Scheduled System Maintenance:
Some services will be unavailable Sunday, March 29th through Monday, March 30th. We apologize for the inconvenience.
By Topic

Subadditivity and stability of a class of discrete-event systems

Sign In

Full text access may be available.

To access full text, please use your member or institutional sign in.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Glasserman, P. ; Graduate Sch. of Bus., Columbia Univ., New York, NY, USA ; Yao, D.D.

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

Published in:

Automatic Control, IEEE Transactions on  (Volume:40 ,  Issue: 9 )