Nonlinear stochastic dynamical systems: Steady state solution and convergence rate of time-dependent Markov chains of queuing networks

Authors:
K. P. Chung
Affiliations:
Bell Communications Research 435 South Street, Rm. 2E-330 Morristown, New Jersey, U.S.A
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
1988

Citing 3
Cited 0

Queueing Networks: A Critique of the State of the Art and Directions for the Future

ACM Computing Surveys (CSUR)
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Markovian models and numerical analysis of computer system behavior

AFIPS '66 (Spring) Proceedings of the April 26-28, 1966, Spring joint computer conference

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Abstract

The differential equations for transient state probabilities for Markovian processes are examined to derive the rate of convergence of transient states to equilibrium states. There is an acute need to solve the balance equations for large states, particularly for handling computer performance modeling with a network of queues that do not satisfy product form solutions or cannot be cast into the forms convenient for mean value analysis. The rate of convergence to equilibrium states is derived for irreducible aperiodic homogeneous Markov chains on the basis of a geometrical interpretation. A numerical integration method with dynamic step-size adjustments is applied and compared against the power method of Wallace and Rosenberg.