Scheduling light-trails on WDM rings

  • Authors:
  • Soumitra Pal;Abhiram Ranade

  • Affiliations:
  • -;-

  • Venue:
  • Journal of Parallel and Distributed Computing
  • Year:
  • 2012

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Abstract

We consider the problem of scheduling communication on optical WDM (wavelength division multiplexing) networks using the light-trails technology. We seek to design scheduling algorithms such that the given transmission requests can be scheduled using a minimum number of wavelengths (optical channels). We provide algorithms and close lower bounds for two versions of the problem on an n processor linear array/ring network. In the stationary version, the pattern of transmissions (given) is assumed to not change over time. For this, a simple lower bound is c, the congestion or the maximum total traffic required to pass through any link. We give an algorithm that schedules the transmissions using O(c+logn) wavelengths. We also show a pattern for which @W(c+logn/loglogn) wavelengths are needed. In the on-line version, the transmissions arrive and depart dynamically, and must be scheduled without upsetting the previously scheduled transmissions. For this case we give an on-line algorithm which has competitive ratio @Q(logn). We show that this is optimal in the sense that every on-line algorithm must have competitive ratio @W(logn). We also give an algorithm that appears to do well in simulations (for the classes of traffic we consider), but which has competitive ratio between @W(log^2n/loglogn) and O(log^2n). We present detailed simulations of both our algorithms.