Abstract
Discrete event simulation as a method for performance evaluation has become an indispensable tool in many fields, e.g., teletraffic engineering. New communication networks and services pose extreme requirements regarding the quality of service, e.g., cell loss probabilities in ATM1 networks in the order of 10 -9. Straightforward simulation for this type of rare event leads to simulation run times in the order of months and years, thus requiring new methods to be investigated and employed. In the following the state of the art in the field of Rare Event Simulation is described and examples are given for the RESTART2 /LRE3 method to demonstrate the type of results that can be achieved by using these methods. In recent years these methods have been applied to relevant quality of service parameters in ATM networks. Future applications will concern the investigation of the emerging quality of service concepts for Next Generation Internets.
RESTART/LRE is a multi-step simulation approach which reduces the simulation run time by several orders of magnitude from, e.g., years to minutes, thus making simulation studies for rare events feasible. The approach can be applied to single nodes and networks. It is a so-called importance splitting method, where system states that lead to the rare event are saved and used as the starting point for new simulation sub-runs. The results of the sub-runs are multiplied with the corresponding weights which are obtained in the previous step and result in the desired probabilities. The statistical evaluation method LRE used in this combined approach has the additional advantage of evaluating the so-called local correlation function which gives insight into the correlation structure of the investigated random variable and is part of an error measure for controlling all phases of a simulation. Examples are given for the loss probability of ATM cells in G/G/1/N4 type systems as well as certain tandem networks that represent a model for ATM reference connections. Additional results are presented where the rare event details of the delay time distribution are the object of the investigation. The RESTART/LRE simulation offers as a result the complementary distribution function of the delay time distribution so that the probability of delays longer than a given maximum can be deduced directly from this result. This is one of the quality of service parameters defined for ATM. Furthermore, new results are available where the method has been used to investigate rare event details of the loss probabilities for handover in wireless ATM networks. The underlying model for an ATM reference connection consists of a network with a sequence of */D/1/N5 queues and an extra delay (propagation and switching) between these queues. Additional traffic is offered to the outgoing connections to model the interference of other ATM connections. Simulation results for the complementary distribution function of the delay time are presented.
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References
A. A. Akyamaç, Z. Haraszti, J. K. Townsend. “Efficient Rare Event Simulation Using DPR for Multidimensional Parameter Spaces”. Proc. 16th Int. Teletraffic Congress, 1999.
R. Andreassen, P.E. Heegaard, B.E. Helvik. “Importance Sampling for Speed-Up Simulation of Heterogeneous MPEG Sources”. In The 13th Nordic Teletraffic Seminar (NTS-13), August, 1996, pp. 190–203, Trondheim, Norway, 1996.
S. Asmussen, R.Y. Rubinstein. “Steady State Rare Event Simulation in Queueing Model and its Complexity Properties”. In J. Dshalalow, editor, Advances in Queueing: Theory, Methods and Open Problems, Vol. I, pp. 429–462. CRC Press, 1995.
Søren Asmussen. “Rare Events Simulation for Heavy-Tailed Distributions”. Workshop 11–12. March 1999, University of Twente, Enschede, The Netherlands, 1999.
A.J. Bayes. “Statistical Techniques for Simulation Models”. The Australian Computer Journal, Vol. 2(4), pp. 180–184, 1970.
N.K.Boots. “Quick Simulation Methods for Estimating Ruin Probabilities in Risk Processes with Subexponential Claims”. Workshop 11–12. March 1999, University of Twente, Enschede, The Netherlands, 1999.
Pieter-Tjerk de Boer. “Analysis and Efficient Simulation of Queueuing Models of Telecommunication Systems”. PhD thesis, Universiteit Twente, 2000.
Pieter-Tjerk de Boer, Victor F. Nicola. “Hybrid Importance Sampling Estimation of Consecutive Cell Loss Probability”. International Journal of Electronics and Communications, Vol. 52, No. 3, pp. 133–140, 1998.
M. Devetsikiotis, J.K. Townsend. “Statistical Optimization of Dynamic Importance Sampling Parameters for Efficient Simulation of Communication Networks”. IEEE/ACM Transactions on Networking, Vol. 1, No. 3, pp. 293–305, June 1993.
M.R. Frater. “Estimation of the Statistics of Rare Events in Data Communications Systems”. PhD thesis, The Australian National University, 1990.
Oliver J. Fuß. “Validierung von Dienstgüteparametern von B-ISDN/ATM-Referenzverbindungen durch das RESTART/LRE-Verfahren zur Simulation seltener Ereignisse”. Diplomarbeit, RWTH Aachen, Lehrstuhl Kommunikationsnetze, Januar 1998.
Marnix J.J. Garvels. “The Splitting Method in Rare Event Simulation”. PhD thesis, Universiteit Twente, 2000.
P. Glasserman, P. Heidelberger, P. Shahabuddin, T. Zajic. “Splitting for Rare Event Simulation: Analysis of Simple Cases”. In 1996 Winter Simulation Conference, pp. 302–308, Coronado, California, USA, December 1996.
A. Goyal, P. Shahabuddin, P. Heidelberger, V.F. Nicola, P.W. Glynn. “A Unified Framework for Simulating Markovian Models of Highly Dependable Systems”. IEEE Trans. on Computers, Vol. 41, No. 1, pp. 36–51, 1992.
C. Görg. “Verkehrstheoretische Modelle und Stochastische Simulationstechniken zur Leistungsanalyse von Kommunikationsnetzen”, Vol. ABMT 13. Verlag der Augustinusbuchhandlung, Aachener Beiträge zur Mobil und Telekommunikation, Aachen, 1997. Habilitationsschrift, Lehrstuhl Kommunikationsnetze, RWTH Aachen.
C. Görg, O. Fuß. “Comparison and Optimization of RESTART Run Time Strategies”. AEÜ, Vol. 52, pp. 197–204, 1998.
C. Görg, O. Fuß. “Simulating Rare Event Details of ATM Delay Time Distributions with RESTART/LRE”. Workshop 11–12. March 1999, University of Twente, Enschede, The Netherlands, 1999.
C. Görg, C. Kelling. “Special Issue on Rare Event Simulation”. Görg, C. and Kelling, Chr. (eds) AEÜ, Vol. 52, 1998.
C. Görg, E. Lamers, R.G. Addie. “Broadband Traffic Modeling: Rare Event Simulation for Gaussian and M/Pareto Processes with the Same Autocovariance”. Workshop 11–12. March 1999, University of Twente, Enschede, The Netherlands, 1999.
C. Görg, F. Schreiber. “The RESTART/LRE Method for Rare Event Simulation”. In l996 Winter Simulation Conference, pp. 390–397, Coronado, California, USA, December 1996.
Z. Haraszti. “How to Set Up my Simulator? — Empirical Guidelines”. Impromptu Session 16th International Teletraffic Congress, 7–10 June 1999, Edinburgh, UK.
P.E. Heegaard. “Efficient Simulation of Network Performance by Importance Sampling”. PhD thesis, NTNU — Norwegian Technical and Scientific University, Trondheim, Norway, 1998.
Poul E. Heegaard. “A Scheme for Adaptive Biasing in Importance Sampling”. International Journal of Electronics and Communications, Vol. 52, No. 3, pp. 172–182, 1998.
P. Heidelberger. “Fast Simulation of Rare Events in Queueing and Reliability Models”. ACM Transactions on Modeling and Computer Simulation, Vol. 5(1), pp. 43–85, 1995.
P. Heidelberger, P. Shahabuddin, V.F. Nicola. “Bounded Relative Error in Estimating Transient Measures of Highly Dependable Non-Markovian Systems”. In S. Ozekici, editor, Reliability and Maintenance of Complex Systems, Vol. 154 of F: Computer and Systems Sciences, pp. 487–515. Springer, 1996.
B.E. Helvik, P.E. Heegaard. “A Technique for Measuring Rare Cell Losses in ATM Systems”. Teletraffic and Datatraffic, Proceedings 14th ITC, Antibes, Juan-Les-Pins, France, June 6–10, 1994, pp. 917–930, 1994.
A.C.M. Hopmans, J.P.C. Kleijnen. “Importance Sampling in Systems Simulation: a Practical Failure?” In Mathematics and Computers in Simulation XXI, pp. 209–220, North-Holland, 1979.
H. Kahn, A.W. Marshall. “Methods of Reducing Sample Size in Monte Carlo Computations”. J. Oper. Res. Society of America, Vol. 1, pp. 263–278, 1953.
C. Kelling. “A Framework for Rare Event Simulation of Stochastic Petri Nets Using “RESTART” ”. In 1996 Winter Simulation Conference, pp. 317–324, Coronado, California, USA, December 1996.
Dirk P. Kroese, Victor F. Nicola. “Efficient Simulation of Backlogs in Fluid Row Lines”. International Journal of Electronics and Communications, Vol. 52, No. 3, pp. 165–171, 1998.
Thomas Kuhlmann, Christian Kelling. “Case Studies on Multidimensional RESTART Simulations”. International Journal of Electronics and Communications, Vol. 52, No. 3, pp. 190–196, 1998.
Eugen Lamers. “Enhancement and Application of the RESTART/LRE-Simulator for Quality of Service Investigations in High Speed Networks”. Diploma thesis, Chair of Communication Networks, RWTH Aachen, June 1999.
P. E. Lassila, J. T. Virtamo. “Efficient Importance Sampling for Monte Carlo Simulation of Loss Systems”. Proc. 16th Int. Teletraffic Congress, 1999.
D. Lieber, R.Y. Rubinstein, D. Elmakis. “Quick Estimation of Rare Events in Stochastic Networks”. IEEE Transactions on Reliability Systems, Vol. 46, No. 2, pp. 254–265, 1997.
Michel Mandjes. “Rare Event Analysis of Communication Networks”. PhD thesis, Vrije Universiteit Amsterdam, 1996.
M.K. Nakayama. “A Characterization of the Simple Failure Biasing Method for Simulation of Highly Reliable Markovian Systems”. ACM Transaction on Modeling and Computer Simulation, Vol. 4, No. 1, pp. 52–88, 1994.
V.F. Nicola, G.A. Hagesteijn. “Efficient Simulation of Consecutive Cell Loss in ATM Networks”. Vol. II. Chapman and Hall, London, 1996.
W. D. Obal II. “Importance Sampling Simulation in UltraSAN”. Simulation, Vol. 62(2), pp. 98–111, 1994.
W. D. Obal II, W. H. Sanders. “Quick Simulation of a Performability Model”. In Proc. 3rd. Intl. Workshop on Performability of Computer and Communication Systems, pp. 6–10, Bloomingdale, IL, USA, 1996.
S. Parekh, J. Walrand. “A Quick Simulation Method for Excessive Backlogs in Networks of Queues”. DEEE Transactions on Automatic Control, pp. 54–66,1989.
Ad Ridder. “Fast Simulation of Discrete Time Queues with Markov Modulated Batch Arrivals and Batch Departures”. International Journal of Electronics and Communications, Vol. 52, No. 3, pp. 127–132, 1998.
Ad Ridder. “Efficient Simulation of Fluid Queues with Many Sources”. Workshop 11.–12. March 1999, University of Twente, Enschede, The Netherlands, 1999.
Reuven Rubinstein. “The Cross-Entropy Method for Combinatorial and Continuous Optimization”. Methodology and Computing in Applied Probability, Vol. l,pp. 127–190, 1999.
Reuven Rubinstein. “Rare Event Simulation via Cross-Entropy and Importance Sampling”. Workshop 11.—12. March 1999, University of Twente, Enschede, The Netherlands, 1999.
Reuven Rubinstein. “Cross-Entropy for Combinatorial Optimization”, to appear in Encyclopaedia of Management Sciences, 2000.
F. Schreiber. “Effective Control of Simulation Runs by a New Evaluation Algorithm for Correlated Random Sequences”. AEÜ, Vol. 42, pp. 347–354, 1988. (see also: Proc. 12th Int. Teletraffic Congr. (ITC), Torino, 1988, p. 4.3B.1.1–9).
F. Schreiber, C. Görg. “Stochastic Simulation: A Simplified LRE-Algorithm for Discrete Random Sequences”. AEÜ, Vol. 50, pp. 233–239, 1996.
P. Shahabuddin. “Rare Event Simulation in Stochastic Models”. In Proceedings of the 1995 Winter Simulation Conference, pp. 178–185, Arlington, Virginia, USA, 1995.
Zarah Siahpoureh. “Vergleich, ModeUierung und Implementierung von simulativen und analytischen Modellen für ATM-Referenzverbindungen in Telekommunikationsnetzen”. Diplomarbeit, RWTH Aachen, Lehrstuhl für Kommunikationsnetze, February 1998.
José Villén-Altamirano. “RESTART Method for the Case Where Rare Events Can Occur in Retrials from any Threshold”. International Journal of Electronics and Communications, Vol. 52, No. 3, pp. 183–189, 1998.
M. Villén-Altamirano, A. Martínez-Marrón, J. Gamo, F. Fernández-Cuesta. “Enhancement of the Accelerated Simulation Method RESTART by Considering Multiple Thresholds”. In Proceedings 14th International Teletraffic Congress, pp. 797–810. North-Holland, 1994.
M. Villén-Altamirano, J. Villén-Altamirano. “Accelerated Simulation of Rare Events Using RESTART Method with Hysteresis”. In J. Filipiak, editor, Telecommunication Services for Developing Economies., pp. 675–686. Proceedings of the ITC Specialist Seminar, Cracow, Poland, April 1991, Elsevier, Amsterdam, Netherlands, 1991.
M. Villén-Altamirano, J. Villén-Altamirano. “RESTART: a Method for Accelerating Rare Event Simulations”. In J.W. Cohen, CD. Pack, editors, Queueing, Performance and Control in ATM, pp. 71–76. 13th International Teletraffic Congress, Copenhagen, North-Holland, 1991.
M. Villén-Altamirano, J. Villén-Altamirano. “RESTART: A Straightforward Method for Fast Simulation of Rare Events”. In Proceedings of the 1994 Winter Simulation Conference, pp. 282–289, 1994.
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Görg, C., Lamers, E., Fuß, O., Heegaard, P. (2002). Rare Event Simulation. In: Ince, A.N. (eds) Modeling and Simulation Environment for Satellite and Terrestrial Communications Networks. The Kluwer International Series in Engineering and Computer Science, vol 645. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0863-2_21
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