Previous |  Up |  Next


message handling system; Markov network; optimization; recursive algorithm
Message handling systems with finitely many servers are mathematically described as homogeneous Markov networks. For hierarchic networks is found a recursive algorithm evaluating after finitely many steps all steady state parameters. Applications to optimization of the system design and management are discussed, as well as a program product 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.
[1] Darbellay G. A., Vajda I.: Entropy expressions for multivariate continuous distributions. IEEE Trans. Inform. Theory 46 (2000), 709–712 DOI 10.1109/18.825848 | MR 1749003 | Zbl 0996.94018
[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
[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 MR 1704667
[6] Menéndez M., Morales D., Pardo, L., Vajda I.: Minimum disparity estimators for discrete and continuous models. Appl. Math. 46 (2001), 401–420 DOI 10.1023/A:1013764612571 | MR 1865516 | Zbl 1059.62001
[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 DOI 10.1081/STA-100001562 | MR 1862592 | Zbl 1008.62540
[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 DOI 10.1007/s001840000060 | MR 1811265
[9] Nelson R.: Probability, Stochastic Processes, and Queueing Theory. Springer, New York 1995 MR 1340628 | Zbl 0839.60002
[10] Norris J. R.: Markov Chains. Cambridge University Press, Cambridge 1997 MR 1600720 | Zbl 1189.60152
[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 MR 1266845
[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 MR 0850012 | Zbl 0665.60107
Partner of
EuDML logo