Informatics and Applications
2014, Volume 8, Issue 1, pp 127-134
STABILITY ANALYSIS OF AN OPTICAL SYSTEM WITH RANDOM DELAY LINES LENGTHS
- E. Morozov
- L. Potakhina
- K. De Turck
Abstract
A newmodel of an optical buffer system is considered, in which the differences {.n} between the lengths
of two adjacent fiber delay lines (FDLs) are random. This is an extension of themodel considered in [1] where these
differences (also referred to as granularity) are constant, i. e., .n const. The system is modeled by utilizing the
random-walk theory and closely-related asymptotic results of the renewal theory, such as the inspection paradox
and the Lordenfs inequality. A stability analysis is performed based on the regenerative approach. Some numerical
results are included as well, showing that the obtained conditions delimit the stability region with high accuracy.
[+] References (9)
- Callegati, F. 2000. Optical buffers for variable length packets.
IEEE Comm. Lett. 4(9):292294.
- Rogiest, W., E. Morozov, D. Fiems, K. Laevens, and
H. Bruneel. 2010. Stability of single-wavelength optical
buffers. Eur. Trans. Telecomm. 21(3):202212.
- Morozov, E., W. Rogiest, K.De Turck, and D. Fiems. 2012.
Stability of multiwavelength optical buffers with delayoriented
scheduling. Trans. Emerging Telecomm. Technol.
23(3):217226.
- Asmussen, S. 2003. Applied probability and queues. 2nd ed.
NY: Springer-Verlag. 440 p.
- Morozov, E., and R. Delgado. 2009. Stability analysis of
regenerative queueing systems. Automation Remote Control
70(12):19771991.
- Feller, W. 1971. An introduction to probability theory and
its applications. Vol. II. New York: John Wiley & Sons.
704 p.
- Chang, J. 1994. Inequalities for the overshoot. Ann. Appl.
Probab. 4(4):12231233.
- Billingsley, P. 1968. Convergence of probability measures.
Wiley. 296 p.
- R Foundation for Statistical Computing. Vienna, Austria.
http://www.R-project.org/.
[+] About this article
Title
STABILITY ANALYSIS OF AN OPTICAL SYSTEM WITH RANDOM DELAY LINES LENGTHS
Journal
Informatics and Applications
2014, Volume 8, Issue 1, pp 127-134
Cover Date
2014-03-31
DOI
10.14357/19922264140113
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
optical buffer; stability; stochastic granularity; renewal theory; regeneration; inspection paradox;
simulation
Authors
E. Morozov  ,  , L. Potakhina , , and K. De Turck 
Author Affiliations
Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Sciences, 11 Pushkinskaya Str., Petrozavodsk 185910, Russian Federation
Petrozavodsk State University, 33 Lenin Str., Petrozavodsk 185910, Russian Federation
Ghent University, TELIN Department, 41 Sint-Pietersnieuwstraat,Gent B-9000, Belgium
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