**4.2.1 Analytical evaluation of the power consumption in SSPN OPS equipped with single-stage fabric switching**

In evaluating the various power consumption in the SS-SSPN Optical Packet Switch we notice from Figs 1,6 that at time *t*:


the average power consumption *<sup>P</sup>B*−*SSPN av*,*<sup>T</sup>* of a SSPN switch equipped with BENES switching

SOA-Based Optical Packet Switching Architectures 77

*d f* <sup>+</sup> *<sup>E</sup>*[*Nc*]*CSOA*

Because the power consumption of turned on SOA in the BENES switching fabric equals *Pal*,2

Finally notice as by inserting Eqs (6)-(8) in Eq. (5) and by using the expressions of *E*[*Na*], *E*[*Nd*] and *E*[*Nd*] evaluated in Appendix-A (Eramo et al., 2008; 2009a;c; 2011), we can able to calculate the average power consumption *<sup>P</sup>B*−*SSPN av*,*<sup>T</sup>* of the synchronous SPN switch equipped

We compare some Optical Packet Switching architecture by taking into account as reference

• the synchronizer described in Fig. 3 is used. Because in each stage and at each time only one of two SOAs is active, assuming a 3 dB attenuation for the couplers and splitters and neglecting the loss occurring in both the OBF and the short FDLs, we have the following

*PSYN* = *NSYNPal*,*<sup>G</sup>*

• The SOA's power consumption model illustrated in Section 4.1 is adopted and allowing us, according to Eq. (1), to express the SOA power consumption as a function of the main SOA parameters (*Vb*, *ib*, *wSOA*, . . . ); A2 commercial SOAs Eramo (2010) produced by manufacture A is used to implement the switching fabric. The A2 parameter values

• As Wavelength Converter, the Delayed Interference Signal Wavelength Converter (DISC) illustrated in Section 2.2 is used. Its power consumption has been evaluated in (Sakaguchi et al., 2007) when commercial SOA produced by some manufactures are employed. In particular we consider the B1 SOA characterized by a Multiple Quantum Well (MQW) type structure and produced by manufacture B. We report in Table 2 the main parameter values for B1. The power consumption, measured in (Sakaguchi et al., 2007), is also reported. It equals 187mW when the WC is operating at bit-rate *B*=40 Gb/s.

*SOA* <sup>=</sup> <sup>4</sup>*NMlog*22*NM* of SOAs to the total number *<sup>N</sup>B*−*SSPN*,*on*

*CSOA*

*CSOA*

*d f* <sup>=</sup> <sup>2</sup>*Pal*,2

*wc* <sup>=</sup> <sup>4</sup>*Pal*,2

*SOA* ] is the number of turned off SOAs; it is given by the total number

*SOA* ]=(4*NM* − 2(*E*[*Na*] + *E*[*Nc*]))*log*22*NM* (6)

*d f* and *<sup>C</sup>SOA*

*wc* :

*SOAlog*22*NM* (7)

*SOAlog*22*NM* (8)

*NMB* where *B* denotes the bit rate carried out

*SOA* |*G*=<sup>4</sup> (9)

*wc* <sup>+</sup> *rCWC* <sup>+</sup> *<sup>E</sup>*[*NB*−*SSPN*,*off*

*SOA* ]*CSOA*

*SOA* = 2(*E*[*Na*] +

*off* (5)

*SOA*,

fabric:

where *<sup>E</sup>*[*NB*−*SSPN*,*off*

with BENES switching fabric.

are reported in Table 1.

on each wavelength.

**4.3 Evaluation of power consumption**

*NB*−*SSPN*,*tot*

*<sup>P</sup>B*−*SSPN av*,*<sup>T</sup>* <sup>=</sup> *<sup>E</sup>*[*Na*]*CSYN* <sup>+</sup> *<sup>E</sup>*[*Na*]*CSOA*

*E*[*Nc*])*log*22*NM* of turned on SOAs that is:

*E*[*NB*−*SSPN*,*off*

we can simply write the following expression for *CSOA*

the average energy consumption per bit *Eav*,*<sup>T</sup>* <sup>=</sup> *Pav*,*<sup>T</sup>*

We perform the analysis under the following assumptions:

expression for the synchronizer's power consumption:

• all of the *r* Wavelength Converters are turned on; this assumption is a consequence of the limited speed of each WC that makes no feasible the use of a WC when only a wavelength conversion has to be performed.

According to these remarks we can write the following expression for the average power consumption *<sup>P</sup>SS*−*SSPN av*,*<sup>T</sup>* for the SS-SSPN switch:

$$P\_{av,T}^{SS-SSPN} = E[\mathbf{N\_d}] \mathbf{C}^{SYN} + E[\mathbf{N\_d}] \mathbf{C\_1^{SOA}} + E[\mathbf{N\_l}](\mathbf{C\_3^{SOA}} + \mathbf{C\_4^{SOA}}) + E[\mathbf{N\_d}] \mathbf{C\_2^{SOA}} + \dots + E[\mathbf{N\_{SOA}}] \mathbf{C\_{SOA}} \tag{3}$$

$$+ r \mathbf{C\_{WC}} + E[\mathbf{N\_{SOA}^{SS-SSPN}}] \mathbf{C\_{off}^{SOA}} \tag{3}$$

wherein:


$$E[\mathbf{N}\_{SOA}^{SS-SSPN.off}] = \mathbf{N}(\mathbf{N} + r)\mathbf{M} + r + \mathbf{N}r + \mathbf{N} - (E[\mathbf{N}\_a] + 2E[\mathbf{N}\_c] + E[\mathbf{N}\_d]) \tag{4}$$
