Figure 1.
The modelled output port as part of a $K \times M$ optical switch.
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A generalized approach to sparse and stable portfolio optimization problem
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 |
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.
Mathematics Subject Classification:
Primary: 68W01; Secondary: 60H30.
Citation:
Kurt Van Hautegem, Wouter Rogiest, Herwig Bruneel. Selective void creation/filling for variable size packets and multiple wavelengths. Journal of Industrial and Management Optimization,
2018, 14
(4)
: 1667-1684.
doi: 10.3934/jimo.2018026
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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. |
| [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. |
| [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. |
| [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.
|
| [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.
|
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [16] |
J. S. Turner,
Terabit burst switching, Journal of High Speed Networks, 8 (1999), 3-16.
doi: 10.21236/ADA411344. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
show all references
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. |
| [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. |
| [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. |
| [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.
|
| [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.
|
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [16] |
J. S. Turner,
Terabit burst switching, Journal of High Speed Networks, 8 (1999), 3-16.
doi: 10.21236/ADA411344. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
Figure 2.
An example of a provisional schedule for a single wavelength when the packet size is variable ($B \neq E[B] = D = 1$ ).
Figure 3.
Evolution of the provisional schedule for a single wavelength when the packet size is fixed and equal to the granularity ($B = E[B] = D$ ).
Figure 5.
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 $a$ .
Figure 6.
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.
Figure 7.
Maximum gain (i.e., reduction giving rise to performance gain) for different performance measures as a function of the number of wavelengths ($c$ ).
Table 1.
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 |
Table 2.
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 % |
Table 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 |
Table 4.
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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