, Control, and Management **fills the gap between mathematical programming theory and its implementation in communication networks. From the basics all the way through to more advanced concepts, its comprehensive coverage provides readers with a solid foundation in mathematical programming for communication networks.

Addressing optimization problems for communication networks, including the shortest path problem, max flow problem, and minimum-cost flow problem, the book covers the fundamentals of linear programming and integer linear programming required to address a wide range of problems. It also:

• Examines several problems on finding disjoint paths for reliable communications

• Addresses optimization problems in optical wavelength-routed networks

• Describes several routing strategies for maximizing network utilization for various traffic-demand models

• Considers routing problems in Internet Protocol (IP) networks

• Presents mathematical puzzles that can be tackled by integer linear programming (ILP)

Using the GNU Linear Programming Kit (GLPK) package, which is designed for solving linear programming and mixed integer programming problems, it explains typical problems and provides solutions for communication networks. The book provides algorithms for these problems as well as helpful examples with demonstrations. Once you gain an understanding of how to solve LP problems for communication networks using the GLPK descriptions in this book, you will also be able to easily apply your knowledge to other solvers.

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formulate an optimization problem that corresponds to the desired communication networks with required parameters, and they solve the problem by running an LP solver on a computer. The engineers want to know how to apply LP to network design and control in their practical situations. However, there is a gap between the theory of LP in the literature and its practical implementation. This book was therefore written to ﬁll this gap. This book is intended to provide the fundamentals of LP as applied

7 6 45 5+14 5+14 (b3) 4 6+25 2+52 5 3+14 (c2) 2 8+52 1 4+14 4+18 (c1) 7 1+14 6 7 6 9+36 7 6 6 2 6 2 3 3 6+14 2 5+14 3 (b2) 2 8 6 5 4 7+14 6 4 4 8 4 5 7 4 (a3) 2 3 6 4 7 5 5 5 3 4 2 6 (b1) 1 6 1 3 6 7 9 1 6 4 6 2 3 7 5 (a2) 2 7 6 5 4 (a1) 2 4 8 2 3 7 6 9 2 6 8 5 5 1 ✐ path2 1 1266+3800 2 545+1588 31801+1588 5 1265+3800 7 +3800 492+1588 543+1588 6 293+1764 4 291+1764 (i3) path3 Figure 5.9: Example

technology to increase the transmission capacity in an optical ﬁber, where multiple wavelengths carry data simultaneously. In addition to the eﬀect of increasing the transmission capacity, WDM is also useful for wavelength-based switching, which enables us to set an optical path, which is routed on several ﬁbers by connecting each wavelength per ﬁber through optical crossconnect(s). A network that is formed by several optical paths is called an optical path network, where each wavelength is

means that the farmer must remove all the items from the left bank as soon as possible. In other words, minimizing this objective function is equivalent to minimizing the number of trips. Let us set f (t) as follows: t−1 f (t) = I f (t ) + 1, where f (0) = 0 t =0 = 0, (I + 1)t−1 , t=0 t ≥ 1. (9.7) For I = 3, f (t) is f (0) = 0, f (1) = 1, f (2) = 4, f (3) = 16, · · · . We are able to prove that f (t) in Eq. (9.7) gives the equivalence between minimizing the objective function in Eq. (9.4a)