zbMATH — the first resource for mathematics

Prognosis and optimization of homogeneous Markov message handling networks. (English) Zbl 1265.60140
Summary: Message handling systems with finitely many servers are mathematically described as homogeneous Markov networks. For hierarchical networks, we find a recursive algorithm evaluating after finitely many steps all steady state parameters. Applications to optimization of system design and management are discussed, as well as the program 5P (program for prognosis of performance parameters and problems) based on the presented theoretical conclusions. The theoretic achievements as well as the practical applicability of the program are illustrated on a hypermarket network with 34 servers at different locations of the Czech Republic.
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
90B15 Stochastic network models in operations research
Full Text: Link EuDML
[1] Darbellay G. A., Vajda I.: Entropy expressions for multivariate continuous distributions. IEEE Trans. Inform. Theory 46 (2000), 709-712 · Zbl 0996.94018 · doi:10.1109/18.825848
[2] Esteban M., Castellanos M., Morales, D., Vajda I.: A comparative study of the normality tests based on sample entropies. Comm. Statist. Simulation Comput., to appear · Zbl 1008.62505
[3] Higginbottom G. N.: Performance Evaluation of Communication Networks. Artech House, Boston 1998 · Zbl 0913.68003
[4] Janžura M., Boček P.: Stochastic Methods of Prognosis of Parameters in Data Networks (in Czech). Research Report No. 1981, Institute of Information Theory and Automation, Prague 2000
[5] Menéndez M., Morales D., Pardo, L., Vajda I.: Inference about stationary distributions of Markov chains based on divergences with observed frequencies. Kybernetika 35 (1999), 265-280 · Zbl 1274.62548 · www.kybernetika.cz
[6] Menéndez M., Morales D., Pardo, L., Vajda I.: Minimum disparity estimators for discrete and continuous models. Appl. Math. 46 (2001), 401-420 · Zbl 1059.62001 · doi:10.1023/A:1013764612571 · eudml:33096
[7] Menéndez M., Morales D., Pardo, L., Vajda I.: Approximations to powers of \(\phi \)-disparity goodness of fit tests. Comm. Statist. Theory Methods 30 (2001), 105-134 · Zbl 1008.62540 · doi:10.1081/STA-100001562
[8] Morales D., Pardo L., Pardo M. C., Vajda I.: Extension of the Wald statistics to models with dependent observations. Metrika 52 (2000), 97-113 · Zbl 1093.62519 · doi:10.1007/s001840000060
[9] Nelson R.: Probability, Stochastic Processes, and Queueing Theory. Springer, New York 1995 · Zbl 0839.60002
[10] Norris J. R.: Markov Chains. Cambridge University Press, Cambridge 1997 · Zbl 1189.60152 · doi:10.1214/07-PS121 · eudml:224003 · arxiv:0710.3269
[11] Pardo M. C., Pardo, L., Vajda I.: Consistent tests of homogeneity for independent samples from arbitrary models, submitte.
[12] Pattavina A.: Switching Theory: Architecture and Performance in Broadbard ATM Networks. Wiley, New York 1998
[13] Dijk N. M. van: Queueing Networks and Product Forms. A System Approach. Wiley, New York 1993
[14] Walrand J.: Introduction to Queueing Networks. Prentice-Hall, Englewood Cliffs, N.J. 1988 · Zbl 0854.60089
[15] Whittle P.: Systems in Stochastic Equilibrium. Wiley, Chichester 1986 · Zbl 0665.60107
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.