Grid Job Routing Algorithms - Phosphorus

Grid Job Routing AlgorithmsPFWM− a L + j∆k L − a L+ j∆kLpre . pre pre pre1. 1 1 1x e −1 x e −1222 111. + . G . .inf SMFA j∆k −a A j∆k −aeff 2 pre pre eff 1 1 1M−a2.L2 + j∆k 2L2− apre .Lpre + j∆k preLpre⎛ j( m− 1)( ∆ kL1 1+∆k 2L2) ⎞ x e −1 222e . ⎜∑e ⎟+. G . G .inf SMF inSMF .6 21024 π .3⎝2 3m=1 ⎠ Aj∆k−aeff 22 2= DP4 2 2 0Mnλco− ( apre .Lpre + a1. L1 ) + j( ∆ kpre Lpre+∆kL 1 1) ⎛ j( m− 1)( ∆ kL1 1+∆k2L2) ⎞ x222e . ⎜∑e ⎟+. G . G . G .inf SMF inSMF inDCF⎝m=⎠ A− a L + j∆k Lepost . post post postj∆kpost−apost−1 . e1 eff 2− ( a L + a L+ a L ) + j(∆ k L + M( ∆ kL+∆k L ))pre . pre 1. 1 2 2 pre pre1 1 2 22(30)where n o is the refractive index , D is the degeneracy factor (D=3 if i=j or D=6 if i≠j), P 0 is the launched signalpower per channel (equal power per channel assumed, and also same polarization assumed) x 111, x 222 is thethird-order nonlinear susceptibility and A eff1 , A eff2 the effective area of the SMF and DCF segments respectively,L is the length of a fiber segment and α is its corresponding attenuation, G is the gain of the amplifiers, M is thenumber of SMF spans which is the same with the number of the DCF spans and ∆k i is the phase mismatchwhich is related to signal frequency differences and chromatic dispersion D i and may be expressed as⎧2 22πλdD λi∆ k = f − f f − f . ⎨D + ⎜ ⎟ f − f + f − fc dλ2c( )i i k j k i i k j k⎩⎛⎝⎞⎠⎫⎬⎭(31)where dD i /dλ is the dispersion slope.In the WDM systems, the total FWM power generated at the frequency, f m is given by [Inoue92]∑ ∑∑ ( )(32)P ( f ) = P f + f − fFWM m i j kf = f + f − f f fk i j m j iIn the equally spaced channel WDM systems, the channels in the middle of the signal band would be affectedseverely because the number of FWM signals is maximum at the center channel [Inoue92]. However, it isnoteworthy that this is not always true if the wavelengths in the WDM system are far from the zero dispersionwavelength, and if there is substantial difference in chromatic dispersion between two channels. This isbecause FWM power, in general, rather than the number of FWM signals on each channel degrades thesystem performance. Methods of reducing the effect of FWM is to increase the channel spacing, apply properdispersion maps and allocate the channels unequally [Kikuchi97], letting new optical frequency fall out of thechannel band.Project:PHOSPHORUSDeliverable Number: D.5.3Date of Issue: 31/06/07EC Contract No.: 034115Document Code: Phosphorus-WP5-D5.341