**4.2.2 Analytical evaluation of the power consumption in SSPN OPS equipped with BENES fabric switching**

Each 1×2 splitter, 2×2 directional coupler and 2×1 coupler shown in Fig. 10 introduce an attenuation of 2 that is recovered by the SOAs located after each splitter, directional coupler and coupler. If a packet is directly forwarded it goes through the BENES switch once. Conversely if the packet has to be wavelength converted the BENES switch is crossed twice and a wavelength converter is used. In particular notice as a directly forwarded packet needs the use of one 1×2 splitter, one 2×1 coupler, 2*log*22*NM* − 2 directional couplers and 2*log*22*NM* SOAs each having a gain equal to 2. On the contrary a wavelength converted packet needs the use of two 1×2 splitters, two 2×1 couplers, 4*log*22*NM* − 4 directional couplers and 4*log*22*NM* SOAs. Let us denote with *CSOA d f* and *<sup>C</sup>SOA wc* the sum of the power consumption of the SOAs involved in the switch paths in the case in which a packet is directly forwarded and wavelength converted respectively. We can write the following expression for 10 Optical Amplifier

• 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

According to these remarks we can write the following expression for the average power

*SOA* ]*CSOA*

*<sup>i</sup>* <sup>=</sup> *<sup>P</sup>al*,*Gi*

*E*[*Nc*] is carried out in in Appendix-A (Eramo et al., 2008; 2009a;c; 2011);

<sup>1</sup> <sup>+</sup> *<sup>E</sup>*[*Nc*](*CSOA*

*<sup>i</sup>* (*i*=1, . . . , 4) is the power consumption of a turned on SOA in the *i*th stage (*i*=1, . . . , 4);

*G*<sup>3</sup> = *NM* and *G*<sup>4</sup> = *N* are the gains needed to overcome the loss for the turned on SOA

*off* is the power consumption of a turned off SOA; it is equal to *Vbioff* where *ioff* is the polarization current of an inactive SOA and needed to guarantee a high SOA switching

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

*SOA* ] = *N*(*N* + *r*)*M* + *r* + *Nr* + *N* − (*E*[*Na*] + 2*E*[*Nc*] + *E*[*Nd*]) (4)

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

*SOA* <sup>=</sup> *<sup>N</sup>*(*<sup>N</sup>* <sup>+</sup> *<sup>r</sup>*)*<sup>M</sup>* <sup>+</sup> *<sup>r</sup>* <sup>+</sup> *Nr* <sup>+</sup> *<sup>N</sup>* of SOAs to the total number *<sup>N</sup>SS*−*SSPN*,*on*

**4.2.2 Analytical evaluation of the power consumption in SSPN OPS equipped with BENES**

Each 1×2 splitter, 2×2 directional coupler and 2×1 coupler shown in Fig. 10 introduce an attenuation of 2 that is recovered by the SOAs located after each splitter, directional coupler and coupler. If a packet is directly forwarded it goes through the BENES switch once. Conversely if the packet has to be wavelength converted the BENES switch is crossed twice and a wavelength converter is used. In particular notice as a directly forwarded packet needs the use of one 1×2 splitter, one 2×1 coupler, 2*log*22*NM* − 2 directional couplers and 2*log*22*NM* SOAs each having a gain equal to 2. On the contrary a wavelength converted packet needs the use of two 1×2 splitters, two 2×1 couplers, 4*log*22*NM* − 4 directional

consumption of the SOAs involved in the switch paths in the case in which a packet is directly forwarded and wavelength converted respectively. We can write the following expression for

• *E*[*Na*], *E*[*Nd*] and *E*[*Nc*] are the steady-state average values of the random processes *Na*(*t*), *Nd*(*t*) and *Nc*(*t*) respectively at an arbitrary epoch; the evaluation of *E*[*Na*], *E*[*Nd*] and

<sup>3</sup> <sup>+</sup> *<sup>C</sup>SOA*

<sup>4</sup> ) + *<sup>E</sup>*[*Nd*]*CSOA*

*off* (3)

*SOA* (*i*=1, . . . , 4) where *G*<sup>1</sup> = *N* + *r*, *G*<sup>2</sup> = *NM* + *r*,

<sup>2</sup> +

*SOA* =

*wc* the sum of the power

conversion has to be performed.

wherein:

• *CSOA*

• *CSOA*

consumption *<sup>P</sup>SS*−*SSPN av*,*<sup>T</sup>* for the SS-SSPN switch:

from Eq. 1 obviously we have *CSOA*

located in the *i*th stage (*i*=1, . . . , 4);

rate (Eramo et al., 2011);

*<sup>E</sup>*[*NSS*−*SSPN*,*off*

**fabric switching**

• *<sup>E</sup>*[*NSS*−*SSPN*,*off*

*NSS*−*SSPN*,*tot*

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

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

• *CSYN* is the power consumption of a turned on synchronizer;

• *CWC* is the power consumption of a Wavelength Converter;

*E*[*Na*] + 2*E*[*Nc*] + *E*[*Nd*] of turned on SOAs that is:

couplers and 4*log*22*NM* SOAs. Let us denote with *CSOA*

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

$$P\_{av,T}^{B-SSPN} = E[\text{N}\_d] \mathbf{C}^{SYN} + E[\text{N}\_d] \mathbf{C}\_{df}^{SOA} + E[\text{N}\_c] \mathbf{C}\_{wc}^{SOA} + r \mathbf{C}\_{WC} + E[\text{N}\_{SOA}^{B-SSPN}] \mathbf{C}\_{off}^{SOA} \tag{5}$$

where *<sup>E</sup>*[*NB*−*SSPN*,*off SOA* ] is the number of turned off SOAs; it is given by the total number *NB*−*SSPN*,*tot SOA* <sup>=</sup> <sup>4</sup>*NMlog*22*NM* of SOAs to the total number *<sup>N</sup>B*−*SSPN*,*on SOA* = 2(*E*[*Na*] + *E*[*Nc*])*log*22*NM* of turned on SOAs that is:

$$E[N\_{SOA}^{B-SSPN,off}] = (4\text{NM} - 2(E[N\_d] + E[N\_c])) \log 2\text{NM} \tag{6}$$

Because the power consumption of turned on SOA in the BENES switching fabric equals *Pal*,2 *SOA*, we can simply write the following expression for *CSOA d f* and *<sup>C</sup>SOA wc* :

$$\mathbb{C}\_{df}^{SOA} = 2P\_{SOA}^{d} \log\_2 2NM \tag{7}$$

$$\mathcal{C}^{SOA}\_{\text{wc}} = 4P^{al}\_{SOA} \log\_2 2NM \tag{8}$$

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 with BENES switching fabric.

### **4.3 Evaluation of power consumption**

We compare some Optical Packet Switching architecture by taking into account as reference the average energy consumption per bit *Eav*,*<sup>T</sup>* <sup>=</sup> *Pav*,*<sup>T</sup> NMB* where *B* denotes the bit rate carried out on each wavelength.

We perform the analysis under the following assumptions:

• 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 expression for the synchronizer's power consumption:

$$P\_{SYN} = N\_{SYN} P\_{SOA}^{al,G} \mid\_{G=4} \tag{9}$$


0

**number of wavelengths** 

0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5 0,55 0,6

Fig. 11. Dimensioning of wavelengths and WCs in SS-ASPW, SS-ASPN, SS-SSPW and SS-SSPN switches so that the PLP is smaller than or equal to 10−6. The number *N* of Input/Output Fibers equal 16 and the offered traffic *p* is varying from 0,1 to 0,6.

stages that leads to both smaller attenuation and SOA power consumption.

*N* of Input/Output Fibers for *M*=64, *NSYN*=16 and *B*=40Gb/s.

switches for the same parameters of Fig. 13.

**Offered Traffic (***p***)**

In Fig. 12, the average energy consumption per bit *Eav*,*<sup>T</sup>* of switch configurations obtained in Fig. 11 as a function of the offered load is presented. Synchronizers with *NSYN*=4 stages are considered. A bandwidth *B*=40Gb/s is occupied by each signal. The SS-ASPW architecture presents itself as the most power-efficient solution among all compared solutions as a consequence of the combination of asynchronous operation and wavelength converter sharing solution that allow the use of smaller Space Switching Module in the 1*st* and 3*rd*

The comparison in power consumption for Synchronous SPN Optical Packet Switches equipped with Single-Stage and BENES switching fabric is reported in Fig. 13 where the average energy consumption per bit *<sup>E</sup>SS*−*SSPN av*,*<sup>T</sup>* and *<sup>E</sup>B*−*SSPN av*,*<sup>T</sup>* are reported versus the number

The turned off SOAs are polarized with injection current *ioff*=7mA needed to increase the switching rate. In fact the rise-time and the fall-time decrease with increasing injection current because of the strong dependence of the carrier lifetime on the carrier density (Ehrhardt et al., 1993). From Fig. 13 we can notice that for *<sup>N</sup>* greater than or equal to 36, *<sup>E</sup>B*−*SSPN av*,*<sup>T</sup>* overcomes *<sup>E</sup>SS*−*SSPN av*,*<sup>T</sup>* and the BENES switch is more efficient in energy consumption than Single-Stage switch for *N* increasing. That is a consequence of the linear dependence *O*(*Nlog*2*N*) of the number of SOA in BENES switch against the quadratic dependence *O*(*N*2) in Single-Stage switch when *N* increases. This different type of dependence allows a reduction in number of turned off SOAs in BENES switch with respect to the Single-Stage switch. That is confirmed in Fig. 14 where we report the number of turned off SOA versus *N* in Single-Stage and BENES

*Dimen. of Wavel. (SS-SSPN-SS-SSPW) Dimen. of Wavel. (SS-ASPN-SS-ASPW)*

SOA-Based Optical Packet Switching Architectures 79

*Dimen. of Conv. (SS-SSPN) Dimen. of Conv. (SS-SSPW) Dimen. of Conv. (SS-ASPN) Dimen. of Conv. (SS-ASPW)*

> *N=*16 *PLP*=10-6

> > 200

400

600

800

1000

**number of converters**

1200

1400

1600

1800


Table 1. Main parameter values for the *A*2 commercial SOAs (Sakaguchi et al., 2007)


Table 2. Main parameter values for the *B*1 commercial SOA (Sakaguchi et al., 2007); the power consumption of DISCs realized with *B*1 SOAs is also reported at bit-rate *B*=40 Gb/s.

Next, we compare the average energy consumption per bit *Eav*,*<sup>T</sup>* of four optical packet switches (OPS) equipped with Single-Stage switching fabric: the Asynchronous Shared-Per-Wavelength (SS-ASPW) and the Asynchronous Shared-Per-Node (SS-ASPN) OPS where the WCs are per wavelength and fully shared respectively, the Synchronous Shared-Per-Wavelength (SS-SSPW) and Synchronous Shared-Per-Node (SS-SSPN) OPSs where the packets are synchronously switched and the WCs are shared per wavelength and per node, respectively. To evaluate power consumption in SS-SSPN OPS, we use the model described in Section 4.2.1. The models described in (Eramo et al., 2009c; Eramo, 2010; Eramo et al., 2011) are used to evaluate the power consumption in SS-ASPN, SS-SSPW and SS-ASPW optical packet switches. Sample switch design is reported in Fig. 11 with target Packet Loss Probability (PLP) smaller than or equal to 10−6. Fig. 11 has been obtained for SS-ASPW, SS-ASPN, SS-SSPN, and SS-SSPW switches by the application of the related models (Eramo et al., 2008; 2009c; Eramo, 2010; Eramo et al., 2011) , for switch size *N* = 16, varying the offered traffic *p*. The number of wavelengths needed to obtain the asymptotic target PLP value (10−6) is calculated first for each value of the offered load. This number of wavelengths depends on output contention only and therefore is influenced by the choice of operational context (synchronous or asynchronous) and not by the switch architecture. As a consequence, the synchronous solutions require fewer wavelengths to achieve the same PLP target. Then the minimum number of wavelength converters to reach that asymptotic PLP target value (Eramo, 2000) is determined. From Fig. 11 you can notice for a given value of offered traffic, the Shared-Per-Node switch needs fewer WCs than Shared-Per-Wavelength Node. This is obviously due to the full WC sharing strategy adopted in SPN nodes (Eramo et al., 2009b).

12 Optical Amplifier

**Symbol Explanation Value**  *Vb* Forward Bias Voltage 2 V

*SOA* Confinement Factor 0.15

*SOA* Material Loss 10<sup>4</sup> *LSOA* Length 700

*wSOA* Active Region Effective Width 2

*dSOA* Active Region Depth 0.1

*N0* Conduction Band Carrier Density 10<sup>24</sup>

Carrier Spontaneous Decay Lifetime 10-9

*Psat* Saturation Power 50 *mW*

*B#1* MQW 1100 1,25 0,038 0,2 187

Next, we compare the average energy consumption per bit *Eav*,*<sup>T</sup>* of four optical packet switches (OPS) equipped with Single-Stage switching fabric: the Asynchronous Shared-Per-Wavelength (SS-ASPW) and the Asynchronous Shared-Per-Node (SS-ASPN) OPS where the WCs are per wavelength and fully shared respectively, the Synchronous Shared-Per-Wavelength (SS-SSPW) and Synchronous Shared-Per-Node (SS-SSPN) OPSs where the packets are synchronously switched and the WCs are shared per wavelength and per node, respectively. To evaluate power consumption in SS-SSPN OPS, we use the model described in Section 4.2.1. The models described in (Eramo et al., 2009c; Eramo, 2010; Eramo et al., 2011) are used to evaluate the power consumption in SS-ASPN, SS-SSPW and SS-ASPW optical packet switches. Sample switch design is reported in Fig. 11 with target Packet Loss Probability (PLP) smaller than or equal to 10−6. Fig. 11 has been obtained for SS-ASPW, SS-ASPN, SS-SSPN, and SS-SSPW switches by the application of the related models (Eramo et al., 2008; 2009c; Eramo, 2010; Eramo et al., 2011) , for switch size *N* = 16, varying the offered traffic *p*. The number of wavelengths needed to obtain the asymptotic target PLP value (10−6) is calculated first for each value of the offered load. This number of wavelengths depends on output contention only and therefore is influenced by the choice of operational context (synchronous or asynchronous) and not by the switch architecture. As a consequence, the synchronous solutions require fewer wavelengths to achieve the same PLP target. Then the minimum number of wavelength converters to reach that asymptotic PLP target value (Eramo, 2000) is determined. From Fig. 11 you can notice for a given value of offered traffic, the Shared-Per-Node switch needs fewer WCs than Shared-Per-Wavelength Node. This is obviously due to the full WC sharing strategy adopted in SPN nodes (Eramo et al., 2009b).

Table 2. Main parameter values for the *B*1 commercial SOA (Sakaguchi et al., 2007); the power consumption of DISCs realized with *B*1 SOAs is also reported at bit-rate *B*=40 Gb/s.

Active region thickness (Pm)

Table 1. Main parameter values for the *A*2 commercial SOAs (Sakaguchi et al., 2007)

Active region width (Pm)

P*m*

P*m*

Confinement Factor

P*m*

> *m* -3

> > *s*

Consumed power (mW) (40Gb/s)

\*

D

W

Type

Active region Length (Pm)

Fig. 11. Dimensioning of wavelengths and WCs in SS-ASPW, SS-ASPN, SS-SSPW and SS-SSPN switches so that the PLP is smaller than or equal to 10−6. The number *N* of Input/Output Fibers equal 16 and the offered traffic *p* is varying from 0,1 to 0,6.

In Fig. 12, the average energy consumption per bit *Eav*,*<sup>T</sup>* of switch configurations obtained in Fig. 11 as a function of the offered load is presented. Synchronizers with *NSYN*=4 stages are considered. A bandwidth *B*=40Gb/s is occupied by each signal. The SS-ASPW architecture presents itself as the most power-efficient solution among all compared solutions as a consequence of the combination of asynchronous operation and wavelength converter sharing solution that allow the use of smaller Space Switching Module in the 1*st* and 3*rd* stages that leads to both smaller attenuation and SOA power consumption.

The comparison in power consumption for Synchronous SPN Optical Packet Switches equipped with Single-Stage and BENES switching fabric is reported in Fig. 13 where the average energy consumption per bit *<sup>E</sup>SS*−*SSPN av*,*<sup>T</sup>* and *<sup>E</sup>B*−*SSPN av*,*<sup>T</sup>* are reported versus the number *N* of Input/Output Fibers for *M*=64, *NSYN*=16 and *B*=40Gb/s.

The turned off SOAs are polarized with injection current *ioff*=7mA needed to increase the switching rate. In fact the rise-time and the fall-time decrease with increasing injection current because of the strong dependence of the carrier lifetime on the carrier density (Ehrhardt et al., 1993). From Fig. 13 we can notice that for *<sup>N</sup>* greater than or equal to 36, *<sup>E</sup>B*−*SSPN av*,*<sup>T</sup>* overcomes *<sup>E</sup>SS*−*SSPN av*,*<sup>T</sup>* and the BENES switch is more efficient in energy consumption than Single-Stage switch for *N* increasing. That is a consequence of the linear dependence *O*(*Nlog*2*N*) of the number of SOA in BENES switch against the quadratic dependence *O*(*N*2) in Single-Stage switch when *N* increases. This different type of dependence allows a reduction in number of turned off SOAs in BENES switch with respect to the Single-Stage switch. That is confirmed in Fig. 14 where we report the number of turned off SOA versus *N* in Single-Stage and BENES switches for the same parameters of Fig. 13.

1,00E+02

the current injection of the turned off SOAs is considered.

**single-stage and BENES switching fabric**

under the following assumptions:

dependent on each other;

4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64

*SS-ASPN (p=0,2) MS-ASPN (p=0,2) SS-ASPN (p=0,4) MS-ASPN (p=0,4) SS-ASPN (p=0,6) MS-ASPN (p=0,6) SS-ASPN (p=0,8) MS-ASPN (p=0,8)*

**Number of Input/Output Fibers (***N***)**

Fig. 14. Number of turned off SOAs in SS-SSPN and B-SSPN switches versus the number *N*

The chapter discussed issues concerning power consumption of future high-capacity optical packet nodes. When using optical buffers, due to attenuation problems, optical nodes consumes more power than electronic nodes. For this reason we have taken into account bufferless OPS equipped with shared Wavelength Converters to solve output packet contentions. We have proposed some sophisticated analytical models in order to evaluate and compare the power consumption in OPSs equipped with Single-Stage and Multi-Stage switching Fabric. The obtained results show that in the case of OPS equipped with Single-Stage switching fabric, the combination of the asynchronous operation with the wavelength-based system partitioning in Asynchronous Shared-Per-Wavelength OPS leads to significant power saving with respect to the other solutions in the range of interest for switching fabric dimensioning. Finally we have also shown that for larger switches, the BENES switch has an energy consumption lower than the one of an Single-Stage switch if

**6. Appendix-A: Evaluation of** *E*[*Na*]**,** *E*[*Nd*] **and** *E*[*Nc*] **in switches equipped with**

The evaluation of *E*[*Na*], *E*[*Nd*] and *E*[*Nc*] in synchronous Optical Packet Switches is carried

• packet arrivals on the *N* × *M* input wavelength channels at each time-slot are not

• packet arrivals occur with probability *p* on each input wavelength channel;

of Input/Output Fibers for *M*=64. The offered traffic *p* is varied from 0,2 to 0,8.

1,00E+03

1,00E+04

1,00E+05

**Number of turned off SOAs**

**5. Conclusions**

1,00E+06

*M=64*

SOA-Based Optical Packet Switching Architectures 81

1,00E+07

Fig. 12. Average energy consumption per bit in Single Stage(SS) ASPW, ASPN, SSPW and SSPN switches versus the offered traffic for *N*=16 and *NSYN*=4. The number *M* of wavelengths and the number of WCs are dimensioned so that the the PLP is smaller than or equal to 10−6.

Fig. 13. Comparison of average energy consumption per bit in Single Stage (SS) SSPN and Benes (B) SSPN switches versus the number *N* of Input/Output Fibers for *M*=6 and *p* varying from 0,2 to 0,8. The turned off SOAs are polarized with a current *ioff*=7mA.

Fig. 14. Number of turned off SOAs in SS-SSPN and B-SSPN switches versus the number *N* of Input/Output Fibers for *M*=64. The offered traffic *p* is varied from 0,2 to 0,8.
