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

The evaluation of *E*[*Na*], *E*[*Nd*] and *E*[*Nc*] in synchronous Optical Packet Switches is carried under the following assumptions:


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• the destination of a packet is uniformly distributed over all *N* OFs, i.e., the probability that an arriving packet is directed to a given OF is equal to <sup>1</sup> *N* .

Due to the synchronous operation mode of the SSPN switches, we can evaluate *E*[*Na*], *E*[*Nd*] and *E*[*Nc*] at a given time-slot.

The average number *E*[*Na*] of forwarded packets can be evaluated by taking into account that the packet loss can be due to either the lack of output wavelength channels or the lack of wavelength converters. We can write:

$$E[\text{N}\_a] = E[\text{N}\_o] - E[\text{N}\_{p, \text{vol}}] - E[\text{N}\_{p, \text{cl}}] \tag{10}$$

wherein:


$$E[N\_{p, \text{vol}}] = N \sum\_{j=M+1}^{NM} (j - M) \binom{NM}{j} \left(\frac{p}{N}\right)^j \left(1 - \frac{p}{N}\right)^{NM - j}. \tag{11}$$

• *E*[*Np*,*cl*] is the average number of lost packets due to the lack of WCs. The evaluation of this term has been evaluated in (Eramo et al., 2002; 2009c) by solving an urn problem (Eramo et al., 2002).

The average number *E*[*Nd*] of OFs in which at least one packet is directed can be simply expressed as:

$$E[N\_d] = N\left(1 - \left(1 - \frac{p}{N}\right)^{NM}\right) \tag{12}$$

Finally the average number *E*[*Nc*] of packets forwarded with wavelength conversion can be computed by subtracting the number *E*[*Nd*] of packets forwarded without wavelength conversion to the average number *E*[*Na*] of forwarded packets, that is:

$$E[\mathcal{N}\_c] = E[\mathcal{N}\_a] - E[\mathcal{N}\_d] \tag{13}$$

Finally by inserting (10)-(13) in (3) and (5) we are able to evaluate the average energy consumption *<sup>E</sup>SS*−*SSPN av*,*<sup>T</sup>* and *<sup>E</sup>B*−*SSPN av*,*<sup>T</sup>* of the switches equipped with Single-Stage and BENES switching fabric respectively.

### **7. Acknowledgment**

The research leading to these results has received funding from the European Community's Seventh Framework Programme FP7/2007-2013 under grant agreements nˇr 247674 (STRONGEST-Scalable, Tuneable and Resilient Optical Networks Guaranteeing Extremely-high Speed Transport).

### **8. References**

Akar, N.; Eramo, V. & Raffaelli, C. (2011). Comparative analysis of power consumption in asynchronous wavelength modular optical switching fabrics. *Optical Switching and Networking*, Vol. 8, No. 3, July 2011, pp. 139-148, ISSN 1573-4277

16 Optical Amplifier

• the destination of a packet is uniformly distributed over all *N* OFs, i.e., the probability that

Due to the synchronous operation mode of the SSPN switches, we can evaluate *E*[*Na*], *E*[*Nd*]

The average number *E*[*Na*] of forwarded packets can be evaluated by taking into account that the packet loss can be due to either the lack of output wavelength channels or the lack of

• *E*[*Np*,*wl*] is the average number of lost packets due to the lack of output wavelength

• *E*[*Np*,*cl*] is the average number of lost packets due to the lack of WCs. The evaluation of this term has been evaluated in (Eramo et al., 2002; 2009c) by solving an urn problem

The average number *E*[*Nd*] of OFs in which at least one packet is directed can be simply

Finally the average number *E*[*Nc*] of packets forwarded with wavelength conversion can be computed by subtracting the number *E*[*Nd*] of packets forwarded without wavelength

Finally by inserting (10)-(13) in (3) and (5) we are able to evaluate the average energy consumption *<sup>E</sup>SS*−*SSPN av*,*<sup>T</sup>* and *<sup>E</sup>B*−*SSPN av*,*<sup>T</sup>* of the switches equipped with Single-Stage and BENES

The research leading to these results has received funding from the European Community's Seventh Framework Programme FP7/2007-2013 under grant agreements nˇr 247674 (STRONGEST-Scalable, Tuneable and Resilient Optical Networks Guaranteeing

Akar, N.; Eramo, V. & Raffaelli, C. (2011). Comparative analysis of power consumption in

*Networking*, Vol. 8, No. 3, July 2011, pp. 139-148, ISSN 1573-4277

asynchronous wavelength modular optical switching fabrics. *Optical Switching and*

*NM j*

 *p N <sup>j</sup>*

*NM*

*E*[*Nc*] = *E*[*Na*] − *E*[*Nd*] (13)

(*j* − *M*)

 1 − <sup>1</sup> <sup>−</sup> *<sup>p</sup> N* *N* .

*E*[*Na*] = *E*[*No*] − *E*[*Np*,*wl*] − *E*[*Np*,*cl*] (10)

<sup>1</sup> <sup>−</sup> *<sup>p</sup> N* *NM*−*<sup>j</sup>*

. (11)

(12)

an arriving packet is directed to a given OF is equal to <sup>1</sup>

• *E*[*No*] = *pNM* is the average number of packets offered to the switch;

*NM* ∑ *j*=*M*+1

*E*[*Nd*] = *N*

conversion to the average number *E*[*Na*] of forwarded packets, that is:

and *E*[*Nc*] at a given time-slot.

wherein:

wavelength converters. We can write:

channels. It is simply given by:

(Eramo et al., 2002).

switching fabric respectively.

Extremely-high Speed Transport).

**7. Acknowledgment**

**8. References**

expressed as:

*E*[*Np*,*wl*] = *N*


**5**

*Hungary* 

**Multi-Functional SOAs**

Eszter Udvary and Tibor Berceli

**in Microwave Photonic Systems** 

 *Department of Broadband Infocommunications and Electromagnetic Theory,* 

The Semiconductor Optical Amplifier (SOA) is a very attractive device for optical communication systems because of their multi-functional capability. The operation of the SOA is controlled by both the electrical and optical input signal. The SOAs have demonstrated their multi-functional capability by combining optical amplification with modulation, gating, photo-detection, dispersion compensation, linearization, etc. The chapter describes the applications of SOA-modulator, SOA-detector and SOA-dispersion

The design and construction of complex optical circuits exhibiting several functionalities are difficult tasks. Optical semiconductor integrated circuits having different functional elements on a single substrate have been developed and intensively studied. In that case individual functional elements need not be connected to each other through passive waveguides. Compared to a case when functional elements are independently formed, it is simpler to apply multifunctional devices. In this case a single device replaces numerous special elements. Multi-functionality in optical communication systems decreases complexity, reduces fabrication, installation and maintenance cost, minimizes the size, enhances the reliability and allows systems to work simultaneously with suitable parameters. However, we have to compromise, because the specialised devices have better operation parameters than multi-functional devices. Therefore, the degradation of the characteristics has to be minimized; hence the study of potential multi-functional devices is

Radio-over-Fibre (RoF) technology [Seeds] offers a perspective solution to the demand for wireless connection to the costumer ("last or first mile problem"). It entails the use of optical fibre links to distribute RF signals from a central location to Remote Antenna Units (RAUs). It combines the properties of the microwave and photonics approaches. In narrowband communication systems and WLANs (wireless local area networks), RF signal processing functions such as frequency up-conversion, carrier modulation, and multiplexing, are performed at the radio base station. RoF makes possible to centralise the RF signal processing functions in one shared location, and then to use optical fibre, which offers low

compensator in microwave photonic communication systems.

**1. Introduction** 

a very important task.

**2. Radio-over-Fibre systems** 

*Budapest University of Technology and Economics,* 

