# EDFA Gain Variation Problem in Transparent Optical Networks

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2 of abrupt gain variation. EDFA gain (in db) can be expressed by G = 10 log(1 + P sat P in ln( G max )) (1) G where, P sat is the amplifier saturation power, G max is the unsaturated gain and P in is the amplifier input power, i.e., the sum of power from all connections passing through the EDFA [2]. EDFA gain variation problem in a dynamic optical network can be explained as follows. Consider a network whose initial state is composed only by the connection that occupies the wavelength λ 1, according Fig. 2. connections passing through the amplifiers and, thus, greater their input power. Calculating the derivative of the gain as a function of input power, one can obtain information about the behavior of the EDFA gain variation regarding input power. To calculate the derivative, the method of derivation of implicit functions is used [11], which can be expressed by P in = (G,P in) P in (G,P in ), (2) = G P sat ln( Gmax P in G Pin 2 + P. (3) sat P in G ) Equation (3) shows the final result of the derivative. Note that gain variation decreases with the square of EDFA input power. Thus, one can expect that when dynamic optical networks operate under high traffic, i.e., when EDFA input power is high, the instability caused by the EDFA gain variation problem decreases. This is confirmed in the simulations presented in the Section IV. III. IA-RWA S In order to evaluate the impact of EDFA gain variation over a dynamic transparent optical network, three RWA algorithms were implemented. The proposed IA-RWA algorithms evaluate blocking probability of connections requests not only in terms of wavelength continuity constraint, but also in terms of a QoT metric. If a request requires a given QoT level, it will be admitted if and only if: (a) it is not blocked by the wavelength continuity constraint; (b) it has a QoT level at or above the QoT level requested, and (c) the new connection does not violate the QoT of connections already present on the network. Figure 3 shows the flowchart of the IA-RWA 1. Fig. 2. EDFA gain variation when adding a connection. Now consider that a new connection is admitted at the wavelength λ 2, and that this connection shares a link (which connects nodes 2 and 5) with the first. Since the two connections share the same amplifier (A 1 25), its gain tends to decrease due to increased EDFA input power. This means that amplifier output power for the same connection λ 1 is not the same anymore. Thus, all amplifiers that cycled through the amplifier A 1 25 in the connection path in λ 2 have changed their gains, e. g., the amplifier A 1 58, which although not on the route in which the new connection was accepted, will have its gain changed. The gain variation problem can also occur when a connection is removed from the network, or if it was considered that the optical path at wavelength λ 2 was removed. At first glance, when analyzing (1), one might believe that when network traffic is high, EDFA gain variation will be high, since the heavier the traffic, the greater the number of Fig. 3. IA-RWA 1 algorithm. As can be observed, the route is found after considering the shortest path, where the link cost is the distance in kilometers. Then, the algorithm performs the wavelength continuity

4 requirements, IA-RWA 1 has a similar blocking probability than Blind RWA. Moreover, it was observed that IA-RWA 2 has gotten a worse blocking probability than IA-RWA 1, showing that it is better to use a routing based on the link distance instead a routing based on the cost specified by (4). And so, this can also bring one benefit in sense of algorithm complexity, since IA-RWA 1 use fixed routing, thus do not demand the actual network state to compute a route. In opposition, IA-RWA 2 uses the actual network state to compute a route. The IA-RWA 2 performance is not good because when it computes the route with less ASE noise, it tends to find paths with more hops than the ones find by IA-RWA 1. And so, future requests may be blocked by wavelength continuity constraint, as is verified in Fig. 7. Note that the use of gain update by IA-RWA 2 causes a higher blocking due to continuity, but decreases significantly blocking due to QoT. IA-RWA 1 presents the same benefit. Bp (%) Network Traffic (Erlangs) IA-RWA 1,w (QoT) IA-RWA 1,wo (QoT) IA-RWA 2,w (QoT) IA-RWA 2,wo (QoT) IA-RWA 2,w (Cont.) IA-RWA 2,wo (Cont.) Fig. 7. Blocking only due to QoT (QoT in the legend), and only due to wavelength continuity constraint (cont.). With (w) and without (wo) gain update to 40 Gbps. simulated operating with 24 wavelengths to 10 Gbps. Observe in Fig. 8 that the results present the same behavior, i.e., IA- RWA s with gain update keep better performance than the scenario without gain update. Figure 9 shows only the results for IA-RWA 1 and Blind algorithm. Observe that, for 100 Er, IA-RWA 1 with gain update (w in the legend) presents blocking probability near to 1% or 0.01, while the same algorithm in a network scenario without gain update (wo in the legend) present blocking close to 4% or For 50 Er, IA- RWA 1 in network scenarios with gain update shows similar performance to Blind algorithm, with blocking probability close to 0.1% or Fig. 4. Gain variation without updates (G 0 ) and with one (G 1 ) and two (G 2 ) updates to 40 Gbps. Fig. 8. Blocking Probability to 10 Gbps and 24 wavelengths. Fig. 5. Blocking Probability to 10 Gbps. Bp (%) Fig Blind RWA IA-RWA 1w IA-RWA 1wo IA-RWA 2w IA-RWA 2wo Network Traffic (Erlangs) Blocking Probability to 40 Gbps. In order to analyze algorithms performance under a low blocking probability, the dynamic optical network has been Fig. 9. Blocking Probability to 10 Gbps and 24 wavelengths. Blind and IA-RWA 1 algorithms. V. CONCLUSION This work presented a study on the benefits that the elimination of EDFA s gain variation can bring to the performance of a dynamic transparent optical network. EDFA s without gain variation can be implemented by using optical amplifiers

5 equipped with Automatic Gain Control (AGC) [14]. Future works will investigate other possibilities for routing strategies as bio-inspired algorithms or meta-heuristics. Reducing of the number of EDFA s with AGC will be also studied. REFERÊNCIAS [1] M. L. F. Abbade, J. D. Marconi, R. L. Cassiolato, V. Ishizuca, I. E. Fonseca, and H. L. Fragnito, Field-trial evaluation of cross-layer effect caused by all-optical wavelength converters on IP network applications, IEEE/OSA Journal of Lightwave Technology, vol. 27, pp , June [2] R. Ramaswami and K. Sivarajan, Optical networks: a practical perspective, 3rd ed. Academic Press, [3] I. Tomkos, S. Azodolmolky, D. Klonidis, M. Aggelou, and M. Margariti, Dynamic impairment aware networking for transparent mesh optical networks: Activities of EU project DICONET, in 10st IEEE International Conference on Transparent Optical Networks. ICTON, 2008, pp [4] T. Deng and S. Subramaniam, Source power management in transparent wavelength-routed mesh networks, in IEEE International Conference on Communications. ICC 2004, june 2004, pp [5] B. B. Ramamurthy and e. al., Impact of transmission impairments on the teletraffic performance of wavelength-routed optical networks, IEEE/OSA Journal of Lightwave Technology, vol. 17, pp , oct [6] J. F. Martins-Filho and e. al., Novel routing algorithm for transparent optical networks based on noise figure and amplifier, in IEEE International Microwave and Opticelectronics Conference. IMOC 2003, sept. 2003, pp [7] I. E. Fonseca, M. R. N. Ribeiro, R. C. Almeida Jr., and H. Waldman, Preserving global optical QoS in FWM impaired dynamic networks, IEE Electronics Letters, vol. 40, pp , feb [8] R. C. Almeida Jr., D. R. Campelo, A. V. T. Cartaxo, and H. Waldman, Efficient wavelength assignment policy for XPM-impaired WDM networks, IEEE Communications Letters, vol. 12, pp , oct [9] M. Ali and L. Tancevski, Impact of polarization-mode dispersion on the design of wavelength-routed networks, IEEE Photonics Technology Letters, vol. 14, pp , may [10] A. G. Rahbar, Review of dynamic impairment-aware routing and wavelength assignment techniques in all-optical wavelength-routed networks, accept to IEEE Communications Surveys & Tutorials, pp. 1 25, [11] G. J. Etgen and S. L. Salas, Cauculus: one variable, 10th ed., ser. ISBN Wiley, [12] H. Zang, J. P. Jue, and B. Mukherjee, A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks, SPIE Optical Network Magazine, vol. 1, pp , dec [13] J. Rebola and A. V. T. Cartaxo, Power penalty assessment in optically preamplified receivers with arbitrary optical filtering and signaldependent noise dominance, IEEE/OSA Journal of Lightwave Technology, vol. 20, pp , mar [14] J. C. R. F. Oliveira, Amplificadores opticos com controle automatico de ganho em redes opticas, Tese de Doutorado, UNICAMP, 2007.

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