替用式繞徑（Alternate routing algorithm） 是在電路交換網路（circuit-switched networks）和全光式波長分工網路（all-optical WDM networks）中常用來建立連結的方法，其中在任意兩點之間的固定路徑組是影響網路效能的一個重要因素。之前最常用的是 hop count based k-shortest paths，但考慮到網路流量需求，k-shortest paths 並不是最好的選擇。

為了降低連線阻斷率（connection blocking probability），本論文提出一個新的路徑組尋找方法。此方法重點在於利用網路上的最佳流量分配，在任一兩點之間，找出最接近最佳流量分配的路徑組。

為了比較兩種方法找出路徑組的差異，本論文在兩種網路型態中，使用兩種替用式繞徑方法來做模擬。從模擬結果得知，本論文所提出的方法，在每一種情況下，都有顯著的效能提升。

An alternate routing algorithm requires a set of predetermined routing paths for each sourcedestination
pair. To reduce the connection blocking probability, it is desirable that the predetermined
routing paths between each source-destination pair be link-disjoint. The predetermined
routing paths used in previous works on alternate routing are the k-shortest paths in terms of hop
count. However, depending on the traffic requirements of all source-destination pairs, hop count
based k-shortest paths may not be the best choice for the predetermined routing paths.
This thesis proposes a method to find a set of link-disjoint routing paths for each sourcedestination
pair to be used by an alternate routing algorithm in order to reduce the connection
blocking probability. The key idea is to utilize the routing paths that are used by the optimal traffic
pattern in the network. Then, for each source-destination pair, we select a set of link-disjoint routing
paths from the routing paths that are used by the optimal traffic pattern such that the selected
set of link-disjoint routing paths carries the most of the traffic between the source-destination pair.
Simulations are performed to compare the performance of two alternate routing algorithms
that use the link-disjoint routing paths found by the proposed method as the predetermined routing
paths and those of the same alternate routing algorithms that employ the hop count based k-shortest
link-disjoint paths as the predetermined routing paths. Our simulation results show that using the
link-disjoint routing paths found by the proposed method yields significantly lower connection
blocking probability than employing the hop count based k-shortest link-disjoint paths.

[1] R. Bhandari, “Optimal Diverse Routing in Telecommunication Fiber Networks,” in Proceedings
of IEEE INFOCOM 1994.
[2] R. Bhandari, Survivable Networks: Algorithms for Diverse Routing, Kluwer Academic Publishers,
Norwell, MA, USA.
[3] A. Birman, “Computing Approximate Blocking Probabilities for a Class of All-optical Networks,”
in IEEE Journal on Selected Areas in Communications, vol. 14, no. 5, pp. 852-857,
June 1996.
[4] C. A. Brackett, , “Dense Wavelength Division Multiplexing Networks: Principles and Applications,”
IEEE Journal on Selected Areas in Communications, vol. 8, issue 6, pp.948-964,
August 1990.
[5] D. Cavendish, A. Kolarov, and B. Sengupta, “Routing and Wavelength Assignment in WDM
Mesh Networks,” in Proceedings of IEEE GLOBECOM 2004, vol. 2, pp. 1016-1022, November
2004.
[6] K. Chan and T. P. Yum, “Analysis of Least Congested Path Routing in WDM Lightwave
Networks,” in Proceedings of IEEE INFOCOM 1994, vol. 2, pp. 962-969, June 1994.
[7] I. C. Choi and D. Goldfarb, “Solving Multicommodity Network Flow Problems by an Interior
Point Method,” in Large-Scale Numerical Optimization, T. Coleman and Q. Li eds., SIAM,
Philadelphia, pp. 58-69, 1990.
[8] X. Chu and B. Li, “A Dynamic RWA Algorithm in a Wavelength-routed All-optical Network
withWavelength Converters,” in Proceedings of IEEE INFOCOM 2003, vol. 3, pp. 1795-1804,
March 2003.
[9] S.-P. Chung and K.W. Ross, “Reduced Load Approximations for Multirate Loss Networks,” in
IEEE Transactions on Communications vol.41, pp. 1222V1231, August 1993.
[10] Z. Dziong and J. W. Roberts, “Congestion Probabilities in A Circuit-Switched Integrated
Services Network,” in Performance Evaluation, vol.7 no.4, pp.267-284, Nov. 1987
[11] L. Fratta, M. Gerla, and L. Kleinrock, “The Flow Deviation Method: An Approach to Storeand-
forward Network Design,” in Networks, 3, pp. 97-133, 1973.
[12] A. Girard, Routing and Dimensioning Circuit-switched Networks, AddisonWesley, 1990.
[13] J. -L. Goffin, J. Gondzio, R. Sarkissian, and J. -P. Vial, “Solving Nonlinear Multicommodity
Flow Problems by the Analytic Center Cutting Plane Method,” in Mathematical Programming,
76, pp. 131-154, 1997.
[14] H. Harai, M. Murata, and H. Miyahara, “Performance of Alternate Routing Methods in Alloptical
Switching Networks,” in Proceedings of IEEE INFOCOM 1997, vol. 2, pp. 516-524,
April 1997.
[15] P. -H. Ho and H. T. Mouftah, “An Approach for Enhancing Fixed Alternate Routing in DynamicWavelength-
RoutedWDM Networks,” in Proceedings of IEEE GLOBECOM 2002, vol.
3, pp. 2792-2797, November 2002.
[16] M. Jin, Q. Hu, Z. Zhang, and W. Hu, “Integer Linear Programming Models and Performance
Evaluation onWavelength Rearrangement in AMesh-Restored All-Optical Network,” in IEEE
Communications Letters, vol.10, no.2, pp. 111- 113, Feburary 2006.
[17] F. P. Kelly, “Blocking Probabilities in Large Circuit-Switched Networks,” in Advances in
Applied Probability 18 (1986), pp.473-505.
[18] L. Li and A. K. Somani, “DynamicWavelength Routing Using Congestion and Neighborhood
Information,” in IEEE/ACM Transactions on Networking, vol. 7, no. 5, pp. 779-786, October
1999.
[19] G. Li, D.Wang, C. Kalmanek, and R. Doverspike, “Efficient Distributed Path Selection for
Shared Restoration Connections,” in Proceedings of IEEE INFOCOM 2002, pp. 140-149.
[20] H.C. Lin, S.W. Wang, and C.P. Tsai, “Traffic Intensity Based Fixed-alternate Routing in Alloptical
WDM Networks,” in Proceedings of IEEE ICC 2006, Istanbul, Turkey, June 11-15,
2006.
[21] D. Mitra and J. B. Seery, “Comparative Evaluations of Randomized and Dynamic Routing
Strategies for Circuit-switched Networks,” IEEE Transactions on Communications, vol. 39,
issue 1, pp.102 - 116, January 1991.
[22] A. Mokhtar and M. Azizoglu, “Adaptive Wavelength Routing in All-optical Networks,” in
IEEE/ACM Transactions on Networking, vol. 6, no. 2, pp. 197-206, April 1998.
[23] R. S. Ramamurthy and B. Mukherjee, “Fixed-alternate Routing and Wavelength Conversion
in Wavelength-routed Optical Networks,” in IEEE/ACM Transactions on Networking, vol. 10,
no. 3, pp. 351-367, June 2002.
[24] C. Siva Ram Murthy and M. Gurusamy, WDM Optical Networks: Concepts, Design, and
Algorithms, Prentice-Hall, 2002.
[25] N. Spring, R. Mahajan, and D. Wetherall, “Measuring ISP Topologies with Rocketfuel,” in
Proceedings of ACM SIGCOMM, Pittsburgh, PA, August 2002.
[26] A. Sridharan and K. N. Sivarajan, “Blocking in All-Optical Networks,” in IEEE/ACM Transactions
on Networking, vol. 12, no. 2, pp. 384-397, April 2004.
[27] S. Subramaniam, M. Azizoglu, and A. K. Somani, “All-Optical Networks with Sparse Wavelength
Conversion,” in IEEE/ACM Transactions on Networking, vol. 4, no. 4, pp. 544-557,
August 1996.
[28] T. Tripathi and K. N. Sivarajan, “Computing Approximate Blocking Probabilities in Wavelength
Routed All-Optical Networks with Limited-range Wavelength Conversion,” in IEEE
Journal on Selected Areas in Communications, vol. 18, issue 10, pp. 2123-2129, October
2000.
[29] D, Xu, Y. Chen and C. Qiao, “A New Heuristic for Finding the Shortest Path with A Disjoint
Counterpart,” in Optical Fiber Communication Conference, 2004.
[30] E. W. Zegura, “GT-ITM: Georgia Tech Internetwork Topology Models (software),”
http://www.cc.gatech.edu/fac/Ellen. Zegura/gt-itm/gt-itm.tar.gz, 1996.
[31] Y. Zhu, G. N. Rouskas, and H. G. Perros, “A Path Decomposition Approach for Computing
Blocking Probabilities in Wavelength-routing Networks,” in IEEE/ACM Transactions on
Networking, vol. 8, issue 6, pp. 747-762, December 2000.
[32] S. Zionts, Linear and Integer Programming, Prentice-Hall, 1974.
19