Abstract
We consider a multiphase service system with a Poisson input flow. Its intensity depends on the number of customers under service. The stationary distribution for this system can be found in an explicit form. We study the rate of convergence to this stationary distribution as well as the bounds for some mixing coefficients. Coupling arguments and Liapunov's function approach form the basis of considerations.
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References
E. Nummelin, General Irreducible Markov Chains and Non-negative Operators (Cambridge Univ. Press, Cambrigde, 1984).
T. Lindvall, Lectures on the Coupling Method (Wiley, New York, 1992).
S.P. Meyn and R.L. Tweedie, Markov Chain and Stochastic Stability, Communications and Control Engineering Series (Springer, Berlin, 1993).
A. Yu. Veretennikov, Ergodicity of service systems with an infinite number of servomechanisms, Soviet Math. Notes 22 (1977) 804–808.
A. Yu. Veretennikov, Ergodicity and invariance principle for multiphase queueing system, Automat. Remote Control 42 (1981) 906–909.
B.A. Sevastyanov, An ergodic theorem for Markov processes and its application to telephone systems with refusals, Probab. Theory Appl. 2 (1957) 104–112.
N.I. Kovalenko, Investigations on Reliability Analysis of Complex Systems (in Russian) (Naukova Dumka, Kiev, 1975).
I.A. Ibragimov and Yu.V. Linnik, Independent and Stationary Sequences of Random Variables (Wolters Noorghoff, New York, 1971).
R. Sh. Liptser and A.N. Shiryaev, Martingale Theory (in Russian) (Nauka, Moscow, 1986).
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Kelbert, M., Veretennikov, A. On the estimation of mixing coefficients for a multiphase service system. Queueing Systems 25, 325–337 (1997). https://doi.org/10.1023/A:1019160619771
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DOI: https://doi.org/10.1023/A:1019160619771