UDC 519.872
1 V.M. Glushkov Institute of Cybernetics, National Academy
of Sciences of Ukraine, Kyiv, Ukraine, and Institute of Physics and Technology
of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine
kuznetsov2016@icloud.com
|
2 Institute of Physics and Technology of the National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine
sea_hawk@icloud.com
|
FAST SIMULATION OF THE CUSTOMER BLOCKING PROBABILITY
IN QUEUEING NETWORKS WITH MULTICAST ACCESS
Abstract. A model of a queuing network with several input Poisson flows is considered.
These flows require connections between given terminals. The connection path depends on the type of the customer,
on the requested resource, on the paths currently occupied and on the load on all communication channels of the network.
A fast simulation method for the evaluation of the blocking probability for customers of the certain flow with a required resource
not lower than a given one is proposed.
Keywords: queueing network, multicast access, blocking probability, Monte Carlo method, stratified sampling, fast simulation method, variance of estimate.
FULL TEXT
REFERENCES
- Ross K.W. Multiservice loss models for broadband telecommunication networks. London: Springer- Verlag, 1995. 343 p.
- Frenkel I.B., Karagrigoriou A., Lisnianski A., Kleyner A.V. Applied reliability engineering and risk analysis: probabilistic models and statistical inference. New York: Wiley, 2013. 448 p.
- Nyberg E., Virtamo J., Aalto S. An exact algorithm for calculating blocking probabilities in multicast networks. Pujolle G., Perros H., Fdida S., Krner U., Stavrakakis I. (Eds.). Networking. Paris, 2000. P. 275–286.
- Karvo J. Efficient simulation of blocking probabilities for multi-layer multicast streams. Gregori E., Conti M., Campbell A., Omidyar C., Zukerman M. (Eds.). Networking. Berlin: Springer-Verlag, 2002. P. 1020–1031.
- Kovalenko I.N., Kuznetsov N.Yu. Methods for calculating highly reliable systems [in Russian]. Moscow: Radio i svyaz', 1988. 176 p.
- Kovalenko I.N., Kuznetsov N.Yu., Pegg Ph.A. Mathematical theory of reliability of time dependent systems with practical applications. Chichester: Wiley, 1997. 303 p.
- Kuznetsov N.Yu. Fast simulation technique in reliability evaluation of Markovian and non-Markovian systems. Simulation and Optimization Methods in Risk and Reliability Theory. New York: Nova Science Publishers, 2009. P. 69–112.
- Heidelberger P. Fast simulation of rare events in queueing and reliability models. ACM Transactions on Modeling and Computer Simulation. 1995. Vol. 5, Iss. 1. P. 43–85.
- Glasserman P. Monte Carlo methods in financial engineering. New York: Springer, 2004. 575 p.
- Ermakov S.M. Importance sampling for simulation of large and moderate deviation probabilities of tests and estimators. Theory Probab. Appl. 2006. Vol. 51, N 2. P. 319–332.
- Li J., Mosleh A., Kang R. Likelihood ratio gradient estimation for dynamic reliability applications. Reliab. Engin. and System Safety. 2011. Vol. 96, N 12. P. 1667–1679.
- Kouikoglou V.S., Yannis A.Ph. Review of a fast simulation method for the analysis of queueing networks. Applied Stochastic Models and Data Analysis. 1998. Vol. 13, Iss. 2. P. 73–83.
- Falkner M., Devetsikiotis M., Lambadaris I. Fast simulation of networks of queues with effective and decoupling bandwidths. ACM Transactions on Modeling and Computer Simulation. 2021. Vol. 31, Iss. 1.
- Kuznetsov N.Yu., Shumskaya A.A. Assessment of the risk of failure of a redundant system using accelerated simulation. Problemy upravleniya i informatiki. 2013. N 3. P. 50–62.
- Fox B.L., Glynn P.W. Discrete-time conversion for simulating finite-horizon Markov processes. SIAM J. Appl. Math. 1990. Vol. 50, N 5. P. 1457–1473.
- Shumskaya A.A. Accelerated modeling of the unavailability ratio of the restored system with a limited relative estimation error. Kibernetika i sistemnyj analiz. 2003. № 3. P. 45–58.
- Glasserman P., Heіdelberger Ph., Shahabuddіn P., Zajіc T. Multilevel splitting for estimating rare event probabilities. Oper. Research. 1999. Vol. 47, N 4. P. 585–600.
- Juneja S., Shahabuddin P., Zajic T. Splitting-based importance-sampling algorithm for fast simulation of Markov reliability models with general repair-policies. IEEE Transactions on Reliab. 2001. Vol. 50, N 3. P. 235–245.
- Lagnoux A. Rare event simulation. Probab. Eng. and Inf. Sci. 2006. Vol. 20, N 1. P. 45–66.
- Gertsbakh I.B., Shpungin Y. Models of network reliability: Analysis, combinatorics, and Monte Carlo. Boca Raton: CRC Press, 2009. 203 p.
- Blanchet J., Lam H. Rare event simulation techniques. Proc. of the 2011 Winter Simulation Conference. 2011. P. 217–231.