Grid Job Routing Algorithms - Phosphorus

Grid Job Routing Algorithmsa = a − jωd( l) ( l) ( l)ikik( l) 2 lb = ω D λ 2 /(4 πc)i i i( l) 2 lq = ω D λ 2 /(4 πc)k k kN( l) 2 2 ( n) ( n)i= ω λi ∑ in= l+1B L D /(4 πc)l−i( l) 2 2 ( n) ( n)kω λk kn=1Q = ∑ L D /(4 πc)(27)Using (Eq. 26) we can obtain an analytic expression for the XPM noise-like variance given by [Pachnicke03]N ∞2 2 1 IM2 2XPM XPM , ik opt.filter kk= 1, k≠i2π−∞σ P(0) H ( ω, L) . H ( ω) . PSD ( ω)dω= ∑ ∫(28)where P(0) is the average channel power, H XPM,ik (ω) the transfer function due to XPM as described above,H opt,filter (ω) the transfer function of the optical filter at the receiver and PSD k (ω) is the power spectral density ofchannel k.Four Wave Mixing (FWM)The final nonlinear impairment that we examine in this study is Four-Wave Mixing (FWM) which is a majorfactor of the degradation of the system performance in multi-channel lightwave systems. The generation ofFWM depends on many characteristics of the system such as channel spacing, fiber length, and chromaticdispersion. In particular, the influence of FWM is larger when the optical channels are equally spaced, andwhen wavelength division multiplexed (WDM) systems operate in the zero dispersion region.FWM is the phenomenon where three waves (or two waves) are mixed during the propagation in the fiber andgenerate the new optical frequency (fourth wave or third wave), which may fall into other channels and causethe in-band crosstalk. Through the FWM process, a fourth (or third) wave will be generated at a frequencyf = f + f − f ( i, j ≠ k)(29)ijk i j kBy modifying [Zeiler96, Inoue94] to be compatible with the link architecture we described in section 5.3 theFWM signal power can be expressed asProject:PHOSPHORUSDeliverable Number: D.5.3Date of Issue: 31/06/07EC Contract No.: 034115Document Code: Phosphorus-WP5-D5.340