Abstract
We study the packet transmission scheduling problem with tuning delay in wavelength-division multiplexed (WDM) optical communication networks with tunable transmitters and fixed-tuned receivers. By treating the numbers of packets as random variables, we conduct probabilistic analysis of the average-case performance ratio for the cyclic packet transmission scheduling algorithm. Our numerical data as well as simulation results demonstrate that the average-case performance ratio of cyclic schedules is very close to one for reasonable system configurations and probability distributions of the numbers of packets. In particular, when the number of receivers that share a channel and/or the granularity of packet transmission are large, the average-case performance ratio approaches one. Better performance can be achieved by overlapping tuning delays with packet transmission. We derive a bound for the normalized tuning delay Δ such that tuning delay can be completely masked with high probability. Our study implies that by using currently available tunable optical transceivers, it is possible to build single-hop WDM networks that efficiently utilize all the wavelengths.
Similar content being viewed by others
References
A. Aggarwal, A. Bar-Noy, D. Coppersmith, R. Ramaswami, B. Schieber and M. Sudan, Efficient routing and scheduling algorithms for optical networks, IBM Research Report, Technical Report RC 18967 (June 1993).
B.C. Arnold, N. Balakrishnan and H.N. Nagaraja, A First Course in Order Statistics (Wiley, New York, 1992).
M. Azizo{ie64-1}lu, R.A. Barry and A. Mokhtar, Impact of tuning delay on the performance of bandwidth-limited optical broadcast networks with uniform traffic, IEEE Journal on Selected Areas in Communications 14(5) (1996) 935-944.
K. Bogineni, K.M. Sivalingam and P.W. Dowd, Low-complexity multiple access protocols for wavelength-division multiplexed photonic networks, IEEE Journal on Selected Areas in Communications 11(4) (1993) 590-604.
M.S. Borella and B. Mukherjee, Efficient scheduling of nonuniform packet traffic in a WDM/TDM local lightwave network with arbitrary transceiver tuning latencies, IEEE Journal on Selected Areas in Communications 14(5) (1996) 923-934.
H. Choi, H.-A. Choi and M. Azizo{ie64-2}lu, Efficient scheduling of transmissions in optical broadcast networks, IEEE/ACM Transactions on Networking 4(6) (1996) 913-920.
B. Dasgupta and M.A. Palis, Provably good algorithms for transmission scheduling in WDM optical networks, Journal of Parallel and Distributed Computing 57 (1999) 345-357.
W. Feller, An Introduction to Probability Theory and Its Applications, Vol. I, 3rd ed. (Wiley, New York, 1968).
M.R. Garey and D.S. Johnson, Computers and Intractability - A Guide to the Theory of NPCompleteness (Freeman, New York, 1979).
T. Gonzalez and S. Sahni, Open shop scheduling to minimize finish time, Journal of the ACM 23(4) (1976) 665-679.
F. Jia, B. Mukherjee and J. Iness, Scheduling variable-length messages in a single-hop multichannel local lightwave network, IEEE/ACM Transactions on Networking 3(4) (1995) 477-488.
J.C. Lu and L. Kleinrock, A wavelength division multiple access protocol for high-speed local area networks with a passive star topology, Performance Evaluation 16 (1992) 223-239.
B. Mukherjee, WDM-based local lightwave networks - Part I: Single hop systems, IEEE Network 6 (1992) 12-27.
G.R. Pieris and G.H. Sasaki, Scheduling transmissions in WDM broadcast-and-select networks, IEEE/ACM Transactions on Networking 2(2) (1994) 105-110.
S. Ross, A First Course in Probability, 4th ed. (Macmillan College Publishing, New York, 1994).
G.N. Rouskas and M.H. Ammar, Analysis and optimization of transmission schedules for single-hop WDM networks, IEEE/ACM Transactions on Networking 3(2) (1995) 211-221.
G.N. Rouskas and V. Sivaraman, Packet scheduling in broadcast WDM networks with arbitrary transceiver tuning latencies, IEEE/ACM Transactions on Networking 5(3) (1997) 359-370.
S.V. Sevastianov and G.J. Woeginger, Makespan minimization in open shops: a polynomial time approximation scheme, Mathematical Programming 82 (1998) 191-198.
G.N.M. Sudhakar, N.D. Georganas and M. Kavehrad, Slotted Aloha and reservation Aloha protocols for very high-speed optical fiber local area networks using passive star topology, Journal of Lightwave Technology 9 (1991) 1411-1422.
D.P. Williamson, L.A. Hall, J.A. Hoogeveen, C.A.J. Hurkens, J.K. Lenstra, S.V. Sevast'janov and D.B. Shmoys, Short shop schedules, Operations Research 45(2) (1997) 288-294.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Li, K. Probabilistic Analysis of Cyclic Packet Transmission Scheduling in WDM Optical Networks. Telecommunication Systems 25, 51–64 (2004). https://doi.org/10.1023/B:TELS.0000011196.85853.5c
Issue Date:
DOI: https://doi.org/10.1023/B:TELS.0000011196.85853.5c