Mathematical Model for Dynamic Pump-Wavelength Selection Switch


This paper presents a mathematical model based on dynamic pump-wavelength selection for an optical packet switch (OPS). In the OPS, multiple packets that carry the same wavelength from different input ports could be addressed to the same output port at the same time slot. This condition is called wavelength contention. Of those contended packets, only one is forwarded to the output fiber while the others are dropped. Parametric wavelength conversion is used to convert the contended wavelengths into available non-contending wavelengths. The OPS based on the dynamic pump-wavelength selection scheme, where the pump-wavelengths are adjusted based on the requests in every time slot, uses a heuristic matching algorithm to minimize the number of packet losses. However, there is no guarantee that the heuristic algorithm outputs the optimum result. The mathematical model presented in this paper is used to confirm the performance of the heuristic matching algorithm for the DPS-based OPS. A simulation shows that the heuristic matching algorithm achieves the same performance as the optimum solution provided by the mathematical model.

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Kitsuwan, N. , Siswanto, D. and Oki, E. (2015) Mathematical Model for Dynamic Pump-Wavelength Selection Switch. Open Journal of Optimization, 4, 1-9. doi: 10.4236/ojop.2015.41001.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Liang, Z. and Xiao, S. (2007) A Quantized Delay Buffer Model for Single-Wavelength Fiber Delay Line Buffer. IEEE Journal of Lightwave Technology, 25, 1978-1985.
[2] Zhang, L., Lu, K. and Jue, J.R. (2006) Shared Fiber Delay Line Buffers in Asynchronous Optical Packet Switches. IEEE Journal on Selected Areas in Communications, 24, 118-127.
[3] Lee, S., Sriram, K., Kim, H. and Song, J. (2005) Contention-Based Limited Deflection Routing Protocol in Optical Burst-Switched Networks. IEEE Journal on Selected Areas in Communications, 23, 1596-1611.
[4] Simmons, J.M. (2002) Analysis of Wavelength Conversion in All-Optical Express Backbone Networks. Proceedings Optical Fiber Communication Conference and Exhibit, Anaheim, 17-22 March 2002, 34-36.
[5] Xiao, G. and Leung, Y.W. (1999) Algorithms for Allocating Wavelength Converters in All-Optical Networks. IEEE/ ACM Transaction on Networking, 7, 545-557.
[6] Elmirghani, J.M.H. and Mouftah, H.T. (2000) All-Optical Wavelength Conversion: Technologies and Applications in DWDM Networks. IEEE Communications Magazine, 38, 86-92.
[7] Oki, E., Shimazaki, D., Shiomoto, K., Matsuura, N., Imajuku, W. and Yamanaka, N. (2002) Performance of Distributed-Controlled Dynamic Wavelength-Conversion GMPLS Networks. Proceedings International Conference on Optical Communications and Networks (ICOCN 2002), Singapore, 11-14 November 2002.
[8] Yao, S., Mukherjee, B., Yoo, S.J.B. and Dixit, S. (2000) All-Optical Packet-Switched Networks: A Study of Contention-Resolution Schemes in an Irregular Mesh Network with Variable-Sized Packets. Proceedings SPIE OptiComm, May 2000.
[9] Watanabe, S., Takeda, S. and Chikama, T. (1998) Interband Wavelength Conversion of 320 Gb/s (32 × 10 Gb/s) WDM Signal Using a Polarization-Insensitive Fiber Four-Wave Mixer. Proceedings European Conference on Optical Communication (ECOC’98), Madrid, 85-86.
[10] Yamawaku, J., Takara, H., Ohara, T., Sato, K., Takada, A., Morioka, T., Tadanaga, O., Miyazawa, H. and Asobe, M. (2003) Simultaneous 25 GHz-Spaced DWDM Wavelength Conversion of 1.03 Tbit/s (103 ch × 10 Gbit/s) Signals in PPLN Waveguide. Electronics Letters, 39, 1144-1145.
[11] Yamawaku, J., Yamazaki, E., Takada, A., Morioka, T. and Suzuki, K. (2006) Field Demonstration of up to 640 Gb/s (64 ch/spl Times/10 Gb/s) GWP Switching Networks with a QPM-LN Wavelength Converter in JGN II Test Bed. IEEE Journal of Selected Topics in Quantum Electronics, 12, 529-535.
[12] Devgan, P., Tang, R., Grigoryan, V. and Kumar, P. (2006) Highly Efficient Multichannel Wavelength Conversion of DPSK Signals. Journal of Lightwave Technology, 24, 3677-3682.
[13] Yu, J., Huang, M. and Chang, G. (2008) Polarization Insensitive Wavelength Conversion for 4 × 112 Gbit/s Polarization Multiplexing RZ-QPSK Signals. Optics Express, 16, 1161-21169.
[14] Okonkwo, C., Almeida, R.C., Martin, R.E. and Guild, K.M. (2008) Performance Analysis of an Optical Packet Switch with Shared Parametric Wavelength Converters. IEEE Communications Letters, 12, 596-598.
[15] Kitsuwan, N., Rojas-Cessa, R., Matsuura, M. and Oki, E. (2010) Performance of Optical Packet Switches Based on Parametric Wavelength Converters. Journal of Optical Communications and Networking, 2, 558-569.
[16] Rojas-Cessa, R., Oki, E. and Chao, H.J. (2004) Maximum Weight Matching Dispatching Scheme in Buffered Clos-Network Packet Switches. Proceedings of the 2004 IEEE International Conference on Communications, Paris, 20-24 June 2004, 1075-1079.
[17] Kitsuwan, N. and Oki, E. (2010) Optical Packet Switch Based on Dynamic Pump Wavelength Selection. Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM2010), Miami, 6-10 December 2010, 1-5.
[18] Kitsuwan, N. and Oki, E. (2011) Optical Packet Switch Based on Dynamic Pump Wavelength Selection. IEEE/OSA Journal of Optical Communications and Networking, 3, 162-171.
[19] Kitsuwan, N., Yatjaroen, J. and Oki, E. (2011) Hybrid Pump-Wavelength Configuration for Optical Packet Switch with Parametric Wavelength Converters. Proceedings of the IEEE International Symposium on Access Spaces (ISAS 2011), Yokohama, 17-19 June 2011, 19-22.
[20] Kitsuwan, N. and Oki, E. (2012) Dynamic Pump-Wavelength Selection for Optical Packet Switch with Recursive Parametric Wavelength Conversion. Proceedings of the IEEE International Conference on High Performance Switching and Routing (HPSR2012), Belgrade, 24-27 June 2012, 174-178.
[21] Kaure, M., Girault, M., Leuthold, J., Honthaas, J., Pellegri, O., Goullancourt, C. and Zirngibl, M. (2003) 16-Channel Digitally Tunable External-Cavity Laser with Nanosecond Switching Time. IEEE Photonics Technology Letters, 15, 371-373.
[22] Furukawa, H., Wada, N., Takezawa, N., Nashimoto, K. and Miyazaki, T. (2008) 640 (2 × 32λ × 10) Gbit/s Polarization-Multiplexed, Wide-Colored Optical Packet Switching Achieved by Polarization Independent High-Speed PLZT Switch. Proceedings of the Optical Fiber Communication Conference and Exposition and National Fiber Optic Engineers Conference (OFC/NFOEC), San Diego, 24-28 February 2008, 1-3.
[23] Oki, E., Jing, Z., Rojas-Cessa, R. and Chao, H.J. (2002) Concurrent Round-Robin-Based Dispatching Schemes for Clos-Network Switches. IEEE/ACM Transactions on Networking, 10, 830-844.
[24] Rojas-Cessa, R., Oki, E., Jing, Z. and Chao, H.J. (2001) CIXB-1: Combined Input-One-Cell-Crosspoint Buffered Switch. Proceedings of the 2001 IEEE Workshop on High Performance Switching and Routing, Dallas, 29-31 May 2001, 324-329.
[25] Bianco, A., Franceschinis, M., Ghisolfi, S., Hill, A.M., Leonardi, E., Neri, F. and Webb, R. (2002) Frame-Based Matching Algorithms for Input-Queued Switches. Proceedings of the IEEE Workshop on High Performance Switching and Routing (HPSR 2002), Kobe, 26-29 May 2002, 69-76.
[26] Beldianu, S.F., Rojas-Cessa, R., Oki, E. and Ziavras, S.G. (2009) Re-Configurable Parallel Match Evaluators Applied to Scheduling Schemes for Input-Queued Packet Switches. Proceedings of the 18th International Conference on Computer Communications and Networks, San Francisco, 3-6 August 2009, 1-6.
[27] Rahmani, A.M., Afzali-Kusha, A. and Pedram, M. (2009) NED: A Novel Synthetic Traffic Pattern for Power/Performance Analysis of Network-on-Chips Using Negative Exponential Distribution. Journal of Low Power Electronics, 5, 1-10.
[28] Oki, E. and Yamanaka, N. (1998) A High-Speed Tandem-Crosspoint ATM Switch Architecture with Input and Output Buffers. IEICE Transactions on Communications, E81-B, 215-223.
[29] Oki, E. and Yamanaka, N. (1997) A High-Speed ATM Switch Based on Scalable Distributed Arbitration. IEICE Transactions on Communications, E80-B, 1372-1376.
[30] Mekkittikul, A. and McKeown, N. (1997) Scheduling VOQ Switches under Non-Uniform Traffic. CSL Technical Report, CSL-TR 97-747, Stanford University, Stanford.

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