Grid Job Routing Algorithms - Phosphorus

Grid Job Routing AlgorithmsFigure 4.3: Illustration of walk-off distanceIn this section we investigate the impact of XPM on the performance of a single link modifying Cartaxoanalytical model [Cartaxo99] to be compatible with the structure of the link presented in Figure 5.4 The XPMinduced intensity modulation (IM) frequency response is described byP ( ω)LH ( ω) = = 2 P(0). g ( L ).exp −jω . γ exp jωd LN ( l)N NIM XPM , iknet ( l) ( n) ( n)XPMik i i T ( l)ιikP( ω )kl= 1 ugil= 1 l=1l−1( n) ( n)−a L ( n). ∏eg .kn=1⎧⎪⎪⎪⎡⎣⎨⎪⎪⎪⎪⎩ ⎡⎣1( l) ( l) ( l)( a ) +ik ( b + qi k )2 2( l) ( l) ( l)( a ) +ik ( b −qi k )⎡ ⎤ ⎡ ⎤⎢ ∑ ⎥ ∑ ⎢⎣∑ ⎥⎣ ⎦⎦( )a .sin( B −Q ) − b + q .cos( B( l) ( l−1) ( l) ( l) ( l) ( l−1) ( l)ik i k i k i( ) ]( l) ( l+ 1) ( l) ( l) ( l) ( l+1) ( l)−aLika .sin( Q − B ) + b + q .cos( Q −B ) . eik k i i k k i1+ + − − +( )( l) ( l−1) ( l) ( l) ( l) ( l−1) ( l). a .sin( B Q ) b q .cos( B Q )2 2 ik i k i k i k( l) ( l+1) ( l) ( l)( l) ( la .sin( Q B ) b q+ 1) ( l)+ik k i i kk i+ − + + −⎡⎣⎡⎣( ) ]( n) ( l ).cos( Q B ) . e −a( n) ( l )ikL−Qk)⎫⎪⎪⎪⎬⎪⎪⎪⎪⎭(26)for multi-segment fiber links, where i stands for the probe signal and k for the pump, P XPM,ik (ω) represents theXPM-induced IM originated by pump channel k, P k (ω) the pump channel , P i (0) the power of channel i at thenetfiber input, gi( LT) the net power gain for the i channel from the transmitter up to the receiver, L T the totalsystem length, N the total number of spans, γ (l) the nonlinearity constant for the l span ,d (l) ik is the walk–offparameter between channels i and k in the l th ( l) −1 ( l) −1segment (given by dik = ( ugi ) − ( ugk) ), a the attenuationconstant andProject:PHOSPHORUSDeliverable Number: D.5.3Date of Issue: 31/06/07EC Contract No.: 034115Document Code: Phosphorus-WP5-D5.339