Performance analysis of FDL buffers: a heuristic approach with impatience and quantization
Authors: 
W. Rogiest, K. De Turck, K. Laevens, D. Fiems, S. Wittevrongel, H. BruneelAuthors Info & Claims
W. Rogiest, K. De Turck, K. Laevens, D. Fiems, S. Wittevrongel, H. BruneelAuthors Info & ClaimsPages 177 - 184
Abstract
For current backbone networks, the capacity limit is not fiber throughput (> 10 Tbit/s per fiber), but rather, switching speed. Optical switching (Optical Packet Switching, Optical Burst Switching, and others) provides a viable alternative, relying on Fiber Delay Lines (FDLs) for buffering. The main feature of such a buffer is the quantization of possible delays: only delays equal to the length of one of the FDLs can be realized.
The impact of quantization on buffer performance is huge. A recent numerical procedure for single-wavelength buffers allows exact numerical evaluation of this impact, but does not allow for practical insight. Moreover, it lacks the potential of generalization, needed to evaluate the performance of buffers with multiple wavelengths at the output.
Countering this, we applied a heuristic combination of two existing queueing models: one with quantization, and one with impatience. As we show in this paper, this combination yields accurate performance results. Key vantage of this heuristic is that it translates the FDL buffer problem into two well-known queueing problems, with accurate performance expressions available in literature, even for multiple wavelengths. This paper presents the heuristic in detail, together with several figures, comparing the heuristic's output to exact results.
References
[1]
G. I. Papadimitriou, C. Papazoglou, and A. S. Pomportsis. Optical switching: switch fabrics, techniques, and architectures. Lightwave Technology, Journal of, 21(2):384--405, 2003.
[2]
R. Van Caenegem, D. Colle, M. Pickavet, P. Demeester, K. Christodoulopoulos, K. Vlachos et al. The design of an all-optical packet switching network. IEEE Communications Magazine, 45(11):52--61, 2007.
[3]
C. Qiao and M. Yoo. Optical Burst Switching-a new paradigm for an Optical Internet. Journal on High-Speed Networks, 8:69--84, 1999.
[4]
Y. Chen, C. Qiao, and X. Yu. Optical burst switching: A new area in optical networking research. IEEE Network, 18(3):16--23, 2004.
[5]
E. Van Breusegem. Study and Design of Optical Network Architectures. PhD thesis, Ghent University, 2003.
[6]
M. De Leenheer, Develder C., J. Buysse, B. Dhoedt, and P. Demeester. Performance analysis and dimensioning of multi-granular optical networks. Optical Switching and Networking (OSN), 6:88--98, 2009.
[7]
E. F. Burmeister and J. P. Mack et al. Photonic integrated circuit optical buffer for packet-switched networks. Optics Express, 17(8):6629--6635, 2009.
[8]
L. Liu, R. Kumar, K. Huybrechts, and T. Spuesens et al. An ultra-small, low-power, all-optical flip-flop memory on a silicon chip. Nature Photonics, 4:182--187, 2010.
[9]
S. J. Ben Yoo. Optical packet and burst switching technologies for the future photonic Internet. Journal of Lightwave Technology, 24(12):4468--4492, 2006.
[10]
G. Appenzeller, I. Keslassy, and N. McKeown. Sizing router buffers. Proceedings of the 2004 ACM Conference of the Special Interest Group on Data Communication, SIGCOMM 2004 (New York), pages 281--292, 2004.
[11]
R. C. Almeida, J. U. Pelegrini, and H. Waldman. A generic-traffic optical buffer modeling for asynchronous optical switching networks. IEEE Communications Letters, 9(2):175--177, 2005.
[12]
W. Rogiest, J. Lambert, D. Fiems, B. Van Houdt, H. Bruneel, and C. Blondia. A unified model for synchronous and asynchronous FDL buffers allowing closed-form solution. Performance Evaluation, 66(7):343--355, 2009.
[13]
W. Rogiest and H. Bruneel. Exact optimization method for an FDL buffer with variable packet length. Photonics Technology Letters, IEEE, 22(4):242--244, 2010.
[14]
W. Rogiest, D. Fiems, K. Laevens, and H. Bruneel. Modeling the performance of FDL buffers with wavelength conversion. IEEE Transactions on Communications, 57(12):3703--3711, 2009.
[15]
J. F Pérez and B. Van Houdt. Wavelength allocation in an optical switch with a Fiber Delay Line buffer and limited-range wavelength conversion. Telecommunication Systems, 41(1):37--49, 2009.
[16]
F. Callegati. Optical buffers for variable length packets. IEEE Communications Letters, 4(9):292--294, 2000.
[17]
Joke Lambert, Wouter Rogiest, Benny Houdt, Dieter Fiems, Chris Blondia, and Herwig Bruneel. A Hessenberg Markov chain for fast Fibre Delay Line length optimization. 5055:101--113, 2008.
[18]
F. Callegati. Approximate modeling of optical buffers for variable length packets. Photonic Network Communications, 3(4):383--390, 2001.
[19]
W. Rogiest, K. Laevens, J. Walraevens, and H. Bruneel. Analyzing a degenerate buffer with general inter-arrival and service times in discrete time. Queueing Systems, 56(3--4):203--212, 2007.
[20]
K. Laevens and H. Bruneel. Analysis of a single-wavelength optical buffer. Proceedings of the 22nd Annual Joint Conference of the IEEE Computer and Communications Societies, INFOCOM 2003 (San Francisco, CA), 2003.
[21]
W. Rogiest, K. Laevens, D. Fiems, and H. Bruneel. A performance model for an asynchronous optical buffer. Performance Evaluation, 62(1--4):313--330, October 2005.
[22]
D. Y. Barrer. Queuing with impatient customers and ordered service. Operations Research, 5(5):650--656, 1957.
[23]
J. Van Velthoven, B. Van Houdt, and C. Blondia. Response time distribution in a D-MAP/PH/1 queue with general customer impatience. Stochastic Models, 21:745--765, 2005.
[24]
J. Van Velthoven, B. Van Houdt, and C. Blondia. On the probability of abandonment in queues with limited sojourn and waiting times. Operations Research Letters, 34(3):333--338, 2006.
[25]
W. Rogiest, D. Fiems, K. Laevens, and H. Bruneel. Tracing an optical buffer's performance: An effective approach. Lecture Notes in Computer Science, NET-COOP 2007 Special Issue, 4465:185--194, 2007.
[26]
W. Rogiest, E. Morozov, D. Fiems, K. Laevens, and H. Bruneel. Stability of single-wavelength optical buffers. European Transactions on Telecommunications, 3(21):202--212, 2010.
[27]
O. Brun and J.-M. Garcia. Analytic solution of finite capacity M/D/1 queues. Applied Probability Trust 37, pages 1092--1098, 2000.
[28]
H. Bruneel and B. G. Kim. Discrete-time models for communication systems including ATM. Boston: Kluwer Academic Publishers, 1993.
[29]
W. Xiong, D. Jagerman, and T. Altiok. M/G/1 queue with deterministic reneging times. Performance Evaluation, 65:308--316, 2008.
[30]
W. Rogiest. Stochastic modeling of optical buffers. PhD thesis, Ghent University, Belgium, 2008.
Recommendations
A latency-aware scheduling algorithm for all-optical packet switching networks with FDL buffers
Optical buffers implemented by fiber delay lines (FDLs) have a volatile nature due to signal loss and noise accumulation. Packets suffer from excessive recirculation through FDLs, and they may be dropped eventually in their routing paths. Because of ...
An analytical model for all-optical packet switching networks with finite FDL buffers
Signal loss and noise accumulation can cause fading in optical buffers implemented by fiber delay lines (FDLs). Optical packets that excessively recirculate through FDLs are easily dropped from their routing paths. Therefore, analytical models and ...
A unified model for synchronous and asynchronous FDL buffers allowing closed-form solution
Novel switching approaches like Optical Burst/Packet Switching have buffering implemented with Fiber Delay Lines (FDLs). Previous performance models of the resulting buffer only allowed for solution by numerical means, and only for one time setting: ...
Comments
Information & Contributors
Information
Published In
Copyright © 2010 ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]
Sponsors
- Beijing Jiaotong University
- Operations Research Society of China
In-Cooperation
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 24 July 2010
Check for updates
Qualifiers
- Research-article
Conference
QTNA '10
Sponsor:
QTNA '10: International Conference on Queueing Theory and Network Applications
July 24 - 26, 2010
Beijing, China
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 70Total Downloads
- Downloads (Last 12 months)1
- Downloads (Last 6 weeks)0
Reflects downloads up to 03 Mar 2025
Other Metrics
Citations
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in