Abstract
The high demand for more bandwidth and high speed networks stimulates research in the design, optimization and performance evaluation of IP over all-optical networks. In this paper we study optical packet filling algorithm applied at ingress nodes of an all-optical network. Arriving electronic packets of variable sizes are stored at a buffer the volume of which is equal to the fixed size of optical packet. When the available space in the buffer is less than the size of an arriving packet, the stored already content of the buffer is sent inside the optical packet and the electronic packet is rescheduled for the next filling cycle. To avoid excessive delays, the optical packet is dispatched also after a specified deadline whatever is the (non-null) content of the buffer. The performance metrics we consider comprises the filling of optical packets (that means the ratio of blocks in the packet to the actual constant size of the packet) and the distribution of optical packets interdeparture times. The paper demonstrates that the variability of the size of arriving packets and the self-similarity of the input traffic have a visible impact on the both parameters.
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References
Holler, J., Tsiatsis, V., Mulligan, C., Karnouskos, S., Avesand, S., Boyle, D.: From Machine-Machine to the Internet of Things: Introduction to the New Age of Intelligence. Elsevier, Waltham (2014)
Gambini, P., et al.: Transparent optical packet switching: network architecture and demonstrators in the KEOPS project. IEEE J. Sel. Areas Commun. 16(7), 1245–1259 (1998)
Kotuliak, I.: Feasibility study of optical packet switching: performance evaluation. Ph.D. thesis, University of Versailles-St-Quentin-en-Yveline (2003)
Domanska, J., Kotuliak, I., Atmaca, T., Czachórski, T.: Optical packet filling. In: 10th Polish Teletraffic Symposium PSRT (2003)
Harrison, G., Knottenbelt, J.: Passage time distributions in large Markov chains. In: Proceedings of the 2002 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, pp. 77–85 (2002)
Park, K., Willinger, W.: Self-Similar Network Traffic and Performance Evaluation. Wiley, New York (2000)
Andersen, A.T., Nielsen, B.F.: A Markovian approach for modeling packet traffic with long-range dependence. IEEE J. Sel. Areas Telecommun. 16(5), 719–732 (1998)
Czachórski, T., Domanski, A., Domanska, J., Rataj, A.: A study of IP router queues with the use of Markov models. In: Gaj, P., Kwiecień, A., Stera, P. (eds) Proceedings of Computer Networks 2016, Brunów, Poland, Communications in Computer and Information Science, vol. 608, Proceedings of Computer Networks 2016, 294–305 (2016). Springer, cham (2016). https://doi.org/10.1007/978-3-319-39207-3_26
Fischer, W., Meier-Hellstern, K.: The Markov-modulated Poisson process (MMPP) cookbook. Perform. Eval. 18(2), 149–171 (1993)
Baskett, F., Chandy, M., Muntz, R., Palacios, J.: Open, closed and mixed networks of queues with different classes of customers. J. ACM 22(2), 249–260 (1975)
Stewart, W.J.: An Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princeton (1994)
Stewart, W.J.: Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press, New Jersey (2009)
Bylina, B.: The inverse iteration with the WZ factorization used to the Markovian models. Ann. UMCS Informatica 2, 15–23 (2004). Lublin
Bylina, B., Bylina, J., Karwacki, M.: Computational aspects of GPU-accelerated sparse matrix-vector multiplication for solving Markov models. Theoret. Appl. Inf. 23(2), 127–145 (2011)
Saad, Y.: Krylov subspace methods for solving large unsymmetric linear systems. Math. Comput. 37, 105–126 (1981)
Saad, Y., Schultz, M.H.: GMRES: a generalized minimal residual algorithm for solving non-symmetric linear systems. SIAM J. Sci. Stat. Comput. 7, 856–869 (1986)
Saad, Y.: Precondtioned Krylov subspace methods for the numerical solution of Markov chains. In: Stewart, W.J. (ed.) Computations with Markov Chains, Proceedings of the 2nd International Workshop on the Numerical Solution of Markov chains. Springer, New York (1995). https://doi.org/10.1007/978-1-4615-2241-6_4
Potier, D.: New User’s Introduction to QNAP2. Rapport Technique no. 40, INRIA, Rocquencourt (1984)
PRISM - probabilistic model checker. www.prismmodelchecker.org/
Pecka, P., Deorowicz, S., Nowak, M.: Efficient representation of transition matrix in the Markov process modeling of computer networks. In: Czachórski, T., et al. Man-Machine Interactions 2, Advances in Intelligent and Soft Computing, vol. 103, pp. 457–464. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-23169-8_49
Kwiatkowska, M., Norman, G., Parker, D.: Tools Session of Aachen 2001 International Multiconference on Measurement, Modelling and Evaluation of Computer-Communication Systems. Technical report 760/2001, pp. 7–12. University of Dortmund (2001)
Hinton, A., Kwiatkowska, M., Norman, G., Parker, D.: PRISM: a tool for automatic verification of probabilistic systems. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 441–444. Springer, Heidelberg (2006). https://doi.org/10.1007/11691372_29
TeamSimpy: Simpy Documentation release 3.0.10. MIT (2017)
Byrne, N., Geraghty, J., Liston, P., Young, P.: The potential role of open source discrete event simulation software in the manufacturing sector. In: Proceedings of the Operational Research Society Simulation Workshop (2012)
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Suila, K.G., Czachórski, T., Rataj, A. (2018). A Queueing Model of the Edge Node in IP over All-Optical Networks. In: Gaj, P., Sawicki, M., Suchacka, G., Kwiecień, A. (eds) Computer Networks. CN 2018. Communications in Computer and Information Science, vol 860. Springer, Cham. https://doi.org/10.1007/978-3-319-92459-5_21
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