# American Institute of Mathematical Sciences

October  2018, 14(4): 1667-1684. doi: 10.3934/jimo.2018026

## Selective void creation/filling for variable size packets and multiple wavelengths

 SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University, St.-Pietersnieuwstraat 41, B-9000 Ghent, Belgium

Received  August 2017 Published  January 2018

With ever-increasing demand for bandwidth, both optical packet switching and optical burst switching are proposed as alternatives to increase the capacity of optical networks in the future. In these packet-based switching techniques, Fiber Delay Lines (for delay assignments) and wavelength conversion (for channel assignments) are used to avoid contention between contending packets. The involved scheduling algorithms decide on which Fiber Delay Line and wavelength each packet is scheduled in order to maximize performance. For the setting without wavelength conversion we proposed a scheduling algorithm for assigning delays called void-creating algorithm that outperforms existing void filling algorithms for a variety of packet size distributions. This is achieved by selectively delaying packets longer than strictly necessary based on a numerical procedure that assigns a theoretical value to each void based on how likely the void will eventually be filled and thus prove useful. This contribution extends the concept of void-creation to the important case with multiple wavelengths, where also the channel has to be assigned. Results obtained by Monte Carlo simulation show that with our void-creating algorithm the obtainable improvement in various performance measures highly depends on the number of wavelengths present.

Citation: Kurt Van Hautegem, Wouter Rogiest, Herwig Bruneel. Selective void creation/filling for variable size packets and multiple wavelengths. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1667-1684. doi: 10.3934/jimo.2018026
##### References:
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Hwang, A burst loss probability model with impatient customer feature for optical burst switching networks, International Journal of Communication Systems, 28 (2015), 1729-1740. doi: 10.1002/dac.2772. Google Scholar [14] A. Triki, I. Popescu, A. Gravey, X. Cao, T. Tsuritani and P. Gravey, TWIN as a future-proof optical transport technology for next generation metro networks, in proceedings of the 17th IEEE International Conference on High Performance Switching and Routing (HPSR), 2016, 87-92. doi: 10.1109/HPSR.2016.7525644. Google Scholar [15] R. Tucker, Scalability and energy consumption of optical and electronic packet switching, Journal of Lightwave Technology, 29 (2011), 2410-2421. doi: 10.1109/JLT.2011.2161602. Google Scholar [16] J. S. Turner, Terabit burst switching, Journal of High Speed Networks, 8 (1999), 3-16. doi: 10.21236/ADA411344. Google Scholar [17] T. van der Vorst, Brennenraedts, D. van Kerkhof and R. Bekkers, Fast Forward: How the speed of the Internet will develop between now and 2020, Technical Report 2013. 048-1262, Dialogic, Utrecht, 2014.Google Scholar [18] K. Van Hautegem, W. Rogiest and H. Bruneel, Fill the void: Improved scheduling for optical switching, proceedings of the 27th International Teletraffic Congress (ITC 27), (2015), 82-88. doi: 10.1109/ITC.2015.17. Google Scholar [19] K. Van Hautegem, W. Rogiest and H. Bruneel, OPS/OBS scheduling algorithms: Incorporating a wavelength conversion cost in the performance analysis, in Proceedings of the 32nd IEEE International Performance, Computing, and Communication Conference (IPCCC), San Diego, 2013. doi: 10.1109/PCCC.2013.6742773. Google Scholar [20] K. Van Hautegem, W. Rogiest and H. Bruneel, Scheduling in optical switching: Deploying shared wavelength converters more effectively, in Proceedings of the 2014 IEEE International Conference on Communications (ICC), Sydney, 2014. doi: 10.1109/ICC.2014.6883850. Google Scholar [21] K. Van Hautegem, W. Rogiest and H. Bruneel, Void-creating algorithm in OPS/OBS: Mind the gap, AIP Conference Proceedings, 1648 (2015), 170002. doi: 10.1063/1.4912460. Google Scholar [22] K. Van Hautegem, W. Rogiest and H. Bruneel, Optical switching for variable size packets: Improved void filling through selective void creation, in Proceedings of the 2016 International Conference on Queueing Theory and Network Applications (QTNA), Wellington, 2016. doi: 10.1145/3016032.3016044. Google Scholar [23] J. Xu, C. Qiao, J. Li and G. Xu, Efficient channel scheduling algorithms in optical burst switched networks, in proceedings of the 22nd IEEE INFOCOM, 3 (2003), 2268-2278. doi: 10.1109/INFCOM.2003.1209247. Google Scholar [24] Y. Yan, G. M. Saridis, Y. Shu, B. R. Rofoee, S. Yan, M. Arslan, T. Bradley, N. V. Wheeler, N. H.-L. Wong, F. Poletti, M. N. Petrovich, D. J. Richardson, S. Poole, G. Zervas and D. Simeonidou, All-optical programmable disaggregated data centre network realized by FPGA-based switch and interface card, Journal of Lightwave Technology, 34 (2016), 1925-1932. doi: 10.1109/JLT.2016.2518492. Google Scholar

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##### References:
 [1] E. Burmeister, D. Blumenthal and J. Bowers, A comparison of optical buffering technologies, Optical Switching and Networking, 5 (2008), 10-18. doi: 10.1016/j.osn.2007.07.001. Google Scholar [2] F. Callegati, A. Campi and W. Cerroni, Fast and versatile scheduler design for optical packet/burst switching, Optical Switching and Networking, 8 (2011), 93-102. doi: 10.1016/j.osn.2010.11.002. Google Scholar [3] F. Callegati, W. Cerroni and G. S. Pavani, Key parameters for contention resolution in multi-fiber optical burst/packet switching nodes in, Proceedings of Broadnets 07 Raleigh, 2007. doi: 10.1109/BROADNETS.2007.4550428. Google Scholar [4] M. Chen, H. Jin, Y. Wen and V. C. M. Leung, Enabling technologies for future data center networking: A primer, IEEE Network, 27 (2013), 8-15. Google Scholar [5] L. G. Dizaji and A. G. Rahbar, Efficient integration of switching mechanisms in all-optical networks, proceedings of the 8th International Symposium on Telecommunications (IST), (2016), 40-44. Google Scholar [6] K. Dolzer, C. Gauger, J. Späth and B. Stefan, Evaluation of reservation mechanisms for optical burst switching, AEU -International Journal of Electronics and Communications, 55 (2001), 18-26. doi: 10.1078/1434-8411-00004. Google Scholar [7] D. H. Hailu, G. G. Lema, E. A. Yekun and S. H. Kebede, Unified study of quality of service (QoS) in OPS/OBS networks, Optical Fiber Technology, 36 (2017), 394-402. doi: 10.1016/j.yofte.2017.05.016. Google Scholar [8] L. Krull, World data transfer record back in Danish hands, 2014, http://www.dtu.dk/english/news/2014/07/verdensrekord-i-dataoverfoersel-paa-danske-haender-igen?id=bed76c33-c9da-4214-91f3-c9ed3f8a0e24.Google Scholar [9] M. Nandi, A. K. Turuk, D. K. Puthal and S. Dutta, Best fit void filling algorithm in optical burst switching networks, in proceedings of the Second International Conference on Emerging Trends in Engineering Technology, 2009,609-614.Google Scholar [10] W. Rogiest, J. Lambert, D. Fiems, B. V. Houdt, H. Bruneel and C. Blondia, A unified model for synchronous and asynchronous FDL buffers allowing closed-form solution, Performance Evaluation, 66 (2009), 343-355. doi: 10.1016/j.peva.2009.01.002. Google Scholar [11] W. Rogiest, D. Fiems and J. -P. Dorsman, Analysis of fibre-loop optical buffers with a void-avoiding schedule, in Proceedings of Valuetools 2014, 15 (2015), e5. doi: 10.4108/icst.valuetools.2014.258180. Google Scholar [12] L. Tancevski, L. Tamil and F. Callegati, Nondegenerate buffers: An approach for building large optical memories, IEEE Photonics Technology Letters, 11 (1999), 1072-1074. doi: 10.1109/68.775350. Google Scholar [13] H.-L. To, S.-H. Lee and W.-J. Hwang, A burst loss probability model with impatient customer feature for optical burst switching networks, International Journal of Communication Systems, 28 (2015), 1729-1740. doi: 10.1002/dac.2772. Google Scholar [14] A. Triki, I. Popescu, A. Gravey, X. Cao, T. Tsuritani and P. Gravey, TWIN as a future-proof optical transport technology for next generation metro networks, in proceedings of the 17th IEEE International Conference on High Performance Switching and Routing (HPSR), 2016, 87-92. doi: 10.1109/HPSR.2016.7525644. Google Scholar [15] R. Tucker, Scalability and energy consumption of optical and electronic packet switching, Journal of Lightwave Technology, 29 (2011), 2410-2421. doi: 10.1109/JLT.2011.2161602. Google Scholar [16] J. S. Turner, Terabit burst switching, Journal of High Speed Networks, 8 (1999), 3-16. doi: 10.21236/ADA411344. Google Scholar [17] T. van der Vorst, Brennenraedts, D. van Kerkhof and R. Bekkers, Fast Forward: How the speed of the Internet will develop between now and 2020, Technical Report 2013. 048-1262, Dialogic, Utrecht, 2014.Google Scholar [18] K. Van Hautegem, W. Rogiest and H. Bruneel, Fill the void: Improved scheduling for optical switching, proceedings of the 27th International Teletraffic Congress (ITC 27), (2015), 82-88. doi: 10.1109/ITC.2015.17. Google Scholar [19] K. Van Hautegem, W. Rogiest and H. Bruneel, OPS/OBS scheduling algorithms: Incorporating a wavelength conversion cost in the performance analysis, in Proceedings of the 32nd IEEE International Performance, Computing, and Communication Conference (IPCCC), San Diego, 2013. doi: 10.1109/PCCC.2013.6742773. Google Scholar [20] K. Van Hautegem, W. Rogiest and H. Bruneel, Scheduling in optical switching: Deploying shared wavelength converters more effectively, in Proceedings of the 2014 IEEE International Conference on Communications (ICC), Sydney, 2014. doi: 10.1109/ICC.2014.6883850. Google Scholar [21] K. Van Hautegem, W. Rogiest and H. Bruneel, Void-creating algorithm in OPS/OBS: Mind the gap, AIP Conference Proceedings, 1648 (2015), 170002. doi: 10.1063/1.4912460. Google Scholar [22] K. Van Hautegem, W. Rogiest and H. Bruneel, Optical switching for variable size packets: Improved void filling through selective void creation, in Proceedings of the 2016 International Conference on Queueing Theory and Network Applications (QTNA), Wellington, 2016. doi: 10.1145/3016032.3016044. Google Scholar [23] J. Xu, C. Qiao, J. Li and G. Xu, Efficient channel scheduling algorithms in optical burst switched networks, in proceedings of the 22nd IEEE INFOCOM, 3 (2003), 2268-2278. doi: 10.1109/INFCOM.2003.1209247. Google Scholar [24] Y. Yan, G. M. Saridis, Y. Shu, B. R. Rofoee, S. Yan, M. Arslan, T. Bradley, N. V. Wheeler, N. H.-L. Wong, F. Poletti, M. N. Petrovich, D. J. Richardson, S. Poole, G. Zervas and D. Simeonidou, All-optical programmable disaggregated data centre network realized by FPGA-based switch and interface card, Journal of Lightwave Technology, 34 (2016), 1925-1932. doi: 10.1109/JLT.2016.2518492. Google Scholar
The modelled output port as part of a $K \times M$ optical switch.
An example of a provisional schedule for a single wavelength when the packet size is variable ($B \neq E[B] = D = 1$).
Evolution of the provisional schedule for a single wavelength when the packet size is fixed and equal to the granularity ($B = E[B] = D$).
Life cycles of the voids created by scheduling on the $\bullet$ and $\blacktriangle$ of Fig. 2.
An example of a provisional schedule for fixed packet size and multiple wavelengths ($c = 4$). The G-VF algorithm will choose to minimize the gap by scheduling on position $a$.
An example of a provisional schedule for fixed packet size and multiple wavelengths ($c = 4$) resulting in a possible void creation on the second wavelength.
Maximum gain (i.e., reduction giving rise to performance gain) for different performance measures as a function of the number of wavelengths ($c$).
Performance measures of D-VF for different packet size distributions and a single wavelength.
 D-VF Fixed B= E[B]=D Exponential E[B]=D Uniform on [0, 2D] Uniform on [0.5D, 1.5D] p=0.6 p=0.8 p=0.6 p=0.8 p=0.6 p=0.8 p=0.6 p=0.8 LP 2.1 % 14.5 % 2.6 % 9.1 % 1.9 % 9.8 % 2.2 % 12.9 % LPlength 2.1 % 14.5 % 3.4 % 11.9 % 2.3 % 11.7 % 2.3 % 13.4 % Packet delay 3.0 6.1 2.5 4.1 2.7 4.8 3.0 5.7 Packet gap 0.36 0.42 0.29 0.30 0.33 0.34 0.37 0.39
 D-VF Fixed B= E[B]=D Exponential E[B]=D Uniform on [0, 2D] Uniform on [0.5D, 1.5D] p=0.6 p=0.8 p=0.6 p=0.8 p=0.6 p=0.8 p=0.6 p=0.8 LP 2.1 % 14.5 % 2.6 % 9.1 % 1.9 % 9.8 % 2.2 % 12.9 % LPlength 2.1 % 14.5 % 3.4 % 11.9 % 2.3 % 11.7 % 2.3 % 13.4 % Packet delay 3.0 6.1 2.5 4.1 2.7 4.8 3.0 5.7 Packet gap 0.36 0.42 0.29 0.30 0.33 0.34 0.37 0.39
Optimal thresholds and corresponding performance improvements of the void value threshold algorithm for a single wavelength.
 (A) Optimal thresholds optimal threshold Fixed B= E[B]=D Exponential E[B]=D Uniform on [0, 2D] Uniform on [0.5D, 1.5D] p=0.6 p=0.8 p=0.6 p=0.8 p=0.6 p=0.8 p=0.6 p=0.8 LP 1.0 1.2 1.1 1.4 1.4 1.6 1.2 1.5 LPlength 1.0 1.2 2.3 3.0 1.9 2.0 1.3 1.6 Packet delay 1.0 1.2 0.9 0.9 1.9 2.0 1.3 1.6 Packet gap 1.2 1.3 3.0 2.3 1.8 2.0 1.5 1.6 (B) Corresponding performance improvements maximum gain Fixed B= E[B]=D Exponential E[B]=D Uniform on [0, 2D] Uniform on [0.5D, 1.5D] p=0.6 p=0.8 p=0.6 p=0.8 p=0.6 p=0.8 p=0.6 p=0.8 LP 54.1 % 36.1 % 4.5 % 6.4 % 5.7 % 6.9 % 28.7 % 19.4 % LPlength 54.1 % 36.1 % 0.2 % 0.1 % 0.6 % 1.9 % 25.0 % 16.5 % Packet delay 16.3 % 16.2 % 0.8 % 3.4 % 1.7 % 3.9 % 8.2 % 8.8 % Packet gap 11.5 % 22.8 % 0.0 % 0.0 % 0.3 % 1.3 % 4.5 % 10.3 %
 (A) Optimal thresholds optimal threshold Fixed B= E[B]=D Exponential E[B]=D Uniform on [0, 2D] Uniform on [0.5D, 1.5D] p=0.6 p=0.8 p=0.6 p=0.8 p=0.6 p=0.8 p=0.6 p=0.8 LP 1.0 1.2 1.1 1.4 1.4 1.6 1.2 1.5 LPlength 1.0 1.2 2.3 3.0 1.9 2.0 1.3 1.6 Packet delay 1.0 1.2 0.9 0.9 1.9 2.0 1.3 1.6 Packet gap 1.2 1.3 3.0 2.3 1.8 2.0 1.5 1.6 (B) Corresponding performance improvements maximum gain Fixed B= E[B]=D Exponential E[B]=D Uniform on [0, 2D] Uniform on [0.5D, 1.5D] p=0.6 p=0.8 p=0.6 p=0.8 p=0.6 p=0.8 p=0.6 p=0.8 LP 54.1 % 36.1 % 4.5 % 6.4 % 5.7 % 6.9 % 28.7 % 19.4 % LPlength 54.1 % 36.1 % 0.2 % 0.1 % 0.6 % 1.9 % 25.0 % 16.5 % Packet delay 16.3 % 16.2 % 0.8 % 3.4 % 1.7 % 3.9 % 8.2 % 8.8 % Packet gap 11.5 % 22.8 % 0.0 % 0.0 % 0.3 % 1.3 % 4.5 % 10.3 %
Performance measures of G-VF for a fixed packet size distribution and a varying number of wavelength ($c = 1,2,4,6$ and $8$).
 G-VF c=1 c=2 c=4 c=6 c=8 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 LP 2.1 % 14.5 % 22.5 % 0.0 % 4.5 % 13.8 % x 0.1 % 5.7 % x 0.0 % 1.7 % x x 0.3 % LPlength 2.1 % 14.5 % 22.5 % 0.0 % 4.5 % 13.8 % x 0.1 % 5.7 % x 0.0 % 1.7 % x x 0.3 % Packet delay 3.0 6.1 7.1 1.0 4.9 7.1 0.4 1.9 6.2 0.2 1.1 4.5 0.1 0.8 2.8 Packet gap 0.36 0.42 0.42 0.13 0.25 0.28 0.03 0.08 0.16 0.01 0.04 0.09 0.01 0.02 0.05
 G-VF c=1 c=2 c=4 c=6 c=8 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 LP 2.1 % 14.5 % 22.5 % 0.0 % 4.5 % 13.8 % x 0.1 % 5.7 % x 0.0 % 1.7 % x x 0.3 % LPlength 2.1 % 14.5 % 22.5 % 0.0 % 4.5 % 13.8 % x 0.1 % 5.7 % x 0.0 % 1.7 % x x 0.3 % Packet delay 3.0 6.1 7.1 1.0 4.9 7.1 0.4 1.9 6.2 0.2 1.1 4.5 0.1 0.8 2.8 Packet gap 0.36 0.42 0.42 0.13 0.25 0.28 0.03 0.08 0.16 0.01 0.04 0.09 0.01 0.02 0.05
Optimal thresholds and corresponding performance improvements of the void value threshold algorithm for a fixed packet size distribution and a varying number of wavelength ($c = 1,2,4,6$ and $8$).
 (A) Optimal thresholds optimal threshold c=1 c=2 c=4 c=6 c=8 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 LP 0.9 1.2 1.3 0.7 1.0 0.9 x 0.8 0.7 x 2.3 0.5 x x 1.4 LPlength 0.9 1.2 1.3 0.7 1.0 0.9 x 0.8 0.7 x 2.3 0.5 x x 1.4 Packet delay 0.9 1.2 1.2 to 1.0 0.9 to to 0.7 to to 1.0 to to 2.4 Packet gap 1.2 1.3 1.3 0.8 0.9 0.9 to 0.7 0.7 to to 0.5 to to 0.5 (B) Corresponding performance improvements maximum gain c=1 c=2 c=4 c=6 c=8 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 LP 53.5 % 35.9 % 26.0 % 47.2 % 41.3 % 25.6 % x 26.6 % 22.1 % x 86.5 % 12.8 % x x 1.8 % LPlength 53.5 % 35.9 % 26.0 % 47.2 % 41.3 % 25.6 % x 26.6 % 22.1 % x 86.5 % 12.8 % x x 1.8 % Packet delay 16.1 % 16.1 % 12.9 % 0 % 14.0 % 11.1 % 0 % 0 % 8.3 % 0 % 0 % 3.2 % 0 % 0 % 1.0 % Packet gap 11.4 % 22.7 % 24.8 % 3.5 % 19.8 % 20.9 % 0 % 5.2 % 14.3 % 0 % 0 % 7.4 % 0 % 0 % 2.1 %
 (A) Optimal thresholds optimal threshold c=1 c=2 c=4 c=6 c=8 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 LP 0.9 1.2 1.3 0.7 1.0 0.9 x 0.8 0.7 x 2.3 0.5 x x 1.4 LPlength 0.9 1.2 1.3 0.7 1.0 0.9 x 0.8 0.7 x 2.3 0.5 x x 1.4 Packet delay 0.9 1.2 1.2 to 1.0 0.9 to to 0.7 to to 1.0 to to 2.4 Packet gap 1.2 1.3 1.3 0.8 0.9 0.9 to 0.7 0.7 to to 0.5 to to 0.5 (B) Corresponding performance improvements maximum gain c=1 c=2 c=4 c=6 c=8 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 p=0.6 p=0.8 p=0.9 LP 53.5 % 35.9 % 26.0 % 47.2 % 41.3 % 25.6 % x 26.6 % 22.1 % x 86.5 % 12.8 % x x 1.8 % LPlength 53.5 % 35.9 % 26.0 % 47.2 % 41.3 % 25.6 % x 26.6 % 22.1 % x 86.5 % 12.8 % x x 1.8 % Packet delay 16.1 % 16.1 % 12.9 % 0 % 14.0 % 11.1 % 0 % 0 % 8.3 % 0 % 0 % 3.2 % 0 % 0 % 1.0 % Packet gap 11.4 % 22.7 % 24.8 % 3.5 % 19.8 % 20.9 % 0 % 5.2 % 14.3 % 0 % 0 % 7.4 % 0 % 0 % 2.1 %
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