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route. 2: Compute (K\u2212 1) routes Ri (2 \u2264 i \u2264 K) as candidate routes, where Ri represents the ith shortest route. 3: For Ri, 2 \u2264 i \u2264 K, compute the transmission powers pi,j (1 \u2264 j \u2264 Li) from each intermediate switch j on Ri . Li means the number of switches on Ri. Find the maximum transmission power Pimax = MAX(pi,j) 4: Find m such that Pmmax = MIN(Pimax) (2 \u2264 i \u2264 K), which means the minimal of the maximum transmission powers of all the candidate routes. 5: Select Rm as the alternate route In this paper, we assume K = 3, i.e an alternate route is selected from the second-shortest route and the third-shortest route. III. SIMULATION RESULTS In this section, we evaluate the performance of the proposed routing by a computer simulation. We compare the proposed routing with the fixed-alternate routing proposed in [6] which does not consider the power constraint. In the computer simulation, the network model in [5] with 21 switches and 114 unidirectional fiber links [5] (shown in figure 1) is used . In this network, every link is assumed to be capable of carrying 8 wavelengths. Amplifiers are placed on the links every 100km. We employ the same model of amplifier as in [5]. The gain available at an amplifier is given by the following function: G(Pin, SSG) = min{SSG, (Pmax \u2212 Pin)} where Pin is the total input power in dBm; Pmax is the max- imum amplifier output power in dBm, and SSG is the gain in dB, which is obtained when saturation is not occurred. We as- sume each switch is connected with an access node ni (1 \u2264 i \u2264 21). Calls for node pair (ni, nj) (1 \u2264 i, j \u2264 21, i 6= j) are generated according to a Poisson process with an arrival rate \u3bb. The holding time for a call is exponentially distributed with an average holding time h and is independent of generation and holding times of other calls. The blocking probability and the forced termination proba- bility is used as performance metric. Blocking probability is defined as a probability that a connection cannot be established Figure 1: topology of the Italian network due to resource contention along the desired route. Forced ter- mination probability is defined as a probability that a connec- tion is terminated by force due to saturation which is brought by another new connection establishment. Figure 2 shows the blocking probabilities and forced termination probabilities vs traffic load \u3c1 which is defined as \u3c1 = \u3bbh. From this figure, we can see that the forced termination probability is drastically improved when using the proposed routing algorithm. This is because the proposed routing avoids occurrence of saturation along a direct route. Also we can see that the blocking probability of proposed routing is slightly higher than that of fixed-alternate routing. This is because the proposed routing, even if a valid wavelength assignment is found, blocks connection requests along the direct route when saturation occurred. In any communication system, we believe that it is more important to reduce the forced termination probability than the blocking probability because the forced termination has a more damaging effect on users. Therefore, the proposed algorithm can make it possible to provide high quality communication. IV. CONCLUSIONS In this paper, we have studied the dynamic RWA problem with power considerations in all-optical WDM networks and pro- posed a routing algorithm that suppresses and avoids the oc- currence of saturation. To evaluate the performance, we com- pared the proposed routing with the fixed-alternate routing by simulation results. It has been shown that the proposed routing Figure 2: blocking probability and forced termination probability versus load algorithm significantly reduces the forced termination proba- bility. Power constraints that we have assumed in this paper can be more often occurred in the situation that traffic load is heavy rather than light. Therefore, the proposal is important es- pecially in the next generation Internet that the traffic volume will explosively increase. REFERENCES [1] B. Mukherjee, Optical Communication Networks, McGraw-Hill, New York, 1997. [2] H. Zang, J. P. Jue, L. Sahasrabuddhe, R. Ramamurthy, B. Mukherjee, \u201cDynamic Lightpath Establishment in Wavelength Routed WDM Networks,\u201d IEEE Communication Magazine, Vol.39 No.9, pp.100-107, Sep. 2001. [3] J. Spath, \u201cDynamic routing and resource allocation in WDM transport networks,\u201d Computer Networks 32 (2000), pp. 519-538. [4] N. Ghani, S. Dixit, T. Wang, \u201cOn IP-over-WDM Integration,\u201d IEEE Communication Magazine, Vol.38, No.3, pp.72-84, Mar. 2000. [5] M.Ali, B. Ramamurthy, J. S. Deogun, \u201c Routing and Wavelength Assignment (RWA) with Power Considerations in All-Optical Wavelength-Routed Networks, \u201d Proc., IEEE GLOBECOM \u201999 pp.1437-43, Dec. 1999. [6] S. Ramaurthy and B. Mukhrjee, \u201cFixed-Alternate Routing and Wavelength Conversion in Wavelength-Routed Optical Networks,\u201d Proc., IEEE GLOBECOM \u201998, Vol.4, pp.2295-2302, Nov.1998.

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