Subadditivity and stability of a class of discrete-event systems

Author

Glasserman, Paul ; Yao, David D.

Author_Institution

Graduate Sch. of Bus., Columbia Univ., New York, NY, USA

Volume

40

Issue

9

fYear

1995

fDate

9/1/1995 12:00:00 AM

Firstpage

1514

Lastpage

1527

Abstract

We investigate the stability of discrete-event systems modeled as generalized semi-Markov processes with event epochs that satisfy (max, +) recursions. We obtain three types of results, under conditions: We show that there exists for each event a cycle time, which is the long-run average time between event occurrences; we characterize the rate of convergence to this limit, bounding the error for finite horizons; and we give conditions for delays (i.e., differences between event epochs) to converge to a stationary regime. The main tools for the cycle time results are (max, +) matrix products and the subadditive ergodic theorem. The convergence rate result (which assumes bounded i.i.d. inputs) is based on a martingale inequality. The stability of delays is derived from existing results on the stability of stochastic difference equations. We discuss connections with these different fields, with the general theory of random matrix products and with results for discrete-event systems

Keywords

Markov processes; difference equations; discrete event systems; matrix algebra; stability; (max, +) matrix products; (max, +) recursions; bounded i.i.d. inputs; convergence rate; cycle time; cycle time results; delay convergence; discrete-event systems; event epochs; finite horizon errors; long-run average time; random matrix products; semi-Markov processes; stability; subadditive ergodic theorem; Convergence; Delay effects; Difference equations; Discrete event systems; Linear matrix inequalities; Q measurement; Stability; Stochastic processes; Stochastic systems; Time measurement;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.412623

Filename

412623