1. Performance Analysis of Wavelength-Routed Optical Networks with Connection Request Retrials Fei Xue+, S. J. Ben Yoo+, Hiroyuki Yokoyama*, and Yukio Horiuchi* +Department of Electrical and Computer Engineering University of California Davis, CA 95616, USA * KDDI R&D Laboratories, Inc. 2-1-15 Ohara Kamifukuoka-shi Saitama 356-8502, Japan Reporter: Pey_Jiuan He 2005-11-17

2. Outline Introduction Approximation analysis with a retrial model Approximation validation Performance analysis Conclusion

3. Introduction Due to the limitations in the network capacity or due to the connection states of the network, some lightpath requests may not be accepted, resulting in blocking. Previous studies which analyzed the request blocking probability are based on a key assumption that the blocked requests are immediately lost, and they do not consider request retrials in performance evaluations.

4. Introduction The path blocking performance of wavelength- routed network is highly related to the blocking probabilities of multiple individual links along a multi- hop lightpath. numerical approximation approaches appear to be the only way to obtain results for multi-server multi- hop networking systems. This paper presents an analytical approach that incorporates the reduced load approximation with a retrial model to evaluate the performance of wavelength-routed networks.

5. Introduction This paper also adopt several performance metrics : fresh request blocking rate, the request loss rate, and the total carried traffic Authors validate the proposed approximation by comparison with simulation results obtained from the NSFnet with retrials.

6. Approximation analysis with a retrial model the wavelength holding time are exponentially distributed with rate The time between entering the retrial pool and issuing a retrial is assumed to be exponential with rate γ,which corresponds to the average backoff time TB=1/ γ. Previous studies have shown that this small γ assumption, yields an accurate approximation.

7. Approximation analysis with a retrial model ( ) ith retrials process to path r Path blocking probability Retrial rate Aggregate requests demanding rate Reduced load offered to link j Link blocking probability

8. Approximation analysis with a retrial model the blocking rate of a fresh request offered to path r the request loss rate on path r: the network-wide fresh request blocking rate: the network-wide request loss rate the total carried traffic

9. Approximation validation N=14 optical routers and J=42 unidirectional fiber links, each link carries W=4 wavelength channels operating at 10 Gb/s. Using the same arrival rate λ, and the average lightpath holding time 1/ μ is set as 1 second. The normalized traffic load to each node, defined as load =(N-1)*λ/(W*μ), varies from 0.5 to 0.9.

10. Approximation validation Without a loss of generality, we consider geometric retrials (p1 = p2) using different low, medium and high retrial probabilities. For validation purposes, we set a relatively large value for the average backoff time (TB=100 sec) to match the lightintensity Due to space limitations, we will present the results for only three paths: path 5 9 →, path 2 7 11 → →, and path 1 2 7 11, representing the 1-hop, 2-hop, and 3-hop paths, respectively.

11. Approximation validation

14. Performance analysis A. the effects of request retrials on network performance

15. Performance analysis A. the effects of request retrials on network performance

16. Performance analysis A. the effects of request retrials on network performance

17. Performance analysis B. The impact of retry parameter (p1) and persistence parameter (p2)

18. Performance analysis B. The impact of retry parameter (p1) and persistence parameter (p2)

19. Performance analysis C. Network performance with different backoff time

20. Conclusion The analytical model in this paper evaluates the performance of wavelength-routed network which approximately extends the reduced load analysis with a retrial model to characterize the customer retrial behavior. Performance analyses show that the retrials increase the blocking rates of fresh requests, while they decrease the request loss rate, thus leading to a high total carried traffic. For the routing schemes considered in this work, the approximation results set a lower bound to the request loss rate and an upper bound to the total carried traffic.