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Published byDaisy Croke Modified about 1 year ago

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1 Optical networks: Basics of WDM

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2 the fiber serves as a transmission medium Electronic switch Optic fiber Optical networks - 1 st generation

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3 Routing in the optical domain Two complementing technologies: - Wavelength Division Multiplexing (WDM): Transmission of data simultaneously at multiple wavelengths over same fiber - Optical switches: the output port is determined according to the input port and the wavelength Optical networks - 2 nd generation

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4 Wavelength Division Multiplexing (WDM) Directed: Symmetric: Undirected: Optic Fiber

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5 Optical Switches No two inputs with the same wavelength should be routed on the same edge.

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6 Lightpaths ADM Data in electronic form

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7 A virtual topology

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8 Lightpaths p1 p2 Valid coloring

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9 The Routing Problem Input : A graph G=(V,E) A set or sequence of node pairs (a i,b i ) Output: A set or sequence of paths p i =(a i, v 1, …, b i )

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10 The Load Given a graph G=(V,E) and a set P of paths on the graph, we define: for any edge e of the graph: the load on this edge l(e)=|P e | The (maximum, minimum, average) load on the network:

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11 Wavelength Assignment Problem (WLA) Input: A graph G=(V,E). A set or sequence of paths P. Output: A coloring w of the paths: Constraint:

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12 Routing and WLA (RLA/WRA) Input : A graph G=(V,E) A set or sequence of node pairs (a i,b i ) Output: A set or sequence of paths p i =(a i, v 1, …, b i ) A coloring w of the paths: Constraint:

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13 Cost Measure: # of colors For any legal coloring w of the paths:

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Static vs. Dynamic vs. Incremental Static: The input is a set (of pairs or paths), the algorithm calculates its output based on the input. Incremental (Online): The input is a sequence of input elements (pairs or paths). It is supplied to the algorithm one element at a time. The output corresponding to the input element is calculated w/o knowledge of the subsequent input elements

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Static vs. Dynamic vs. Incremental Dynamic: Similar to incremental The sequence may contain deletion requests for previous elements.

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WLA (A trivial lower bound) For any instance of the WLA problem: W>=L. Proof: Consider an edge e, such that L=l(e). There are L paths p 1, …, p |L| using e, because the paths are simple. Therefore :

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WLA (A trivial lower bound) For some instances W > L. L=2 W=3

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Static WLA on Path Topologies The GREEDY algorithm: // The set of integers for i = 1 to |V| do for each path p=(x,i) do for each path p=(i,x) do

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Static WLA on Path Topologies Let the value of after node i is processed. Clearly, Prove by induction on i that Therefore:

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