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

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Transcript of Optic fiber Electronic switch the fiber serves as a transmission medium Optical networks - 1 st...

  • Slide 1
  • Optic fiber Electronic switch the fiber serves as a transmission medium Optical networks - 1 st generation 1. Optical networks basic notions
  • Slide 2
  • 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
  • Slide 3
  • lightpaths ADM OADM Data in electronic form
  • Slide 4
  • lightpaths p1 p2 Valid coloring
  • Slide 5
  • Optical switch lightpath OADM (optical add-drop multiplexer) No two inputs with the same wavelength should be routed on the same edge.
  • Slide 6
  • Electronic device at the endpoints of lightpaths ADM (electronic add-drop multiplexer)
  • Slide 7
  • Where can we save? an ADM can be shared by two lightpaths 2 ADMs1 ADM
  • Slide 8
  • 123 123
  • Slide 9
  • low capacity requests can be groomed into high capacity wavelengths (colors). colors can be assigned such that at most g lightpaths with the same color can share an edge g is the grooming factor Traffic grooming
  • Slide 10
  • lightpaths - with grooming Valid coloring g=2
  • Slide 11
  • Optical networks ADMs, OADMs, grooming Graph theoretical model Coloring and routing
  • Slide 12
  • 12 W=2, ADM=8 W=3, ADM=7 2. Minimize number of ADMs
  • Slide 13
  • minADM Input: a graph, a set of lightpaths, t>o. Output: can the lightpath be colored such that #ADMs t ? Output: can the lightpath be colored such that #ADMs t ?
  • Slide 14
  • The problem is easy on a path network
  • Slide 15
  • k = 4 Reminder: coloring of an interval graph
  • Slide 16
  • Go from left to right
  • Slide 17
  • 2.1 minADM is NPC for a ring minADM Input: a graph, a set of lightpaths, t>o. Output: can the lightpath be colored such that #ADMs t ? Output: can the lightpath be colored such that #ADMs t ?
  • Slide 18
  • Coloring of a circular arc graph
  • Slide 19
  • Not always possible with max load
  • Slide 20
  • Input: circular arc graph G, k>o. Output: can the arcs be colored by k colors? Output: can the arcs be colored by k colors? Coloring of a circular arc graph
  • Slide 21
  • Input: circular arc graph G, k>o. Output: can the arcs be colored with k colors? Output: can the arcs be colored with k colors? minADM Input: a graph, a set of lightpaths, t>o. Output: can the lightpath be colored such that #ADMs t ? Output: can the lightpath be colored such that #ADMs t ? G
  • Slide 22
  • Given an instance of the circular arc graph problem, construct an instance H of minADM:
  • Slide 23
  • Claim: Claim: can color G with k colors iff can color H with k colors iff can color H with #ADMs N. G H
  • Slide 24
  • Assume a coloring with 3 colors Claim: Claim: can color H with 3 colors iff can color H with #ADMs 13
  • Slide 25
  • Claim: Claim: can color with 3 colors iff ca n color the lightpaths with 13 ADMs Assume a coloring with 13 ADMs
  • Slide 26
  • 2.2 three basic observations
  • Slide 27
  • #ADMs = N + #chains N lightpaths cycles chains Cycles are good, chains are bad A. Structure of a solution
  • Slide 28
  • In the approximation algorithms there are two common techniques for saving ADMs: Eliminate cycles of lightpaths Find matchings of lightpaths #ADMs = N + #chains
  • Slide 29
  • cost(S) = N + chains=13+6=19 costs Every path costs 1 ADM cost(S) = 2N-savings=26-7=19 saves Every connection saves 1 ADM N lightpaths N=13
  • Slide 30
  • w/out grooming: ALG 2N N OPT ALG 2 OPT N: # of lightpaths ALG: #ADMs used by algorithm OPT: #ADMs used by an optimal solution w/ grooming: ALG 2N N/g OPT ALG 2g OPT B. The competitive ratio
  • Slide 31
  • Lemma: Assume that a solution ALG saves y ADMs, and OPT saves x ADMs. C. A basic lemma
  • Slide 32
  • Optimal solution OPT saves x ADMs a solution ALG saves y ADMs